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Food Powder Processing

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4Handling and Processing of Food Powdersand Particulates

Enrique Ortega-RivasFood and Chemical Engineering ProgramUniversity of ChihuahuaChihuahuaMexico

CONTENTS

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76II. Relevant Properties of Powdered Food Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

A. Size, Shape, and Distribution of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771. Equivalent Diameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782. Shape of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813. Particle Size Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

B. Types of Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841. Particle Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862. Bulk Density and Porosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

C. Failure Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921. Determinations Using Shear Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 922. Direct Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

D. Reconstitution Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96III. Handling of Food Particulate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

A. Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 991. Elements of Bulk Solids’ Gravity Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 992. Flow Patterns in Storage Bins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1003. Wall Stresses in Bins and Silos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024. Solids Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

B. Mechanical Conveying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1061. Bucket Elevators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1072. Screw Conveyors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

C. Pneumatic Conveying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1121. Theoretical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1122. Classification of Conveying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1133. Dilute-Phase Conveyors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

75

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IV. Processing of Food Powders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116A. Size Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

1. Comminution Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1172. Size Reduction Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1183. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

B. Size Enlargement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1231. Aggregation Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1232. Agglomeration Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1263. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

C. Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1301. Mixing Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1312. Degree of Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1313. Powder Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1334. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

D. Cyclonic Separations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1351. Operating Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1362. Dimensionless Scale-up Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1383. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

V. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

I. INTRODUCTION

The food processing industry is one of the largest manufacturing industries worldwide.Undoubtedly, it possesses global strategic importance, so it has a critical need for growthbased on future research directions detected by an integrated interdisciplinary approach toproblems in food process engineering. This industry, like many other processing indus-tries, handles and processes numerous raw materials and finished products in powderedand particulate form. In this sense, future competitiveness may be critically dependent onknowledge originated by research activities in the field known as powder technology orparticle technology, which deals with the systematic study of particulate systems in a broadsense. For the case of food products and materials some important applications of powdertechnology can be mentioned. For example, particle size in wheat flour is an importantfactor in the functionality of food products, attrition of instant powdered foods reducestheir reconstitutability, uneven powder flow in extrusion hoppers may affect the rheology ofthe paste, and an appropriate characterization of fluid–particle interactions could optimizeclarification of juices. The optimum operation of many food processes rely heavily on asound knowledge of the behavior of particles and particle assemblies, either in dry form oras suspensions.

Research efforts in particle technology have shown a tremendous growth recently.European and Asian professional associations and societies have recognized the importanceof powder technology for some time. Some of these associations, such as the Institution ofChemical Engineers (IChemE) and the Society of Chemical Industry (SCI) in the UnitedKingdom include established research groups on the topic, and organize meetings andconferences on a regular basis. In the United States the importance of powder technologywas recognized only in 1992 when a division, known as the Particle Technology Forum,was formed within the American Institute of Chemical Engineers (AIChE). In a moreglobal context, diverse international associations organize conferences and congresses on

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Handling and Processing of Food Powders and Particulates 77

particle technology with delegates from around the world attending to present the mostadvanced developments in the area. With reference to powder and particle technologyapplied specifically to food and biological materials, there has not been as much activity as inthe field of inert materials. The main conferences and meetings of professional associationsand societies related to food processing, such as the Institute of Food Technologists (IFT)in the United States, the Institute of Food Science and Technology (IFST) in the UnitedKingdom and the global International Union of Food Science and Technology (IUFoST),do not normally include sessions about food powders. Some isolated efforts have beenmade to promote exchange of ideas among powder technologists with an interest in foodand biological materials and some publications have resulted from such efforts (Schubert,1993; Ortega-Rivas, 1997).

This chapter deals with the process and design aspects of unit operations involvingparticulate solids, within the context of food and biological materials. Theoretical con-siderations, operating principles, and applications of different techniques used to handleand process powders and particulates in the food industry, are reviewed. It attempts toprovide criteria and information for students, academics, and industrialists, who may per-ceive that future growth of this strategic industry may be dependent on a deep knowledgeand understanding of this focused discipline.

II. RELEVANT PROPERTIES OF POWDEREDFOOD MATERIALS

Particle characterization, that is, description of the primary properties of food powders in aparticulate system, underlies all work in particle technology. Primary properties of particlessuch as particle shape and particle density, together with the primary properties of a fluid(viscosity and density), together with the concentration and state of dispersion, govern thesecondary properties such as settling velocity of particles, rehydration rate of powders,resistance of filter cakes, etc. It could be argued that it is simpler, and more reliable, tomeasure the secondary properties directly without reference to the primary ones. Directmeasurement of secondary properties can be done in practice, but the ultimate aim is topredict them from the primary ones, as when determining pipe resistance to flow fromknown relationships, feeding in data from primary properties of a given liquid (viscosityand density), as well as properties of a pipeline (roughness). As many relationships inpowder technology are rather complex and often not available in many areas, such as foodpowder processing, particle properties are mainly used for qualitative assessment of thebehavior of suspensions and powders, for example, as an equipment selection guide. Sincea powder is considered to be a dispersed two-phase system consisting of a dispersed phase ofsolid particles of different sizes and a gas as the continuous phase, complete characterizationof powdered materials is dependent on the properties of the particle as an individual entity,the properties of the assembly of particles, and the interactions between those assembliesand a fluid.

A. Size, Shape, and Distribution of Particles

There are several single particle characteristics that are very important to product proper-ties (Davies, 1984). They include particle size, particle shape, surface density, hardness,adsorption properties, etc. Of all the mentioned features, particle size is the most essentialand important one. The term “size” of a powder or particulate material is very relative. Itis often used to classify, categorize, or characterize a powder, but even the term powder is

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Table 1 Terms Recommended by the BritishPharmacopoeia for Use with Powdered Materials

B.S. meshes

Powder type All passes Not more than 40% passes

Coarse 10 44Moderately coarse 22 60Moderately fine 44 85Fine 85 —Very fine 120 —

Table 2 Approximate Ranges of the MedianSizes of Some Common Food Powders

Commodity B.S. mesh Microns

Rice and barley grains 6–8 2800–2000Granulated sugar 30–34 500–355Table salt 52–72 300–210Cocoa 200–300 75–53Icing sugar 350 45

not clearly defined and common convention considers that for a particulate material to beconsidered powder its approximate median size (50% of the material is smaller than themedian size and 50% is larger) should be less than 1 mm. It is also common practice totalk about “fine” and “coarse” powders; several attempts have been made at standardizingparticle nomenclature in certain fields. For example, Table 1 shows the terms recommen-ded by the British Pharmacopoeia with reference to standard sieve apertures. Also, byconvention, particle sizes may be expressed in different units depending on the size rangeinvolved. Coarse particles may be measured in centimeters or millimeters, fine particles interms of screen size, and very fine particles in micrometers or nanometers. However, due tothe recommendations of the International Organization for Standardization (ISO), SI unitshave been adopted in many countries and, thus, particle size may be expressed in meterswhen doing engineering calculations, or in micrometers in virtue of the small range nor-mally covered or when plotting graphs. A wide variety of food powders may be consideredin the fine size range. Some median sizes of common food commodities are presented inTable 2.

1. Equivalent Diameters

The selection of a relevant characteristic particle size to start any sort of analysis or meas-urement often poses a problem. In practice, the particles forming a powder will rarely havea spherical shape. Many industrial powders are of mineral (metallic or nonmetallic) originand have been derived from hard materials by any sort of size reduction process. In sucha case, the comminuted particles resemble polyhedrons with nearly plane faces, in a num-ber from 4 to 7, and sharp edges and corners. The particles may be compact, with length,breadth, and thickness nearly equal but, sometimes, they may be plate-like or needle-like.As the particles get smaller, and by the influence of attrition due to handling, their edges maybecome smoother; thus, they can be considered spherical. The term “diameter” is therefore,often used to refer to the characteristic linear dimension. All these geometrical features of

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Handling and Processing of Food Powders and Particulates 79

important industrial powders, such as cement, clay, and chalk, are related to the intimatestructure of their forming elements, whose arrangements are normally symmetrical withdefinite shapes like cubes, octahedrons, etc. On the other hand, particulate food materialsare mostly organic in origin, and their individual grain shapes could have a great diversityof structures, since their chemical compositions are more complex than those of inorganicindustrial powders. Shape variations in food powders are enormous ranging from extremedegrees of irregularity (ground materials like spices and sugar), to an approximate sphericity(starch and dry yeast) or well-defined crystalline shapes (granulated sugar and salt).

Considering the aspects mentioned above, expressing a single particle size is notsimple when its shape is irregular. This is often the case with many applications, mostlywhen dealing with food powders of truly organic origin. Irregular particles can be describedby a number of sizes. There are three groups of definitions, as listed in Tables 3, 4, and 5:equivalent sphere diameters, equivalent circle diameters, and statistical diameters. In thefirst group, the diameters of a sphere, which would have the same property of the particleitself, are found (e.g., the same volume, the same settling velocity, etc.). In the second group,the diameters of a circle, which would have the same property of the projected outline of theparticle, are considered (e.g., projected area or perimeter). The third group is obtained whena linear dimension is measured (usually by microscopy) parallel to a fixed direction. Themost relative measurements of the diameters mentioned above would probably be the stat-istical diameters because they are practically determined by direct microscopy observations.Thus, for any given particle Martin’s and Feret’s diameters could be radically different bothfrom a circle of equal perimeter or equal area (see Figure 1). In practice, most of the equi-valent diameters will be measured indirectly for a given number of particles taken from arepresentative sample and, therefore, it would be most practical to use a quick, less accuratemeasure on a large number of particles than a very accurate measure on very few particles.Also, it would be rather difficult to perceive the equivalence of the actual particles with anideal sphericity. Furthermore, such equivalence would depend on the method employed todetermine the size. For example, Figure 2 shows an approximate equivalence of an irregularparticle depending on different equivalent properties of spheres.

Taking into account the concepts presented above, it is obvious that the measurementof particle size results depend upon the conventions involved in the particle size definitionand also the physical principles employed in the determination process (Herdan, 1960).When different physical principles are used in particle size determination, it can hardly beassumed that they would give identical results. For this reason it is recommended to select

Table 3 A List of Definitions of “Equivalent Sphere Diameters”

Symbol Name Equivalent property of a sphere

xv Volume diameter Volumexs Surface diameter Surfacexsv Surface–volume diameter Surface-to-volume ratioxd Drag diameter Resistance to motion in the same

fluid at the same velocityxf Free-falling diameter Free-falling speed in the same

liquid, same particle densityxst Stokes’ diameter Free-falling speed if Stokes’ law

is used (Rep< 0.2)xA Sieve diameter Passing through the same square

aperture

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Table 4 A List of Definitions of “Equivalent Circle Diameters”

Symbol Name Equivalent property of a circle

xa Projected area diameter Projected area if particle is resting in astable position

xp Projected area diameter Projected area if particle is randomlyorientated

xc Perimeter diameter Perimeter of the outline

Table 5 A List of Definitions of “Statistical Diameters”

Symbol Name Dimension measured

xF Feret’s diameter Distance between two tangents onopposite sides of particle

xM Martin’s diameter Length of the line which bisects theimage of particle

xSH Shear diameter Particle width obtained with an imageshearing eyepiece

xCH Maximum cord diameter Maximum length of a line limited bythe contour of the particle

Feret’s diameter

Martin’s diameter

Maximumlinear

diameter Minimumlineardiameter

Circle of equal perimeter

Circle of equal area

Fixed direction

Figure 1 Methods used to measure diameter of nonspherical particles.

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Volume

DragSurface

Irregular particle

Figure 2 Equivalent spheres.

Table 6 General Definitions of Particle Shape

Shape name Shape description

Acicular Needle shapeAngular Roughly polyhedral shapeCrystalline Freely developed geometric shape in a fluid mediumDentritic Branched crystalline shapeFibrous Regularly or irregular thread-likeFlaky Plate-likeGranular Approximately equidimensional irregular shapeIrregular Lacking any symmetryModular Rounded irregular shapeSpherical Global shape

a characteristic particle size that can be measured according to the property or the process,which is under study. Thus, for example, in pneumatic conveying or gas cleaning, it ismore relevant to choose to determine the Stokes’ diameter, as it represents the diameterof a sphere of the same density as the particle itself, which would fall into the gas at thesame velocity as the real particle. In flow through packed or fluidized beds, on the otherhand, it is the surface–volume diameter, that is, the diameter of a sphere having the samesurface-to-volume ratio as the particle, which is more relevant to the aerodynamic process.

2. Shape of Particles

General definitions of particle shapes are listed in Table 6. It is obvious that such simpledefinitions are not enough to compare particle size measured by different methods orto incorporate it as a parameter into equations where particle shapes are not the same(Herdan, 1960; Allen, 1981). Shape, in its broadest meaning, is very important in particlebehavior and just looking at the particle shapes, with no attempt at quantification, can

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(a) (b)

Figure 3 Relation between: (a) perimeter, and (b) convex perimeter of a particle.

be beneficial. Shape can be used as a filter before size classification is performed. Forexample, as shown in Figure 3, all rough outlines could be eliminated, by using the ratio:(perimeter)/(convex perimeter), or all particles with an extreme elongation ratio. The earliestmethods of describing the shape of particle outlines used length L, breadth B, and thicknessT , in expressions such as the elongation ratio (L/B) and the flakiness ratio (B/T). Thedrawback with simple, one-number shape measurements is the possibility of ambiguity;the same single number may be obtained from more than one shape. Nevertheless, a meas-urement of this type, which has been successfully employed for many years, is the so-calledsphericity, �s, defined by the relation:

�s = 6Vp

xpsp(1)

where xp is the equivalent diameter of particle, sp is the surface area of one particle, andVp is the volume of one particle. For spherical particles �s equals unity, while for manycrushed materials its value lies between 0.6 and 0.7. Since direct measurement of particlevolume and surface is not possible, to evaluate such variables a specific equivalent diametershould be used to perform the task indirectly. For example, when using the mean projecteddiameter xa, as defined in Table 4, the volume and surface of particles may be calculatedusing:

Vp = αvx3p (2)

and

sp = αsx2p (3)

where αv and αs are the volume and surface factors, respectively, and their numerical valuesare all dependent on the particle shape and the precise definition of the diameter (Parfitt andSing, 1976). The projected diameter xp is usually transferred into the volume diameter xvof a sphere particle, as defined in Table 3, which is used as a comparison standard for theirregular particle size description, thus the sphere with the equivalent diameter has the samevolume as the particle. The relationship between the projected and the equivalent diametersin terms of volume is expressed as follows:

xv = xp

[6αv

π

]1/3

(4)

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where xv is the equivalent diameter of the sphere of the same volume as the particle. Whenthe mean particle surface area is known, the relationship between those two diameters is:

xv = xp

[αs

π

]1/2(5)

where all the variables have been previously defined.

3. Particle Size Measurement

Particle size distribution measurement is a common method in any physical, mechanical,or chemical process because it is directly related to material behavior and/or physical prop-erties of products. Foods are frequently in the form of fine particles during processing andmarketing (Schubert, 1987), and their bulk density, compressibility, and flowability arehighly dependent on the particle size and its distribution (Barbosa-Cánovas et al., 1987).Segregation will take place in a free-flowing powder mixture because of the differencesin particle size (Barbosa-Cánovas et al., 1985). Size distribution is also one of the factorsaffecting the flowability of food powders (Peleg, 1977). For quality control or systemproperty description, the need to represent the particle size distribution of food powdersbecomes paramount and proper descriptors in the analysis of the handling, processing, andfunctionality of each food powder.

In measuring particle size two most important decisions have to be made before atechnique can be selected for the analysis; these are concerned with the two variables meas-ured, the type of particle size and the occurrence of such size. Particle size was previouslydiscussed and, emphasizing what has been already presented, it is important to bear in mindthat great care must be taken when selecting the particle size, as an equivalent diameter, inorder to choose the one most relevant to the property or process that is to be controlled. Theoccurrence of amount of particle matter belonging to specified size classes may be classifiedor arranged by diverse criteria as to obtain tables or graphs. In powder technology the useof graphs is convenient and customary for a number of reasons. For example, a particularsize that is to be used as the main reference of a given material is easily read from a specifictype of plot.

There are four different particle size distributions for a given particulate material,depending on the quantity measured: by number fN(x), by length fL(x), by surface fS(x),and by mass (or volume) fM(x). Of the above, the second mentioned is not used in practiceas the length of a particle by itself is not a complete definition of its dimensions. Thesedistributions are related but conversions from one to another are possible only in cases whenthe shape factor is constant, that is, when the particle shape is independent of the particlesize. The following relationships show the basis of such conversions:

fL(x) = k1 · x · fN(x) (6)

fS(x) = k2 · x2 · fN(x) (7)

fM(x) = k3 · x3 · fN(x) (8)

where constants k1, k2, and k3 contain a shape factor that may often be particle size depend-ent making an accurate conversion impossible without full quantitative knowledge of itsdependence on particle size. If the shape of the particles does not vary with size, the constants

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fN (x): bylength

fN (x): bynumber

Particle size (x)

f(x)

fN (x): by surface fN (x): by mass

Figure 4 Four particle size distributions of a given particle population.

mentioned above can be easily found by definition of the distribution frequency:

∞∫0

f (x) dx = 1 (9)

therefore, the areas under the curve should be equal to 1.Different methods give different types of distributions and the selection of a method

should be based on both the particle size and the type of distribution required. In foodprocesses, many types of specific distributions would be most relevant. For example, whenclarifying fruit juices, for primary removal of suspended solids the size distribution bymass should be the one of interest because this particular stage would be defined by gra-vimetric efficiency. Final clarification, however, would be better described by surface, oreven number, distribution because of the low concentration of solids, which cause turbidity.Ortega-Rivas et al. (1997) successfully described suspended solids’ removal in apple juiceusing particle size distributions by mass. Figure 4 shows the four types of distribution.

There is an abundance of methods available for measurement of particle size distri-butions and several textbooks, such as some referred to in this chapter (Allen, 1981; Kaye,1981), are available, and review the field in great depth. Table 7 gives a schematic reviewof the methods available, size ranges covered, and the types of particle size and size dis-tribution that are measured. Only a preliminary selection can be attempted using Table 7,because it is impossible to list all the important factors influencing the choice, such as typeof equivalent diameter required, quantity to be measured, size range, quantity of sampleavailable, degree of automation required, etc.

B. Types of Densities

The density of a particle is defined as its total mass divided by its total volume. It isconsidered quite relevant for determining other particle properties such as bulk powderstructure and particle size, therefore it requires careful definition (Okuyama and Kousaka,1991). Depending on how the total volume is measured, different definitions of particledensity can be given: the true particle density, the apparent particle density, and the effective(or aerodynamic) particle density. Since particles usually contain cracks, flaws, hollows,and closed pores, it follows that all these definitions may be clearly different. The true

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Handling and Processing of Food Powders and Particulates 85

Table 7 Analytical Techniques of Particle Size Measurement

TechniqueApproximate

size range (µm)Type of

particle sizeType of sizedistribution

SievingWoven wire 37–4000 xA By massElectro formed 5–120 xA By massMicroscopyOptical 0.8–150 xa, xF, xM By numberElectron 0.001–5 xSH, xCHGravity sedimentationIncremental 2–100 xst , xf By massCumulative 2–100 xst , xf By massCentrifugal sedimentationTwo layer-incremental 0.01–10 xst , xf By massCumulativeHomogeneous-incrementalFlow classification xst , xfGravity elutriation (dry) 5–100 xst , xf By massCentrifugal elutriation (dry) 2–50 xst , xf By massImpact separation (dry) 0.3–50 xst , xf By mass or numberCyclonic separation (wet or dry) 5–50 xst , xf By massParticle countersCoulter principle (wet) 0.8–200 xv By number

Table 8 Densities of Common Food Powders

Powder Density (kg/m3)

Glucose 1560Sucrose 1590Starch 1500Cellulose 1270–1610Protein (globular) ∼1400Fat 900–950Salt 2160Citric acid 1540

particle density represents the mass of the particle divided by its volume excluding openand closed pores, and is the density of the solid material of which the particle is made. Forpure chemical substances, organic or inorganic, this is the density quoted in reference booksof physical/chemical data. Since most inorganic materials consist of rigid particles, whereasmost organic substances are normally soft, porous particles, the true density of many foodpowders would be considerably lower than those of mineral and metallic powders. Typicalnonmetallic minerals, as some previously mentioned, would have true particle densitieswell over 2000 kg/m3, while some metallic powders can present true densities of the orderof 7000 kg/m3. By contrast, most food particles have considerably lower densities of about1000 to 1500 kg/m3. Table 8 lists typical densities for some food powders. As can beobserved, salt (which is of inorganic origin) presents a notably higher density than theother substances that are listed. The apparent particle density is defined as the mass ofa particle divided by its volume excluding only the open pores, and is measured by gas

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86 Enrique Ortega-Rivas

or liquid displacement methods such as liquid or air pycnometry. The effective particledensity is referred to as the mass of a particle divided by its volume including both open andclosed pores. In this case, the volume is within an aerodynamic envelope as “seen” by a gasflowing past the particle and, as such, this density is of primary importance in applicationsinvolving flow round particles, for instance, in fluidization, sedimentation, or flow throughpacked beds.

None of the three particle densities defined above should be confused with bulk densityof materials, which includes the voids between the particles in the volume measured. Thedifferent values of particle density can also be expressed in a dimensionless form, as relativedensity or specific gravity, which is simply the ratio of the density of the particle to the densityof water. It is easy to determine the mass of particles accurately but difficult to evaluatetheir volume because they have irregular shapes and voids between them.

1. Particle Density

The apparent particle density, or if the particles have no closed pores also the true density,can be measured by fluid displacement methods, that is, pycnometry, which are in commonuse in the industry. The displacement can be carried out using either a liquid or a gas, withthe gas employed normally being air. Thus, the two known techniques to determine true orapparent density, when applicable, are liquid pycnometry and air pycnometry.

Liquid pycnometry can be used to determine particle density of fine and coarse mater-ials depending on the volume of the pycnometer bottle that is used. For fine powders apycnometer bottle of 50 ml volume is normally employed, while coarse materials mayrequire larger calibrated containers. Figure 5 shows a schematic diagram of the sequenceof events involved in measuring particle density using a liquid pycnometer. The particledensity ρs is clearly the net weight of dry powder divided by the net volume of the powder,

(b) (c)

(d) (e) (f)

Glass stopper

Calibrated50 ml bottle

(a)

Capillary

Figure 5 Descriptive diagram of density determination by liquid pycnometry: (a) description ofpycnometer, (b) weighing, (c) filling to about 1/2 with powder, (d) adding liquid to almost full,(e) eliminating bubbles, (f) topping and final weighing.

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Handling and Processing of Food Powders and Particulates 87

calculated from the volume of the bottle, subtracting the volume of the added liquid, that is:

ρs = (ms − mo)ρ

(ml − mo)− (msl − ms)(10)

where ms is the weight of the bottle filled with the powder, mo is the weight of the emptybottle, ρ is the density of the liquid, ml is the weight of the bottle filled with the liquid,and msl is the weight of the bottle filled with both the solid and the liquid. Air bubblesadhering to particles and/or liquid absorbed by the particles can cause errors in densitymeasurement. Therefore, a liquid that absorbs particles slowly and that has low surfacetension should be selected. Sometimes, when heating or boiling procedures are neededto do the gas evacuation, the liquid that has a high boiling point and does not dissolvethe particle should be used (Okuyama and Kousaka, 1991). When the density of larger,irregularly shaped solid objects, such as compressed or aggregated bulk powders is needed,a method available to evaluate fruit or vegetable volumes may be used. A schematic diagramof a top-loading platform scale for volume and density measurement is shown in Figure 6.A beaker big enough to host the solid is partially filled with some kind of liquid that willnot dissolve the solid. The weight of the beaker with the liquid in it is recorded and thesolid object is completely immersed and suspended at the same time, using a string, sothat it does not touch either the sides or the bottom of the beaker. The total weight of thisarrangement is recorded again, and the volume of the solid Vs can be calculated (Ma et al.,1997) by:

Vs = mLCS − mLC

ρL(11)

where mLCS is the weight of the container with liquid and submerged solid, mLC is theweight of the container partially filled with liquid, and ρL is the density of the liquid.

Air pycnometry can be performed in an instrument, which usually consists of twocylinders and two pistons, as shown in Figure 7. One is a reference cylinder, which is always

Sinker rod

Liquid

Platform scale

Stand

Sample

Beaker

Figure 6 Top-loading platform scale for density determination of irregularly shaped objects.

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88 Enrique Ortega-Rivas

(c)

Volume in mlSample volume

Readingscale

Valves

Measuringpiston

Referencepiston

Pressure difference indicatorStop

Cup

End Start

Pistons moving

(a) (b)

(d)

Powder

Figure 7 Descriptive diagram of density determination by air pycnometry: (a) description ofinstrument, (b) filling of cup, (c) pistons displacement, (d) reading.

empty, and the other has a facility for inserting a cup with the sample of the powder. Withno sample present, the volume in each cylinder is the same so that, if the connecting valveis closed and one of the pistons is moved, the change must be duplicated by an identicalstroke in the other so as to maintain the same pressure on each side of the differentialpressure indicator. But, if a sample is introduced in the measuring cylinder (Figure 7), andthe piston in the reference cylinder is advanced all the way to the stop, to equalize thepressures, the measuring piston will have to be moved by a smaller distance because of theextra volume occupied by the sample. The difference in the distance covered by the twopistons, which is proportional to the sample volume, can be calibrated to read directly incubic centimeters, usually with a digital counter. The method will measure the true particledensity if the particles have no closed pores, or the apparent particle density if there are anyclosed pores, because the volume measured normally excludes any open pores. If, however,the open pores are filled either by wax impregnation or by adding water, the method willalso measure the envelope volume. By measuring the difference between the two volumesthe open pore volume will be obtained, and can be used as a measure of porosity.

2. Bulk Density and Porosity

The bulk density of food powders is so fundamental to their storage, processing, anddistribution that it merits particular consideration. When a powder fills a vessel of known

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Handling and Processing of Food Powders and Particulates 89

volume V and the mass of the powder is m then the bulk density of the powder is m/V .However, if the vessel is tapped, it will be found in most cases that the powder will settleand more powder has to be added to fill the vessel completely. If the mass now filling thevessel is m′, the bulk density is m′/V > m/V . Clearly, this change in density just describedhas been caused by the influence of the fraction of volume not occupied by a particle,known as porosity. The bulk density is, therefore, the mass of particles that occupies a unitvolume of a bed, while porosity or voidage is defined as the volume of the void within thebed divided by the total volume of the bed. These two properties are in fact related via theparticle density in that, for a unit volume of the bulk powder, there must be the followingmass balance:

ρ b = ρs(1− ε)+ ρaε (12)

where ρ b is the powder bulk density, ρs is the particle density, ε is the porosity, and ρa isthe air density. As the air density is small relative to the powder density, it can be neglectedand the porosity can thus be calculated as:

ε = (ρs − ρ b)

ρs(13)

Equation (13) gives the porosity or voidage of the powder, and whether or not thisincludes the pores within the particles depends on the definition of particle density used insuch evaluation.

Over the years, in order of increasing values, three classes of bulk density have becomeconventional: aerated, poured, and tap. Each of these classes depends on the treatment towhich the sample is subjected and, although there is a move toward standard procedures,these are far from being universally adopted. There is still some confusion in the open liter-ature with regard to the interpretation of these terms. Some people consider the poured bulkdensity as loose bulk density while others refer to it as apparent density. The actual mean-ing of the term aerated density can also be considered quite confusing. Strictly speaking, itmeans that individual particles are separated by a film of air and are not in direct contact witheach other. Some authors, however, interpret it to mean the bulk density after the powder hasbeen aerated. Such interpretation yields, in fact, the most loosely packed bulk density when,for cohesive materials, the strong interparticle forces prevent the particles from rolling overeach other. Considering this second interpretation, aerated and bulk densities could both besimply regarded as loose bulk density, and this approach is implied in many investigationswhen dealing with cohesive powders. For many food powders, which are more cohesivein behavior, the terms more commonly used to express bulk density are loose bulk density,and as poured and tapped bulk density after vibration. Another way to express bulk densityis in the form of a fraction of its particles’ solid density, which is sometimes referred to asthe “theoretical density.” This expression, as well as the use of porosity instead of density,enables and facilitates the unified treatment and meaningful comparison of powders havingconsiderably different particle densities.

The aerated bulk density is, in practical terms, the density when the powder is inits most loosely packed form. Such a form can be achieved by dropping a well-dispersed“cloud” of individual particles down into a measuring vessel. Aerated bulk density can bedetermined using an apparatus like the one illustrated in Figure 8. As shown, an assemblyof screen cover, screen, a spacer ring, and a chute is attached to a mains-operated vibratorof variable amplitude. A stationary chute is aligned with the center of a preweighed 100 mlcup. The powder is poured through a vibrating sieve and allowed to fall from a fixed height

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90 Enrique Ortega-Rivas

Standard100 cc cup

Scoop

Screen cover

Screen

Spacerring

Vibratingchute

Stationarychute

Airbornefines

Cuplocation

Figure 8 Determination of aerated bulk density.

of 25 cm approximately through the stationary chute into the cylindrical cup. The amplitudeof the vibration is set so that the powder will fill the cup in 20 to 30 sec. The excess powder isskimmed from the top of the cup using the sharp edge of a knife or ruler, without disturbingor compacting the loosely settled powder.

Poured density is widely used, but the measurement is often performed in a mannerfound suitable for the requirements of the individual company or industry. In some cases thevolume occupied by a particular mass of powder is measured, but the elimination of oper-ation judgment, and thus possible error, in any measurement is advisable. To achieve this,the use of a standard volume and the measurement of the mass of powder to fill it areneeded. Certain precautions are to be taken, for example, the measuring vessel shouldbe fat rather than slim, the powder should always be poured from the same height, and thepossibility of bias in the filling should be made as small as possible. Although measurement

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Handling and Processing of Food Powders and Particulates 91

of poured bulk density is far from being standardized, many industries use a sawn-off funnelwith a trap door or stop, to pour the powder through into the measuring container.

The tap bulk density, as its name implies, is the bulk density of a powder that hassettled into a packing closer than that which existed in the poured state, by tapping, jolting,or vibrating the measuring vessel. As with poured bulk density, the volume of a particularmass of powder may be observed, but it is generally better to measure the mass of powderin a fixed volume. Although many people in industry measure tap density by tappingthe sample manually, it is best to use a mechanical tapping device so that the conditionsof sample preparation are more reproducible. An instrument that is useful in achievingsuch reproducibility is the Hosakawa powder characteristic tester, which has a standardcup (100 ml) and a cam-operated tapping device that moves the cup upward and drops itperiodically (once in every 1.2 sec). A cup extension piece has to be fitted and powderadded during the sample preparation to ensure that the powder never packs below the rimof the cup. After the tapping, excess powder is scraped from the rim of the cup and the bulkdensity is determined by weighing the cup.

Approximate values of loose bulk density of different food powders are given inTable 9. As can be seen, with very few exceptions, food powders have apparent densitiesin the range of 300 to 800 kg/m3. As previously mentioned, the solid density of most foodpowders is about 1400 kg/m3, so these values are an indication that food powders havehigh porosity, which can be internal, external, or both. There are many published theoret-ical and experimental studies of porosity as a function of the particle size, distribution,and shape. Most of them pertain to free-flowing powders or models (e.g., steel shotsand metal powders), where porosity can be treated as primarily due to geometrical and

Table 9 Approximate Bulk Density and Moisture of Different FoodPowders

Powder Bulk density (kg/m3) Moisture content (%)

Baby formula 400 2.5Cocoa 480 3–5Coffee (ground and roasted) 330 7Coffee (instant) 470 2.5Coffee creamer 660 3Corn meal 560 12Corn starch 340 12Egg (whole) 680 2–4Gelatin (ground) 680 12Microcrystalline cellulose 610 6Milk 430 2–4Oatmeal 510 8Onion (powdered) 960 1–4Salt (granulated) 950 0.2Salt (powdered) 280 0.2Soy protein (precipitated) 800 2–3Sugar (granulated) 480 0.5Sugar (powdered) 480 0.5Wheat flour 800 12Wheat (whole) 560 12Whey 520 4.5Yeast (active dry baker’s) 820 8Yeast (active dry wine) 8

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92 Enrique Ortega-Rivas

statistical factors (Gray, 1968; McGeary, 1967). Even though in these cases porosity canvary considerably, depending on factors such as the concentration of fines, it is still evid-ent that the exceedingly low density of food powders cannot be explained by geometricalconsiderations alone. Most food powders are known to be cohesive and, therefore, an openbed structure supported by interparticle forces is very likely to exist (Scoville and Peleg,1980; Moreyra and Peleg, 1981; Dobbs et al., 1982). Since the bulk density of food powdersdepends on the combined effect of interrelated factors, such as the intensity of attractiveinterparticle forces, the particle size, and the number of contact points (Rumpf, 1961), it isclear that a change in any of the powder characteristics may result in a significant changein the powder bulk density. Furthermore, the magnitude of such change cannot always beanticipated. There is an intricate relationship between the factors affecting food powderbulk density, as well as surface activity and cohesion.

C. Failure properties

To make powders flow, their strength should be less than the load put on them, that is, theymust fail. The basic properties describing this condition are known as “failure properties”and they are: the angle of wall friction, the effective angle of internal friction, the failurefunction, the cohesion, and the ultimate tensile strength. The failure properties take intoaccount the state of compaction of the powder as this strongly affects its flowability unlessthe powder is cohesionless, like dry sand, and it gains no strength on compression. Theseproperties may also be strongly affected by humidity and, especially in the case of foodand biological materials, by temperature. The time of consolidation can also have an effecton failure properties of powders. It is therefore important, to test such properties undercontrolled conditions using sealed powder samples or air-conditioned rooms or enclosures.Also, time consolidating samples must be tested to simulate storage conditions.

The angle of wall friction φ is equivalent to the angle of friction between two solidsurfaces except that one of the two surfaces is a powder. It describes the friction betweenthe powder and the material of construction used to confine the powder, for example, ahopper wall. The wall friction causes some of the weight to be supported by the walls ofa hopper. The effective angle of internal friction δ is a measure of the friction betweenparticles and depends on their size, shape, roughness, and hardness. The failure functionFF is a graph showing the relationship between unconfined yield stress (or the strength ofa free surface of the powder) and the consolidating stress, and gives the strength of thecohesive material in the surface of an arch as a function of the stress under which the archwas formed. The cohesion is, as mentioned earlier, a function of interparticle attraction andis due to the effect of internal forces within the bulk, which tend to prevent planar slidingof one internal surface of particles upon another. The tensile strength of a powder compactis the most fundamental strength mechanism, representing the minimum force required tocause separation of the bulk structure without major complications of particle disturbanceswithin the plane of failure.

1. Determinations Using Shear Cells

There are several ways, direct or indirect, of testing the five failure properties defined above.All of them can be determined using a shear cell, but simplified or alternative procedurescan be adopted when the aim is to monitor the flowability of the output from a process orto compare a number of materials. There are basically two types of shear cells availablefor powder testing: the Jenike shear cell, also known as the translational shear box, and

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Handling and Processing of Food Powders and Particulates 93

the annular or ring shear cell, also called the rotational shear box. The Jenike shear cell iscircular in the cross section, with an internal diameter of 95 mm. A vertical cross sectionthrough the cell is shown in Figure 9. It consists of a base and a ring, which can slidehorizontally over the base. The ring and base are filled with the powder and a lid is placedin position. By means of a weight carrier, which hangs from a point at the center of the lid,a vertical compacting load can be applied to the powder sample. The lid carries a bracketwith a projecting pin and a measured horizontal force is applied to the bracket, causing thering and its contents, as well as the lid, to move forward at a constant speed. The shear forceneeded to make the powder flow can thus be obtained. Five or six different vertical loadsare applied to a set of identical samples and the shear force needed to initiate flow is foundin each case. Every determined force is divided by the cross-sectional area of the cell, inorder to calculate the stress. The derived shear stresses are, then, plotted against normalstresses. The resulting graph is a yield locus (Figure 10), and it is a line that gives the stressconditions needed to produce flow for the powder when compacted to a fixed bulk density.

If the material being tested is cohesive, the yield locus is not a straight line and doesnot pass through the origin. It can be shown that the graph when extrapolated downward cutsthe horizontal axis normally. As shown in Figure 10, the intercept T is the tensile strengthof the powder compacts tested and the intercept C is called the cohesion of the powder; theyield locus ends at the point A. A yield locus represents the results of a series of tests onsamples that have the initial bulk density. More yield loci can be obtained by changing thesample preparation procedure and a family of yield loci can be obtained. This family ofyield loci contains all the information needed to characterize the flowability of a particularmaterial; it is not, however, in a convenient form. For many powders, yield locus curves

Lid

Ring

Base

Powder

Figure 9 Diagram of Jenike shear cell.

·A

Normal stress

She

ar s

tres

s

C

T

Figure 10 The Jenike yield locus.

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94 Enrique Ortega-Rivas

can be described by the empirical Warren–Spring equation (Chasseray, 1994):( τC

)n = σ

T+ 1 (14)

where τ is the shear stress, C the material’s cohesion, σ the normal stress, T the tensilestress, and n the shear index (1 < n < 2). As mentioned before, cohesion is a very importantproperty in food powders. Table 10 lists cohesion values for several food powders.

Two important properties defined above can be obtained from the yield loci: the first isthe effective angle of internal friction while the second is the failure function of the powder.The angle of wall friction can be measured by replacing the base of a Jenike shear cell bya plate of the material of which the hopper (or any sort of container) is to be made. Thering from the shear cell is placed on the plate and filled with powder and the lid is put inposition. The shear force needed to maintain uniform displacement of the ring is found fordifferent vertical loads on the lid. The slope of the graph of shear force against normal forcegives the angle of friction between the particles and the wall, or angle of wall friction. Thismeasure would complete the testing of a particulate material using only a Jenike shear cell.

In annular shear cells, the shear stress is applied by rotating the top portion of anannular shear, as represented in Figure 11. These devices allow much larger shear distancesto be covered both in sample preparation and its testing allowing a study of flow propertiesafter testing, but their geometry creates some problems. The distribution of stress is not

Table 10 Cohesion for Some Food Powders

Material Moisture content (%) Cohesion (g/cm2)

Corn starch <11.0 4–6Corn starch 18.5 13Gelatin 10.0 1Grapefruit juice 1.8 8Grapefruit juice 2.6 10–11Milk 1.0 7Milk 4.4 10Onion <3.0 <7Onion 3.6 8–15Soy flour 8.0 1

Trough

Normal load

Powder

Ring

Figure 11 Diagram of an annular shear cell.

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Handling and Processing of Food Powders and Particulates 95

uniform in the radial direction but, for the ratio of the inner and outer radii of the annuligreater than 0.8, the geometrical effects are often considered negligible. The annular shearcells tend to give lower values for yield strength than the Jenike shear cell tester. There isanother type of shear cell known as the ring shear or ring shear tester. In this device the cellis in the form of a full ring and is rotated like the annular shear cell. It has been reportedto have the advantages of nearly unlimited shear deformation, possibility of measurementsat very low consolidation stresses, ease of operation, and possibility of time consolidationmeasurements using a consolidation bench (Schulze, 1996). In contrast to the annular shearcell, the results obtained using a ring shear tester are in reasonable agreement with thoseobtained with the Jenike shear cell.

2. Direct Measurements

The angle of internal friction can be measured directly by the “grooved plate” method. Thebase of the Jenike shear cell is replaced by a metal plate, in which a number of saw-toothedgrooves are cut (Figure 12). These grooves are filled with the powder to be tested. The ringfrom the Jenike cell is then placed on the plate and filled with the powder and the lid isplaced into position. A load is placed on the lid and the ring is pushed across the groovesuntil the shear force settles out at a constant value, which is measured, and this action isrepeated for different vertical loads. The graph of shear force against normal force will bea straight line with its slope being the angle of internal friction of the powder.

For direct measurement of the failure function, a split cylindrical die as shown inFigure 13 is used. The bore of the cylinder may conveniently be about 50 mm and itsheight should be a little more than twice the bore. The cylinder is clamped so that the twohalves cannot separate and it is filled with the powder to be tested, which is then scrapedoff, level with the top face. By means of a plunger the specimen is subjected to a knownconsolidating stress. The plunger is then removed and the two halves of the split die areseparated, leaving a self-standing column of the compacted powder. A plate is then placedon top of the specimen and an increasing vertical load is applied to it until the columncollapses. The stress at which this occurs is the unconfined yield stress, that is, the stressthat has to be applied to the free vertical surface on the column to cause failure. If this isrepeated for different compacting loads and the unconfined yield stress is plotted againstthe compacting stress, the failure function of the powder will be obtained. Although theresults of this method can be used for monitoring or for comparison, the failure functionobtained will not be the same as that given by shear cell tests, due to the effect of die wallfriction when forming the compact. A method of correcting for friction has been describedelsewhere (Williams et al., 1971).

Two methods can be used for direct measurement of tensile strength. In the first,a mold of the same diameter as the Jenike cell is split across a diameter. The base of

Lid

Ring

Powder

Grooved plate

Figure 12 The grooved plate method for measuring the angle of internal friction.

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96 Enrique Ortega-Rivas

Figure 13 Device for direct measurement of failure function.

the cell is roughened, by sticking sandpaper to it. The two halves are clamped together,the cell is filled with the powder, and then a lid is placed in position. The specimen iscompacted by the application of a known vertical force to the lid and this, along withthe clamp, are removed. The two halves of the cell, containing the specimen, rest ona base plate in which slots have been cut to form an air bearing. Air is introduced sothat the cell can move horizontally without friction and the force needed to pull the twohalves of the specimen are determined. Knowing the cross-sectional area of the specimenallows the tensile strength to be found. Measurements are made for a number of com-pacting loads and the tensile strength is plotted against compacting stress. This methodis quite difficult to perform properly, requiring careful attention to details. The secondmethod is easier to use and gives results with less scatter. In this case a mold of the samediameter as the Jenike shear cell, and a lid which just fits inside it, are used. The baseof the cell and the lower face of the lid are covered with sticking tape on which glue isspread. The cell is filled with the powder, which is scraped level with the top of the celland the lid is placed in position. A compacting load is applied to the lid by means of aweight hanger and left in position until the glue has hardened. The lid is then attachedthrough a tensile load cell to an electric motor, by which the lid is slowly lifted. Thestress required to break the specimen is thus obtained. After failure, the lid and the base ofthe cell are examined and the result is accepted only if both are completely covered withpowder, showing that tensile failure has occurred within the powder specimen and not atthe surface. Figure 14 presents a diagram of these two methods for direct measurement oftensile strength.

D. Reconstitution Properties

In the context of food drying, reconstitutability is the term that is used to describe the rateat which dried foods pick up and absorb water reverting to a condition that resembles theundried material, when put in contact with an excessive amount of this liquid (Masters,1976). In the case of powdered, dried biological materials, a number of properties mayinfluence the overall reconstitution characteristics. For instance, wettability describes

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Handling and Processing of Food Powders and Particulates 97

(a)

(b)

Figure 14 Methods for measuring tensile strength: (a) horizontal split cell, (b) lifting lid cell.

the capacity of the powder particles to absorb water on their surface, thus initiatingreconstitution. Such a property depends largely on particle size. Since small particles have alarge surface area : mass ratio, they may not be wetted individually. In fact, they may clumptogether sharing a wetted surface layer. This layer reduces the rate at which water penetratesinto the particle clump. Increasing particle size and agglomerating particles can reduce theincidence of clumping. The nature of the particle surface can also affect wettability. Forexample, the presence of free fat on the surface reduces wettability. The selective use ofsurface-active agents, such as lecithin, can sometimes improve wettability in dried powderscontaining fat.

Another important property is sinkability, which describes the ability of the powderparticles to sink quickly into the water. This depends mainly on the size and density of theparticles. Larger, denser particles sink more rapidly than finer, lighter ones. Particles with ahigh content of occluded air may be relatively large but exhibit poor sinkability because oftheir low density. Finally, dispersability describes the ease with which the powder may bedistributed as single particles over the surface and throughout the bulk of the reconstitutingwater, while solubility refers to the rate and extent to which the components of the powderparticles dissolve in the water. Dispersability is reduced by clump formation and is improvedwhen the sinkability is high, whereas solubility depends mainly on the chemical compositionof the powder and its physical state.

Food dried powders and particulates are normally reconstituted for consumption. Fora dried product to exhibit good reconstitution characteristics there has to be a correct balancebetween the individual properties discussed above. In many cases, alteration of one or twoof these properties can markedly change the rehydrating behavior. Several measures canbe taken in order to improve reconstitutability of dried food products. The selected dryingmethod and adjustment of drying conditions can result in a product with good rehydrationproperties. For example, it is well known that freeze drying is a process by which ice

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98 Enrique Ortega-Rivas

crystals are produced and sublimated at very low pressures (Heldman and Singh, 1981).This procedure results in food particles with an open pore structure, which absorb watereasily when they are reconstituted.

Another alternative is the use of the so-called combined methods, such as osmoticdehydration followed by conventional drying. In osmotic dehydration, food particles areimmersed in a concentrated solution. By osmotic pressure, the water inside the particlestends to migrate to the solution in order to equate water activities on both sides of thecellular wall (Monsalve-Gonzalez et al., 1993). This partial dehydration will aid in thefinal stage of drying, and textural damage of the biological materials will be minimized.In this sense, biological materials dehydrated by combined methods will also have anopen pore structure and, similar to freeze-dried materials, will present good reconstitutionproperties. Beltran-Reyes et al. (1996) developed an apple-powdered ingredient by grindingdried apples obtained by osmotic dehydration followed by conventional heated air drying.They determined that the firmness of the rehydrated mash, measured as an extrusion forcein a texture analyzer, was a direct function of the particle size. For the same ingredient,Ortega-Rivas and Beltran-Reyes (1997), reported that rehydration improved as particlesize decreased.

The most efficient method to improve the rehydration characteristics of dried foodpowders is probably the use of agglomeration (Barletta and Barbosa-Canovas, 1993). Inorder to agglomerate particles, the powder is treated with steam or warm, humid air suchthat condensation occurs on the particle surface. Interparticle contact is promoted, oftenby swirling the wetted powder in a vortex. Agglomerates are formed and then dried in achamber and cooled on a vibrating fluidized bed. Agglomeration, as a unit operation, willbe discussed further in a subsequent section.

III. HANDLING OF FOOD PARTICULATE SYSTEMS

The food and related industries handle considerable quantities of powders and particulatematerials every year. Materials handling mainly implies storage and conveying and is con-cerned with open and confined storing, as well as with movement of materials in differentcases, for instance, from supply point to store or process, between stages during processes,or to packing and distribution.

The handling of materials is a crucial activity, which adds nothing to the value ofthe product, but can represent an added cost if not managed properly. For this reason,responsibility for materials’ handling is normally vested in specialist handling engineers,and many food manufacturers adopt this procedure. When a specific materials’ handlingdepartment has not been provided, the responsibility for efficient handling of materialsfalls on the production manager and his/her staff. It is important, therefore, for pro-duction executives to have a sound knowledge of the fundamentals of good handlingpractice.

Silos, bins, and hoppers that are used to store materials in the food industry varyin capacity from a few kilos to multiton-capacity vessels. Startup delays and ongoinginefficiencies are common in solids processing plants. An important cause for theseproblems is the improper design of bulk solids handling equipment. For bulk par-ticulate or powdered food materials, which fall within the scope of this chapter, aconvenient classification of conveyors would comprise those using direct mechanicalpower to move the conveying elements, such as belt, chain, and screw conveyors, andthose relying on a stream to carry particulates in it, such as hydraulic and pneumaticconveyors.

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Handling and Processing of Food Powders and Particulates 99

A. Storage

The design of bins, hoppers, and silos has never been given the attention it deserves.Approaches using properties such as angle of repose or angle of spatula in design consider-ations are ineffective, because the resulting values bear no relation to the design parametersneeded to ensure reliable flow, mainly because particulate solids tend to compact or consol-idate when stored. Attempts to try and model bulk solids as fluids also leads to a bottleneck,due to the fact that flowing bulk solids generate shear stresses and are able to maintain thesestresses even when their flow rate is changed dramatically. It is also improper to considerbulk solids as having viscosity since almost all bulk solids exhibit flow properties that areflow-rate independent. The systematic approach for designing powder handling and pro-cessing plants started in the mid-1950s with the pioneering work of Andrew W. Jenike.His concept was to model bulk solids using the principles of continuum mechanics. Theresulting comprehensive theory (Jenike, 1964) describing the flow of bulk solids has beenapplied and perfected over the years, but is generally recognized worldwide as the onlyscientific guide to bulk solids’ flow.

The procedures for the design of a bulk solids’ handling plant are well establishedand follow four basic steps: (1) determination of the strength and flow properties of thebulk solids for the worst likely flow conditions expected to occur in practice; (2) calculationof the bin, stockpile, feeder, or chute geometry to give the desired capacity to provide aflow pattern with acceptable characteristics, in order to ensure that discharge is reliable andpredictable; (3) estimation of the loadings on the bin and hopper walls and on the feeders andchutes under operating conditions; (4) design and detailing of the handling plant includingthe structure and equipment.

1. Elements of Bulk Solids’ Gravity Flow

Only fluids can flow; bulk solids under gravity forces can fall, slide, or roll, but againstgravity, they must be lifted by mechanical means. Solids cannot be pumped by centrifugalor reciprocating pumps, so they have to be suspended in liquids or gases. There is nosatisfactory term for “flow” of bulk solids, as they do not follow strict definitions of fluidbehavior, since a fluid is considered to be a continuum in which there are no voids. Fora fluid, when the shear rate is linearly proportional to the shear stress, it is said to beNewtonian and the coefficient of proportionality is called absolute viscosity. Any deviationfrom this definition makes the fluid non-Newtonian. Solids in suspension can be referred toas non-Newtonian mixtures to differentiate them from a number of non-Newtonian fluids,which are a continuum or are perfectly homogeneous liquids. For all these reasons, bulksolids in suspension are occasionally referred to as “imperfect fluids.”

The gravity flow of bulk solids occurs under the pressure corresponding to the equi-valent of a “static head” of the material. Such head would be caused by the height of a solidcolumn in a bin, but in practice is often not available to produce the flow due to phenomenaknown as “arching” or “bridging.” The velocity head at discharge from the bin is usually asmall fraction of the head, with the major part being consumed by the friction of the movingsolids against the walls of the bin, as well as against like solids. Friction is the resistancethat one body offers to the motion of a second body when the latter slides over the former.The friction force is tangent to the surfaces of contact of the two bodies and always opposesmotion. The coefficient of static friction µ for any two surfaces is the ratio of the limitingfriction to the corresponding normal pressure, that is:

µ = F

N(15)

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100 Enrique Ortega-Rivas

where F is the maximum friction of impeding motion and N is the normalpressure.

If a body rests on an inclined plane and if the angle of inclination of the plane to thehorizontal, α, is such that the motion of the body impends, this angle α is defined as theangle of repose, so it follows that:

µ = tan α (16)

When two surfaces move relative to each other, the ratio of the friction created to thenormal pressure is called the coefficient of kinetic friction and is independent of the normalpressure. The coefficient of kinetic friction is also less than the coefficient of static frictionand independent of the relative velocity of the rubbing surfaces. There is experimentalevidence, which supports the theory that the value of the kinetic friction coefficient increasesas the velocity decreases, and passes without discontinuity into that of static friction. Allthese principles would hold under conditions of a particular test, but must be modifiedin order to be applied to different conditions. Herein lies the main difficulty in applyingexisting test data on series of new tests because of the great variety in flowing conditionsof bulk solids. The problem is particularly complicated as the properties of the flowingmaterial depend on time and method of storage.

When granular solids are stored in an enclosed container, the lateral pressure exertedon the walls at any point is less than that predicted from the head of the material above such apoint. There is usually friction between the wall and the solid particles, and the interlockingof these particles causes a frictional effect throughout the bulk solid mass. The frictionalforce at the wall tends to offset the weight of the solid and reduces the effect of the headof solids on the floor of the container. In an extreme case, such frictional force causes themass of bulk solids to arch, or bridge, so that it would not fall even if the material below isdischarged. For many granular solids, when the height of the solid bed reaches about threetimes the diameter of the bin, additional head of material shows virtually no effect on thepressure at the bin floor.

Solids tend to flow out of any opening near the bottom of a bin but are best dischargedthrough an opening in the floor. The pressure at a side outlet is smaller than the verticalpressure at the same level and removal of solids from one side of a bin considerably increasesthe lateral pressure on the opposite side while the solids flow. When an outlet at the bottomof a bin containing free-flowing solids is opened, the material immediately above such anopening begins to flow. A central column of solids moves downward without disturbing thematerial at the sides. Eventually lateral flow begins, starting from the top layer of solids anda conical depression forms in the surface of the mass of bulk solids being discharged. Thematerial slides laterally into the central column moving at an angle approaching the angle ofinternal friction of the solids and the solids at the bin floor are the last to move. If additionalmaterial is added at the top of the bin, at the same rate as the material leaving through thebottom outlet, the solids near the bin walls remain stagnant and do not discharge as long asflow persists. The rate of flow of granular solids by gravity through a circular opening inthe bottom of a bin is dependent on the diameter of the opening as well as on the propertiesof the solid and is independent, within wide limits, on the head or height of the solids.

2. Flow Patterns in Storage Bins

The general theory pertaining to gravity flow of bulk solids has been documented over theyears (Arnold et al., 1982; Roberts, 1988) and from a standpoint of flow patterns, thereare basically three types of flow in symmetrical geometry: mass flow, funnel flow andexpanded flow (Figure 15). In mass-flow bins, the flow is uniform and the bulk density of

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Handling and Processing of Food Powders and Particulates 101

D

B

u

u

b

u

B

D

H H

HD

Deadcapacity

D

Mass flow

Funnelflow

B

(a)

(c)

(b)

Figure 15 Types of flow patterns in hoppers: (a) mass flow, (b) funnel flow, and (c) expanded flow.

the feed is practically independent of the head of solids in the bin. Mass flow guaranteescomplete discharge of the bin’s contents at predictable flow rates. When properly designed,a mass-flow bin can remix the bulk of the solid during discharge even if segregation ispromoted during filling. Mass-flow bins are generally recommended for cohesive materials,for materials that degrade with time, for fine powders, and for particulate systems that have tobe prevented from segregating. Normally food powders are highly cohesive and, therefore,the use of mass-flow bins would represent a preferred alternative for their storage.

Funnel flow occurs when the hopper is not sufficiently steep and smooth to forcethe bulk solid to slide along the walls. It also occurs when the outlet of the bin is notfully effective, due to poor feeder or gate design. In a funnel-flow bin the stored materialflows toward the outlet through a vertical channel forming within the stagnant solids. Thediameter of such a channel approximates the largest dimension of the effective outlet. Flowout of this type of bin is generally erratic and gives rise to segregation problems. However,

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102 Enrique Ortega-Rivas

flow will continue until the level of the bulk solid in the bin drops an amount equal tothe drawdown. At this level the bulk strength of the contained material is sufficient tosustain a stable rathole as illustrated in Figure 15(b). Once the level defined by HD inFigure 15(b) is reached, there is no further flow and the material below this level representsdead storage. For complete discharge, the bin opening has to be at least equal to the criticalrathole dimension, determined at the bottom of the bin corresponding to the bulk strengthat this level. For many cohesive bulk solids, and for normal consolidation heads occurringin practice, ratholes measuring several meters high are often observed. This makes controlof the product discharge rate quite difficult and funnel flow somewhat impractical. Funnelflow has the advantage of providing wear protection of the bin walls as the material flowsagainst stationary material. Funnel-flow bins are suitable for coarse, free-flowing, or slightlycohesive, nondegrading solids when segregation is unimportant. With reference to foodsystems, funnel-flow bins may be used for grains, pulses, oilseeds, and so on, mainly forthe application of feeding such materials to processing directly, as in cereal extrusion orcereal milling.

The expanded-flow bin combines characteristics of mass flow and funnel flow. Thehigher part of the hopper operates in funnel flow while the lower operates in mass flow.The mass-flow outlet usually requires a smaller feeder than would be the case for funnelflow. The mass-flow hopper should expand the flow channel to a diagonal or diameterequal to or greater than the critical rathole diameter, thus eliminating the likelihood ofratholing. Funnel-flow bins provide the wall protection of funnel flow, together with thereliable discharge of mass flow. Expanded flow is ideal where large tons of bulk solidsneed to be stored and is particularly suitable for storing large quantities of bulk solidswhile maintaining acceptable head heights. The concept of expanded flow may be usedto advantage in the case of bins or bunkers with multiple outlets. Expanded flow bins arerecommended for the storage of large quantities of nondegrading solids. This design isalso useful as a modification of existing funnel-flow bins to correct erratic flow caused byarching, ratholing, or flushing.

3. Wall Stresses in Bins and Silos

The prediction of wall loads in bins is an important piece of information for their design.It is necessary to estimate the pressures at the wall, which are generated when the bin isoperated, in order to design the bin structure efficiently and economically. The approachesto the study of bin wall loads are varied and involve analytical and numerical techniques,such as finite element analysis. Despite these varied approaches, it is clear that the loads aredirectly related to the flow patterns that are created in the bin. The flow pattern in mass-flowbins is reasonably easy to predict but in funnel-flow bins such prediction becomes quitea difficult task. For this reason, unless there are compelling reasons to do otherwise, binshapes should be kept simple and symmetric.

Research relating to wall stresses dates back to the 1800s when Janssen (1895) pub-lished his now famous theory. More recent investigations include those reported by Walker(1966), Walker and Blanchard (1967), Jenike and Johanson (1968, 1969), Walters (1973),Clague (1973), Arnold et al. (1982), Roberts (1988), and Thompson et al. (1997). Examin-ation of these papers shows that the solution of the problem of stress distributions in bins isextremely complex. However, most researchers agree that the loads acting on a bin wall aredifferent during the initial stage of filling and during the stage of flowing in discharge. Whenbulk solids are charged into an empty bin, with the gate closed or with the feeder at rest, thebulk solids settle as the solids’ head rises. In this settlement, the solids contract verticallyin the cylindrical section and partially vertically in the hopper section. The principal stress

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Handling and Processing of Food Powders and Particulates 103

tends to align with the direction of contraction of the solids, forming what is termed as anactive or peaked stress field. It is assumed that the solids are charged into the bin withoutsignificant impact to cause packing, and that powders are charged at a sufficiently low rateso that they deaerate. It is also assumed that the bin and feeder have been designed cor-rectly for the solids to flow without obstruction. When the gate is fully opened or the feederoperates so that the solids start flowing out of the outlet, there is vertical expansion of thesolids within the forming flow channel and the flowing mass of solids contract laterally.The principal stresses within the flow channel tend to align with the lateral contractions andthe stress field is said to be passive or arched.

The region of switch from an active to a passive stress field originates at the outlet ofthe bin, when the gate is opened, or the feeder is started, and rapidly moves upward intothe bin as the solids are withdrawn. At the switch level a fairly large overpressure may bepresent, and it is assumed to travel upward with the switch at least to the level at which thechannel intersects the vertical section of the bin. For a typical bin consisting of a hopperplus a cylindrical section above it, five stress fields have been recognized during the fill anddischarge sequences: (1) in the cylindrical section during initial filling, where the state ofstress is peaked or active; (2) in the cylindrical section during emptying, where the stateof stress is either peaked or changes to arched, depending on whether the switch level isassumed to be caught at the transition; (3) in the converging hopper section during filling,where the state of stress is assumed to be peaked; (4) in the converging hopper sectionduring emptying, where the state of stress is assumed to be arched; and (5) the switch field,that is, the region in the bin where the peaked stress field established during initial fillingis transformed into the arched stress field. This switch starts at the outlet of the hopper, ifnewly filled from being completely empty, and then travels up very quickly as emptyingcontinues, generally to become caught in the transition. Most of the researchers mentionedagree upon a wall pressure or stress distribution as shown in Figure 16.

The Janssen theory mentioned above (Janssen, 1895) includes, possibly, the oldestreported attempt to calculate pressures in silos. Janssen derived an equation for the calcu-lation of vertical and horizontal pressures and wall shear stresses. He assumed a verticalforce balance at a slice element spanning the full cross section of a silo being filled withbulk solids (see Figure 17), and determined the wall friction coefficient with a shear testeras well as the horizontal pressure ratio from pressure measurements in a model bin. Healso assumed a constant vertical pressure across the cross section of the slice element andrestricted his evaluation to vertical silo walls. The Janssen equation for the vertical pressurepv on dependence of the depth z below the bulk solids’ top level reads as follows for acylindrical silo:

pv = gρ bD

4µ′K ′

[1− e

−(

4µ′K ′zD

)](17)

where g is the acceleration due to gravity, ρ b is the bulk density of solids, D is the silodiameter, µ′ is the sliding friction coefficient along the wall, and K ′ is the ratio of thehorizontal to the vertical pressure, which can be expressed as:

K ′ = 1− sin δ

1+ sin δ(18)

where δ is the angle of internal friction of solids.The advantage of the Janssen equation is its simplicity, that is, of an analytical equation

and its general good agreement with pressure measurements in silos for the state of filling.The disadvantages are its nonvalidity for the hopper section, its assumption of a constantvertical stress across the cross section, and its assumption of plastic equilibrium throughout

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104 Enrique Ortega-Rivas

Switchstress

Dynamic or dischargeconditions

Static or fillconditions

Hei

ght

Hei

ght

Normal wallNormal wall load

Normalwallload

Mass-flow bin

Figure 16 Wall load distribution in silo.

tw

pv+ dpv

pv

gpv

phdH

HCross section

Figure 17 Force equilibrium at a slice element for full cross section of silo.

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Handling and Processing of Food Powders and Particulates 105

the stress field in the silo. But the Janssen equation cannot explain the increase in horizontalpressure when discharge is initiated. This disadvantage can only be overcome by using finiteelement methods, more sophisticated yield criteria, and a very high degree of computationaleffort (Häußler and Eibl, 1984).

Simplicity and analytical solution made the Janssen equation the basis for the firststandard for the calculation of loads in silos more than 35 years ago. This equation is stillthe most widely used analytical solution for the calculation of pressures in silos. However,the structural design of silos requires the incorporation of experience, measurement resultsin model bins, and full-scale silos, as well as accepted safety margins for uncertainties.Major factors contributing to the loads in silos are the flow profile, the flow behavior, theinteraction between wall material and bulk solids, and the performance of feeders anddischarge aids (Jenike, 1964). The loads in silos are influenced by many factors. Some ofthem are related to the bin structure, its construction material and size. Many other factors,however, depend on the bulk solids’ flow properties, the design of outlet size, the typeof feeder, the discharge aids, and the operating conditions. These factors are especiallyimportant for nonfree-flowing, cohesive bulk solids.

4. Solids Discharge

The amount of solids discharged through an opening at the bottom of a bin, and failure torestart the flow after intermission, depend on the bin design, shape, and the location of theopening, apart from the flow properties of the solid. The flow properties of the granularmaterial include grain nature, size, moisture content, temperature, adhesion, cohesion and,above all, time of consolidation at rest. There are very few solids that are free-flowingand that will restart flow after an extended period at rest. Examples include inert materialssuch as graded gravel and dry sand. In contrast, as has been stated, food powders aremostly cohesive and their flow is very difficult, even without consolidation time. Pressuredistribution within a bin affects its design for strength, but does not enter into calculationof the solids flow from the hopper. It has been mentioned that the volume of bulk solidsdischarged is independent of the head above the orifice, due to the arching effect. Therefore,the design of bins or silos in terms of their ability to initiate flow without any aid is basedon solid mechanics theories taking into consideration only the hopper of the container.

Food powders are complex because of their composition (Schubert, 1987), their largedistribution in particle size and the presence of solid–liquid–gas phases in the particle.Moisture has a great influence on flowability and its presence and proportion within thefood powder depend on the relative humidity of the surrounding atmosphere. The remain-ing factors that affect most powders’ flowability, that is, failure properties, particle andbulk density, and so on, also affect food powder flowability and, therefore, have a directinfluence on the design of bin geometry for mass flow. Teunou et al. (1999) characterizedrepresentative food powders for their flowability and design of hoppers for mass flow, andtheir main findings are summarized in Table 11.

In order to ensure flow from bins, even after the hopper geometry has been determinedfollowing careful calculations, flow promotion may be necessary. Classification of flowpromotion may be termed as passive and active, involving energy. A third class of flowpromotion may also be considered, that is, the use of feeders, which are useful not onlyto promote flow, but also to control the flow rate. Passive devices normally include insertsusually placed within the hopper section of a bin, with the purpose of expanding the size ofthe active flow channel in a funnel-flow bin so as to approach mass flow. Another aim of aninsert is to relieve pressure at the outlet region. Inverted cones and pyramids have been usedfor years in this regard, but with limited success. Vibrating hoppers by the use of electrical

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106 Enrique Ortega-Rivas

Table 11 Physical Properties and Hopper Dimensions of FoodPowders*

Powder X (%) ff δ(◦) φ(◦) θ(◦) B (mm)

Flour 12.6 2.71 32 12.6 37 110Skim milk 4.6 11.04 50 13.0 32 270Tea 6.6 4.22 43 15.0 31 130Whey-permeate 3.8 5.85 49 15.0 30 180

Note: *X is the water content in wet basis while the remaining variables areas defined in this text.

Source: Adapted from Teunou, E., Fitzpatrick, J.J., and Synnott, E.C. (1999).J. Food Eng. 39: 31. With permission.

Table 12 Guide for Selection of Feeders

Bulk solid characteristics Type of feeder

Fine, free-flowing solids Apron, vibratory, screw, starNonabrasive, granular materials Apron, vibratory, screwDifficult-to-handle (abrasive, hot, etc.) materials Apron, vibratoryHeavy, lumpy, or highly abrasive materials Apron, vibratory

motors, pneumatic knockers, eccentric drives, or electromagnetic units, are one of the mostimportant and versatile flow assisters or active device types. Air cannons or air blasters arealso commonly used to promote gravity flow in bins.

In designing hoppers for silos, the procedure described so far would consist of makingcalculations to determine optimum hopper slope and outlet opening in order to ensure flow.In case flow does not occur, a flow promotion device can be selected after careful studyof conditions and factors. Once flow out of a bin is guaranteed, the next step, to completethe proper design of the bulk storage plant, would be to control the flow rate, so as toprovide adequate feed to any given food powder process. In order to do so, the use ofa feeder will become necessary. A feeder is a device used to control the flow of bulksolids from a bin. A feeder must be selected to suit a particular bulk solid and the rangeof feed rates required. It is particularly important to design the hopper and feeder as anintegral unit, to ensure that the flow from the hopper is fully developed with uniform drawof material from the entire hopper outlet. There are several types of feeders but the mostcommon are the belt or apron feeder, the screw feeder, the vibratory feeder, and the starfeeder. Careful considerations, such as those described above, should be taken in selectinga feeder for a particular application. Table 12 provides a preliminary guide in choosinga feeder.

B. Mechanical Conveying

The main types of mechanical conveyors are belt, chain, and screw conveyors. In the foodindustry belt conveyors are not widely used. The main application in food systems hasbeen in conveying grains. In fact, it has been mentioned (Wright et al., 1997) that the beltconveyor drive power calculation has its origin in grain handling in the late 1700s in theUnited States. Possibly, the most common devices for transportation of food granules andparticulates, using mechanical forces, are the bucket elevator and the screw conveyor.

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Handling and Processing of Food Powders and Particulates 107

1. Bucket Elevators

Bucket elevator systems comprise high capacity units primarily intended for bulk elevationof relatively free-flowing materials and may be considered a special adaptation of chainconveying. Bucket elevators are the simplest and most dependable equipment units forvertical lifting of different types of granular materials. They are available in a wide range ofcapacities and may operate either entirely in the open or be totally enclosed. High efficiencyin bucket elevators results from the absence of frictional loss from sliding the material onthe housing, and this feature distinguishes it from the vertical, or nearly vertical, scraperconveyor. The material carrying element of this sort of conveying is the bucket, which maybe enclosed in a single housing called a leg, or two legs may be used. The return leg may belocated some distance from the elevator leg. A single or double chain is used to attach thebuckets. The most important considerations affecting the design and operation of bucketelevators are: (1) the physical properties of the conveyed material, (2) the shape and spacingof the buckets, (3) the speed at which the elevator is driven, (4) the method of loading theelevator, and (5) the method of discharging the elevator.

Important physical properties of the material being elevated are particle size, lumpsize, moisture content, angle of repose, flowability, abrasiveness, friability, etc. The designof the buckets has to do, principally, with capacity and ease of discharge. They may beconstructed out of malleable iron or steel and can be shaped with either sharp or roundbottoms. Mounting and spacing of the buckets will conform to a specific elevator design.Some typical bucket elevators are shown schematically in Figure 18. They may be fastened tothe chain at the back (Figure 18[a]) or at the side if mounted on two chains (Figure 18[b]).Guides are sometimes used for two-chain installations, particularly in the upward leg.Single-chain installations have no guides or supports between the head and foot wheelsexcept, possibly, an idler or two placed at strategic points to eliminate whip. The centerspacing of buckets varies with their size, shape, speed, as well as head and foot wheeldiameter. The buckets must be placed so that the centrifugal discharging grain does nothit the bucket ahead of the one discharging. For general purposes, the spacing will be 2to 3 times the projected width. The speed of the drive in bucket elevators, although much

(a) (b) (c) (d)

Figure 18 Bucket elevators: (a) centrifugal-discharge spaced buckets, (b) positive-discharge spacedbuckets, (c) continuous bucket, (d) supercapacity continuous bucket.

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108 Enrique Ortega-Rivas

depending on the type of material, is mainly controlled by the rate and method of discharge.Bucket elevators can be mainly loaded in three different ways. Spaced buckets receive partof the charge directly from a chute and part of the change by scooping; continuous bucketsare filled as they pass through a loading leg with a feed spout above the tail wheel and, theycan also be loaded in a bottomless boot with a cleanout door. Three main types of dischargeare generally recognized: centrifugal, positive, and continuous. A fourth type of dischargemay sometimes be considered: gravity discharge, in which buckets are carried pivoted ontwo chains and are tipped mechanically to facilitate discharge.

Except for overlapping buckets, which are not extensively used in processing, dis-charge depends upon centrifugal force in part or in full, or the ability of the material to bethrown into a chute as the buckets go over the head pulley. The characteristics of this featureand, in particular, the trajectory of the material after it leaves the bucket, are important toproperly design and operate bucket elevators. Centrifugal discharge requires the speed ofthe chain to be held within close limits so that the trajectory will fall within a specifiedregion. Figure 19 shows a head wheel and a bucket in a series of positions. A unit massof grain is subjected to two forces at the point the bucket starts to turn around the pulley.These forces are the weight of the unit volume W and the centrifugal force Fc acting radiallywhich is:

AQ: The positionof R is notindicated in thefigure. Pleaseindicate where theresultant R has tobe placed in thefigure.

Fc = Wv2t

3600gr(19)

1

2

3

45

6

7

8

9

r

r

r1

r2

Figure 19 Force diagram of the loads in a head-wheel bucket in a number of different positions.The effective radius of the head-wheel bucket varies from r1 to r2.

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Handling and Processing of Food Powders and Particulates 109

where W is the weight of elemental mass, vt is the tangential velocity, g is the accelerationdue to gravity, and r is the effective radius.

The resultant of these forces R, shown in Figure 19, determines the point at whichdischarge takes place and its characteristics. The resultant for positions 1 to 4 in Figure 19is of such a direction that the material is held in the bucket, at position 5, Fc and W areopposing and R is zero, so there is no force on the material. Discharge begins at this point,the initial velocity and trajectory being that of the projected speed of the wheel at that point.Note that R in positions 6 to 8 is nearly in the same direction of motion of the bucket forcing,discharge. In order to produce this condition, Fc and W must be equal at a point near thetop of the travel, that is:

Fc = W = Wv2t

3600gr(20)

so that

v2 = 3600gr (21)

since

v = 2πrN (22)

where N is r/min, then:

N = 54.19

[1√r

](23)

Equation (23) shows the relationship between the effective head-wheel radius andits revolutions per minute for the most satisfactory discharge conditions. Discharge is notuniform or instantaneous because the effective radius varies from r1 to r2 as shown inFigure 19. Thus, the material at the outer edge of the bucket discharges first.

Bucket elevator horsepower can be calculated quite easily using the followingequations:

1. Horsepower, HP, for spaced buckets and digging boots:

HP = TH

152(24)

2. Horsepower, HP, for continuous buckets with loading leg:

HP = TH

167(25)

In Equations (24) and (25), T is the bucket capacity in tons/h and H is lift in meters.Both equations include normal drive losses, as well as loading pickup losses, and areapplicable for vertical or slightly inclined lifts.

As previously mentioned, bucket elevators are by far the most efficient way of elev-ating granular and particulate materials in a number of processing industries. In the foodindustry they are employed extensively for elevating a variety of commodities such as sugar,beans, oilseeds, salt, and cereals.

2. Screw Conveyors

These conveyors are used to handle finely divided powders, damp materials, hot substancesthat may be chemically active, and granular materials of all types. They operate on theprinciple of a rotating helical screw, moving material in a trough or casing. Flights are

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110 Enrique Ortega-Rivas

made out of stainless steel, copper, brass, aluminum, or cast iron, principally. They may behard-surfaced with Stellite or similar materials to resist highly abrasive materials. Althoughscrew conveyors are simple and relatively inexpensive, power requirements are high andsingle sections are limited in length. The standard pitch screw has a pitch approximatelyequal to the diameter and is used on most horizontal installations and on inclines up to 20◦.Half-standard pitch screws may be used for inclines greater than 20◦. Double-flight andtriple-flight, variable-pitch and steeped-diameter screws are available for moving difficultmaterials and controlling feed rate. Ribbon screws are used for wet or sticky substances,while specially cut flight and ribbon screws are used for mixing. Figure 20 shows the maincomponents of screw conveyors.

Screw conveyors are usually made up of standard sections coupled together, so specialattention should be given to bending stresses in the couplings. Hanger bearings supportingthe flights can obstruct the flow of material when the trough is loaded above its level. Thus,with difficult materials, the load in the trough must be kept below this level. Alternatively,special hanger bearings, which minimize obstruction, should be selected. Since screwconveyors operate at relatively low rotational speeds, the fact that the outer edge of theflight may be moving at a relatively high linear speed is often neglected. This may create awear problem, and if wear is too severe it can be reduced by the use of hard-surfaced edges,detachable, hardened flight segments, rubber covering, or high-carbon steels.

(a)

(b)

(c)

Figure 20 Screw conveyor components: (a) flight, (b) screw, formed by mounting flights on an axle,(c) trough.

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Handling and Processing of Food Powders and Particulates 111

Concise data and formulae are normally not available for individual screw conveyordesign and it is best to consult specialized engineers when designing and installing largescrew conveying systems. Data that could be available to assist in selection and designare normally empirical in nature. Roberts (1999, 2000), presents analytical data to pre-dict the performance of screw conveyors. The power requirement of a screw conveyor isa function of its length, elevation, type of hanger brackets, type of flights, the viscosity orinternal resistance of the material, the coefficient of friction of the material on the flightsand housing, and the weight of the material. Consideration must also be given to additionalpower needed to start a full screw, to free a jammed screw, or to operate with material thathas a tendency to stick to the trough sides. The HP required to drive a screw conveyordepends upon the dimensions of the system and the characteristics of the material. A roughapproximation for normal horizontal operation can be determined from the followingrelation:

HP = CLρ bF

4500(26)

where C is the capacity in m3/min, L is the conveyor length in meters, ρ b is the apparentdensity of material in kg/m3, and F is a factor depending on the type of material, as appearingin Table 13.

In Equation (26) if HP is less than 1, it should be doubled; if it ranges from 1 to 2, itshould be multiplied by 1.5; if it ranges from 2 to 4, it should be multiplied by 1.25; and ifit ranges from 4 to 5, it should be multiplied by 1.1. No correction is necessary for valuesabove 5 hp.

Screw conveyors are very versatile devices for handling a wide variety of materialshorizontally, at an inclination, and even vertically. They are suited for both dry bulk materialsas well as semiliquid, nonabrasive materials. In the food industry the applications arenumerous and they have been used (1) for conveying different grains and oilseeds such asbarley, corn, rice, rye, wheat, cottonseed, and soy beans; (2) for moving fine food powderssuch as flour, icing sugar, starch, and powdered milk; and (3) for handling viscous foodmaterials such as sugar-beet pulp, peanut butter, and comminuted meat.

Table 13 Material Factors for Horizontal Screw Conveyors

Type a (F = 1.2)a Type b (F = 1.4–1.8)b Type c (F = 2.0–2.5)c Type d (F = 3.0–4.0)d

Barley Soy meal Granular moist malt Raw sugarGranular dried malt Cacao seeds Cocoa Bone mealCorn flour Coffee seeds Dehydrated milkCotton seed flour Corn StarchWheat flour Corn meal Icing sugarMalt Jelly granulesRiceWheat

Notes:aLight, fine, nonabrasive, free-flowing materials ρ b:480–640 kg/m3.b Nonabrasive, granular or fines mixed with lumps ρ b: up to 830 kg/m3.c Non and mildly abrasive, granular or fines mixed with lumps ρ b: 640–1200 kg/m3.d Mildly abrasive or abrasive, fine, granular or fines with lumps ρ b: 830–1600 kg/m3.

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112 Enrique Ortega-Rivas

C. Pneumatic Conveying

One of the most important bulk solids handling techniques in food processing is themovement of material suspended in a stream of air over horizontal, inclined, or verticalsurfaces, ranging from a few to several hundred meters. This type of conveying is one ofthe most versatile, handling materials ranging from fine powders through 6.35 mm pelletsand bulk densities of 16 to more than 3200 kg/m3. As compared with previously discussedmethods, pneumatic conveying offers the containment and flexibility of pipeline transportfor bulk solids that, otherwise, will be exposed to direct contact with moving mechanicalparts. Most of the food powders and particulates handled in the food processing industrieswould present hygiene and contamination problems when conveyed through the opening;in such an instance, pneumatic conveying represents an obvious choice for duties in whichintegrity of handled products is paramount.

Pneumatic conveying has been used extensively for many years in many food processoperations. In fact, as reported by Reed and Bradley (1991), one of the earliest recordeduses was for unloading wheat from barges to flour mills at the end of the 19th centuryin London. Some other grains, as well as different cargo such as alumina, cement, andplastic resins are still unloaded using the same basic methods. Other common applicationsinclude unloading trucks, railcars, and barges, transferring materials to and from storagevessels, injecting solids into reactors and combustion chambers, and collecting fugitivedust by vacuum. The limitations on what can be conveyed depend more upon the physicalnature of the material than on its generic classification. Particle size, hardness, resistanceto damage, and cohesive properties are key factors in determining whether a material issuitable for this sort of conveying. Cohesive or sticky materials are often difficult to handlein a pneumatic conveyor. Moist substances that are wet enough to stick to the pipeline wallsusually cannot be conveyed successfully. Materials with high oil or fat contents can alsocause severe buildup in pipelines making conveying impractical.

1. Theoretical Aspects

In contrast with the conveying methods previously discussed, pneumatic conveying canbe perfectly identified as a case of two-phase flow, which is a topic well covered by fluidmechanics. Flow of gas in a pipeline is well understood with the conveying gas obeying theideal gas law, and its density ρg being a function of pressure and temperature, as given by:

ρg = P

RT(27)

where P is the absolute pressure, R is the universal gas constant, and T is theabsolute temperature.

Mean gas velocity v in a pipeline is a function of mass flow rate of the gas and thedensity of the flow area:

v = m

ρgA(28)

where m is the mass flow rate of gas and A is the flow area.By combining Equations (27) and (28), it follows that the mean gas velocity is a

function of the gas pressure, that is:

v = mRT

PA(29)

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Handling and Processing of Food Powders and Particulates 113

Assuming that the mass flow rate of the gas and the flow area are constant, as well asthe gas temperature, the velocity at any two points in the line becomes proportional to theabsolute gas pressure:

v2

v1= P1

P2(30)

where P1 and P2 are absolute pressures.The relationship between gas velocity and pressure drop, in a straight pipe, is found

by the following simple equation:

�P = f

(L

D

)[(ρgu2)

2

](31)

where f is the fanning friction factor, L is the pipe length, D is the pipe diameter, and u isthe local gas velocity.

As Equation (31) indicates, the pressure drop in a pipe is approximately proportionalto the square of the gas velocity. The increase in velocity from one end of the pipe to the other,results in a difference in pressure drop per unit length of more than 2. This illustrates thesignificance of density changes in the gas, as flow proceeds through the pipeline. Changesin the gas velocity also affect the suspension of solids in the gas stream. At low velocitiesparticles may be sliding on the bottom of the pipe, while at higher velocities particles willbe fully suspended by the gas.

The moving gas stream applies drag and lift to the particles. For particles to beconveyed in such a gas stream, the velocity of the gas must be sufficiently high to stopparticles from settling out. In flow through horizontal pipes, the minimum air velocityto stop particles settling to the bottom of the pipe is called the saltation velocity. Theequivalent velocity for flow through vertical pipes is known as the choking velocity. Thesaltation velocity is a function of the density of the gas and the solids, as well as particleand pipeline diameter (Cabrejos and Klinzing, 1994). There is also a direct relationshipbetween the saltation velocity and the solids loading ratio. Generally, saltation occurs athigher velocities when the solids loading ratio is also high. In terms of designing equipmentfor pneumatic conveying, there is another type of velocity, that is, the minimum conveyingvelocity, that is used to describe the correlation of gas velocity to the behavior of solidparticles inside a pipeline. This velocity is the lowest one necessary to prevent pluggingthe line in a given system for a given material. Some researchers have suggested using thesaltation velocity with a safety factor, while others have developed empirical correlations.Some of these correlations, however, often predict widely differing velocities for the sameset of conditions (Wypych, 1999).

2. Classification of Conveying Systems

Pneumatic conveying systems can be categorized in a number of ways depending on theirfunction as well as type and magnitude of operating pressure. Solids loading is a usefulcriterion to classify pneumatic conveyors, which can run over a wide range of conditions,bounded on one end by gas alone with no entrained solids, and at the other end by acompletely full pipe where the solids are plugging the line. Most industrial conveyingsystems operate somewhere in between these two extremes, being ranked broadly as eitherdense-phase or dilute-phase systems, depending upon the relative solids loading and velocityof the system. This is best illustrated graphically in a general state diagram, which is a plot ofpressure per unit length of pipe as a function of conveying gas velocity, with constant solidsflow rate. As shown in Figure 21, at higher velocities particles are generally suspended in the

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114 Enrique Ortega-Rivas

Pre

ssur

e dr

op, ∆

P/L

Lines of constant solids flow rate

Stabledense flowNo flow

Unstabledense flow

Dilute phase

Increasingsolids flow

Mean gas velocity, u

Figure 21 General state diagram for flow of solids in a pipe.

gas with low solids loading ratio, typically below 15, and termed as dilute-phase conveying.If the gas velocity is slowly decreased, the pressure required to convey a constant amount ofsolids also drops. After reaching a minimum, a further reduction in gas velocity results inan increase in pressure, as particles begin to fall out of suspension and interparticle collisionincreases. This region, with a solids loading ratio typically higher than 15 and gas velocitybelow the saltation velocity, is that of dense-phase conveying. With many materials it isdifficult to establish a definite boundary separating dense-phase and dilute-phase regions,and conveying can occur over a continuous range from a fully suspended to a slow movingbed. With other materials very distinct regions are observed and the conveying progressesin either a very stable or unstable way.

Dense-phase conveying, also termed “nonsuspension” conveying, is normally usedto discharge particulate solids or to move materials over short distances. There are severaltypes of equipment such as plug-phase conveyors, fluidized systems, blow tanks, and, moreinnovative, long-distance systems. Dilute-phase, or dispersed-phase conveyors, are moreversatile in use and can be considered the typical pneumatic conveying systems as describedin the literature. The most accepted classification of dilute-phase conveyors comprises:pressure, vacuum, combined, and closed-loop systems.

3. Dilute-Phase Conveyors

Dilute-phase conveying is the commonly employed method for transporting a widevariety of suspended solids using air flowing axially along a pipeline. The method is mainlycharacterized by the low solids-to-air ratio and by the fact that air and solids flow as atwo-phase system inside a pipeline. Figure 22 shows the four main types of dilute-phaseconveying systems. The pressure system, also called positive-pressure, or push system,operates at superatmospheric pressure and is used for delivery to several outlets from oneinlet (Figure 22[a]). Although most applications of these systems lie within the scope ofdilute-phase conveying, under certain arrangements they can also operate as high-pressure,dense-phase conveyors. In general, pressure systems can hold higher capacities and longerconveying distances than negative pressure systems. The vacuum, negative-pressure or pull

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Handling and Processing of Food Powders and Particulates 115

Separator

Silo

BlowerSlidevalves

Silos

Silo

Separators

Blower

Airfilter

Slidevalves

Silos

(a) (b)

(c)(d)

Separators

Silos

Blower

Feed

Airfilter

Silos

Separators

Blower

FeedAirfilter

Figure 22 Dilute-phase pneumatic conveyors: (a) pressure system, (b) vacuum system, (c) combinedsystem, (d) closed-loop system.

system, works at subatmospheric pressure and is used for delivery to one outlet from sev-eral inlets (Figure 22[b]). Vacuum systems are usually limited to shorter distances thanpositive ones and are more restrained to operate with dilute, low solids loading than pres-sure systems. When both features of pressure and vacuum systems are combined in a unit,the advantages of each can be exploited (Figure 22[c]). This arrangement consists of twosections: a pull/push system with a negative-pressure front end, followed by a positive-pressure loop. The benefit is that they capitalize on the ease of feeding into a vacuum andcombine this with the higher capacity and longer conveying distance when using positivepressure. Recirculation of the conveying air, as in the closed-loop system (Figure 22[d]),reduces contamination of product by air and limits product dehydration. However, suchsystems are often difficult to control and an intercooler may be required to prevent thepump from overheating the recirculated air.

Most food materials may be conveyed satisfactorily at air speeds within the rangeof 15 to 25 m/sec. Above this, abrasion of tube bends and product damage may represent

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116 Enrique Ortega-Rivas

difficulties. At extremely low speeds, solids tend to settle out and block horizontal pipe runs.In terms of pressure drop, if air at high pressure is used, its correspondingly high initialenergy will enable more conveying to be accomplished, per kilogram of air, than if low-pressure air is used. High-pressure systems are, however, proportionately more expensivethan low-pressure ones. The maximum pressure recommended for general purpose, dilute-phase conveying of food materials is about 170 kPa. With regard to solid–air ratio, formaximum efficiency this should be as high as possible, but without invading the range ofdense-phase conveying. For flour and salt such ratio may be up to 80 kg of solid/m3 ofair, while for wheat it may be limited to 30 kg of solid/m3 of air. There is an upper limitfor this ratio for specific materials; exceeding it will cause blockage of the system due tosaltation. Finally, material properties such as size, shape, density, and surface properties,need to be carefully considered in the operation and selection of dilute-phase conveyingsystems. Other important properties are friability, hygroscopicity, as well as susceptibilityto impact, abrasion damage, or oxidation.

4. Applications

Pneumatic conveying is, possibly, the most applicable type of technology for diverse con-veying tasks in the food industry. All the many advantages previously mentioned pertainingto the various types of pneumatic conveyors described, suit food materials perfectly. Thepredominant features of many food powders and particulates, in the sense of being sus-ceptible to damage when handled, makes pneumatic conveying an obvious alternative forfood processing. It is worth pointing out, however, that a number of examples already men-tioned such as sugar, spray-dried milk powder, as well as powdered and granulated coffee,have found in this type of conveying the most appropriate way of being transported withminimum amount of damage. A final reference of the advantages of pneumatic conveyingsystems related to handling of food materials, has to do with their self-cleaning capacity,virtual dustless operation, and general sanitary conditions

IV. PROCESSING OF FOOD POWDERS

Relevant recent developments in instrumentation and measuring techniques, has made thedeeper understanding of foods microstructure and properties possible. The detailed study ofphysical properties of foods has revealed an important impact on how these properties mayaffect food processes. Among these properties, those related to bulk particulate systemssuch as particle size distribution and particle shape, are directly involved in an importantnumber of unit operations such as size reduction, mixing, agglomeration, dehydration,and filtration. The optimum operation of many food processes relies heavily on a goodknowledge of the behavior of particles and particle assemblies, either in dry form or assuspensions. Some relevant unit operations involving food particles and particulates willbe reviewed.

A. Size Reduction

In many food processes it is frequently required to reduce the size of solid materials fordifferent purposes. For example, size reduction may aid other processes such as expressionand extraction, or may shorten heat treatments such as blanching and cooking. Comminutionis the generic term used for size reduction and includes different operations such as crushing,grinding, milling, mincing, and dicing. Most of these terms are related to a particular

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Handling and Processing of Food Powders and Particulates 117

Table 14 Types of Force Used in Size ReductionEquipment

Force Principle Examples of equipment

Compressive Nutcracker Crushing rollsImpact Hammer Hammer millAttrition File Disk attrition millCut Scissors Rotary knife cutter

application, for example, milling of cereals, mincing of beef, dicing of tubers, or grindingof spices. The reduction mechanism consists of deforming the food piece until it breaksor tears. Breaking of hard materials along cracks or defects in their structures is achievedby applying diverse forces. The types of forces commonly used in food processes arecompressive, impact, attrition or shear, and cutting. In a comminution operation more thanone type of force is usually acting. Table 14 summarizes these types of forces commonlyused in some of the mills in the food industry.

1. Comminution Laws

In the breakdown of hard and brittle food solid materials, two stages of breakage arerecognized: (1) initial fracture along existing fissures within the structure of the material,and, (2) formation of new fissures or crack tips followed by fracture along these fissures. It isalso accepted that only a small percentage of the energy supplied to the grinding equipmentis actually used in the breakdown operation. Figures of less than 2% efficiency have beenquoted (Coulson and Richardson, 1996) and, thus, grinding is a very inefficient process,

AQ: Coulson andRichardson, 1992 isnot in list. But there isan entry for Coulsonand Richardson 1996.Please clarify.

perhaps the more inefficient of the traditional unit operations. Much of the input energy islost in deforming the particles within their elastic limits and through interparticle friction.A large amount of this wasted energy is released as heat, which, in turn, may be responsiblefor heat damage of biological materials. Theoretical considerations suggest that the energyrequired to produce a small change in the size of unit mass of the material can be expressedas a power function of the size of the material, that is:

dE

dx= −K

xn(32)

where dE is the change in energy, dx is the change in size, K is a constant, and x is theparticle size. Equation (32) is often referred to as the general law of comminution and hasbeen used by a number of workers to derive more specific laws depending on the application.

Rittinger considered that for the grinding of solids, the energy required should beproportional to the new surface produced and gave to the power n the value of 2, obtainingthus the so-called Rittinger’s law by integration of Equation (32):

E = K

[1

x2− 1

x1

](33)

where E is the energy per unit mass required for the production of a new surface by reduction,K is called Rittinger’s constant and is determined for a particular equipment and material,x1 is the average initial feed size, and x2 is the average final product size. Rittinger’s lawhas been found to hold better for fine grinding, where a large increase in surface results.

Kick reckoned that the energy required for a given size reduction was proportional tothe size reduction ratio and took the value of the power n as 1. In such a way, by integration

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118 Enrique Ortega-Rivas

of Equation (32), the following relation, known as Kick’s law is obtained:

E = K

[ln

x1

x2

](34)

where x1/x2 is the size reduction ratio. Kick’s law has been found to hold more accurately forcoarser crushing where most of the energy is used in causing fracture along existing cracks.

A third version of the comminution law is the one attributed to Bond, who consideredthat the work necessary for reduction was inversely proportional to the square root of thesize produced. In Bond’s consideration n takes the value of 3

2 , giving the following version(Bond’s law), also by integrating Equation (32):

E = 2K

[1√x2− 1√

x1

](35)

When x1 and x2 are measured in micrometers and E in kWh/ton, K = 5Ei, where Ei is theBond Work Index, defined as the energy required to reduce a unit mass of material from aninfinite particle size to a size such that 80% passes a 100 µm sieve.

2. Size Reduction Equipment

Size reduction is a unit operation widely used in a number of processing industries. Manytypes of equipment are used in size reduction operations. In a broad sense, size reductionmachines may be classified as crushers used mainly for coarse reduction, grinders employedprincipally in intermediate and fine reduction, ultrafine grinders utilized in ultrafine reduc-tion, and cutting machines used for exact reduction (McCabe et al., 1992). Table 15 lists theprincipal size reduction machines for applications in food processing, while a general guideto equipment selection, as a function of food material and reduction range, is presented inTable 16.

In crushing rolls, two or more heavy steel cylinders revolve toward each other(Figure 23) so particles of feed are nipped and pulled through. The nipped particles aresubjected to compressive force causing reduction in size. In some designs differential speedis maintained so as to exert shearing forces also on the particles. The roller surface can besmooth or can carry corrugations, breaker bars, or teeth, as a manner of increased frictionand facilitate trapping of particles between the rolls. Tooth-roll crushers can be mountedin pairs, like the smooth-roll crushers, or with only one roll working against a stationarycurved breaker plate. Tooth-roll crushers are much more versatile than smooth-roll crushersbut they cannot handle very hard solids. They operate by compression, impact, and shearand not by compression alone, as do smooth-roll crushers.

Figure 24 shows a hammer mill equipment that contains a high-speed rotor turninginside a cylindrical case. The rotor carries a collar bearing a number of hammers around

Table 15 Size Reduction Machines Used in Food Process Engineering

Range of reduction Generic name of equipment Type of equipment

Coarse and intermediate Crushers Crushing rollsIntermediate and fine Grinders Hammer mills

Disk attrition millsTumbling mills (rod mills)

Fine and ultrafine Ultrafine grinders Hammer millsTumbling mills (ball mills)

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Handling and Processing of Food Powders and Particulates 119

Table 16 Application Examples of Size Reduction Machines

Crushing rolls Hammer mills Attrition mills Tumbling mills

Fineness rangeCoarse •

Intermediate • • • •Fine and ultrafine • • •

Chocolate • •Cocoa • •

Corn (wet) •Dried fruits •Dried milk •

Dried vegetables •Grains • •Pepper • •Pulses •

Roasted nuts •Salt • •

Spices •Starch (wet) •

Sugar • •

Feed

Product

Reliefspring

Roll

Figure 23 Diagram of crushing rolls.

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120 Enrique Ortega-Rivas

Feed

Product

Screen

Hammer

Figure 24 A hammer mill.

its periphery. By a rotatory action, the hammers swing through a circular path inside thecasing containing a toughened breaker plate. Feed passes into the action zone with thehammers driving the material against the breaker plate and forcing it to pass through abottom-mounted screen by gravity when the particles attain a proper size. Reduction ismainly due to impact forces, although under choke-feeding conditions, attrition forces canalso play a part in such reduction. By replacing the hammers with knives or other elements,tough, ductile, or fibrous materials can be handled. The hammer mill is a very versatilepiece of equipment, which gives high-reduction ratios and may handle a wide variety ofmaterials from hard and abrasive to fibrous and sticky.

Disk attrition mills, as those illustrated in Figure 25, make use of shear forces forsize reduction, mainly in the fine size range of particles. There are several basic designs ofattrition mills. The single-disk mill (Figure 25[a]) has a high-speed rotating grooved discleaving a narrow gap with its stationary casing. Intense shearing action results in commin-ution of the feed. The gap is adjustable, depending on feed size and product requirements.In the double-disk mill (Figure 25[b]) the casing contains two rotating disks that rotate in

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Handling and Processing of Food Powders and Particulates 121

Feed

Rotatingdisk

Rotatingdisk

Product

Feed

Product

Fixeddisk

Rotating disk(a) (b)

Feed

ProductProduct

(c)

Figure 25 Disk attrition mills: (a) single disk mill, (b) double disk mill, (c) Buhr mill.

opposite directions giving a greater degree of shear compared with the single-disk mill. Thepin-disk mill carries pins or pegs on the rotating elements. In this case impact forces alsoplay an important role in particle size reduction. The Buhr mill (Figure 25[c]), which is theolder type of attrition mill originally used in flour milling, consists of two circular stonesmounted on a vertical axis. The upper stone is normally fixed and has a feed entry port,while the lower stone rotates. The product is discharged over the edge of the lower stone.

Tumbling mills are used in many industries for fine grinding. They basically consistof a horizontal slow-speed rotating cylinder partially filled with either balls or rods. Thecylinder shell is usually of steel, lined with carbon-steel plate, porcelain, silica rock, orrubber. The balls are normally made out of steel or flint stones, while the rods are usually

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122 Enrique Ortega-Rivas

manufactured by high carbon steel. The reduction mechanism is carried out as follows: as thecylinder rotates, the grinding medium is lifted up the sides of the cylinder and drops on to thematerial being comminuted, which fills the void spaces between the medium. The grindingmedium components also tumble over each other, exerting a shearing action on the feedmaterial. This combination of impact and shearing forces brings about a very effective sizereduction. As a tumbling mill basically operates in a batchwise manner, different designshave been developed to make the process continuous. As illustrated in Figure 26(a), in atrunnion overflow mill, the raw material is fed in through a hollow trunnion at one end ofthe mill and the ground product overflows at the opposite end. Putting slotted transversepartitions in a tube mill converts it into a compartment mill (Figure 26[b]). One compartmentmay contain large balls, another small balls, and a third pebbles, thus achieving a segregationof the grinding media with the consequent rationalization of energy. A very efficient way ofsegregating the grinding medium is the use of the conical ball mill shown in Figure 26(c).

Product

Feed

Balls

(a)

Product

FeedRotating cylinder

Rotating cylinder

Large balls Medium balls Small balls

(b)

Product

Small ballsLarge balls

Conical grate

Drive gear

Feedinlet

(c)

Figure 26 Tumbling mills: (a) trunnion overflow mill, (b) compartment mill, (c) conical mill.

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Handling and Processing of Food Powders and Particulates 123

While the solid feed enters from the left into the primary grinding zone where the diameterof the shell is maximum, the comminuted product leaves through the cone at the right endwhere the diameter of the shell is minimum. As the shell rotates, the large balls move towardthe point of maximum diameter, and the small balls migrate toward the discharge outlet.The initial breaking of feed particles is performed, therefore, as the largest balls drop to thegreatest distance. On the other hand, final reduction of small particles is carried out becausethe small balls drop a smaller distance. In such an arrangement, the efficiency of the millingoperation is greatly increased.

3. Applications

For the food industry size reduction is, without doubt, one of the most important processingsteps. Size reduction is normally applied in an infinite variety of grinding processes. Theserange from readily grindable (sugar and salt), through tough-fibrous (dried vegetables)and very tough (gelatin), to those materials, which tend to deposit (full-fat soy, full-fat milkpowder). The fineness requirements may vary immensely from case to case. Some examplesof applications of size reduction in food processes are the milling of wheat, the refining ofchocolate, the grinding of spices and dried vegetables, the breaking of cocoa kernels, thepreparation of cocoa powder, the degermination of corn, the production of fish-meal, themanufacture of chocolate, etc.

B. Size Enlargement

Size enlargement operations are used in the process industries with different aims such asimproving handling and flowability, reducing dusting or material losses, producing struc-turally useful forms, enhancing appearance, etc. Size enlargement operations are known bymany names, including compaction, granulation, tableting, briquetting, pelletizing, encap-sulation, sintering, and agglomeration. While some of these operations could be consideredrather similar, for example, tableting and pelletizing, some others are relevant to a specifictype of industry, for example, sintering in metallurgical processes. In the food industry,the term agglomeration is applied to the process, where the main objective is to controlporosity and density of materials in order to influence properties like dispersibility andsolubility. In this case the operation is also often referred to as instantizing, because rehyd-ration and reconstitution are important functional properties in food processes. On the otherhand, when size enlargement is used with the objective of obtaining definite shapes, thefood industry takes advantage of a process known as extrusion, which can shape and cookat the same time. In a more general context, however, instantizing and extrusion of foodprocesses are the two common categories of agglomeration: tumble/growth and pressureagglomeration, and are referred to as such in the literature.

1. Aggregation Fundamentals

Agglomeration can be defined as the process by which particles join or bind with oneanother in a random way, resulting in an aggregate of porous structure much larger in sizethan the original material. The term includes varied unit operations and processing tech-niques aimed at agglomerating particles (Green and Maloney, 1999). As mentioned above,agglomeration is used in food processes mainly to improve properties related to handlingand reconstitution. Figure 27 shows some common binding mechanisms of agglomerationwith bridges or force fields at the coordination points between particles (Pietsch, 1991).The two-dimensional structure represented in the figure is, in reality, three-dimensional

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124 Enrique Ortega-Rivas

(a) (b) (c)

(d) (e) (f)

Figure 27 Different binding mechanisms in agglomeration: (a) partial melting sinter bridges,(b) chemical reaction hardening binders, (c) liquid bridges hardening binders, (d) molecular andlike-type of forces, (e) interlocking bonds, (f) capillary forces.

containing a large number of particles. Each particle interacts with several otherssurrounding it and the points of interaction may be characterized by contact, or by a dis-tance small enough for the development of binder bridges. Alternatively, sufficiently highattraction forces can be caused by one of the short-range force fields. The number of allinteraction sites of one particle within the agglomerate structure is called the coordinationnumber. Particles in an agglomerate could be quite numerous, making it difficult to estimatethe coordination number. Indirect measurement of the coordination number can be made asa function of other properties of the agglomerate. In regular packs of monosized sphericalparticles the coordination number k and the porosity or void volume ε, are related by:

kε ≈ π (36)

Equation (36) gives good approximation of the coordination numbers of ideal agglom-erate structures. Table 17 lists several values of coordination numbers calculated usingEquation (36) and compared with the ideal number for different structures, such as thoseillustrated in Figure 28.

A general relation describing the tensile strength of agglomerates σt held together bybinding mechanisms acting at the coordination points is:

σt = 1− επ

k

∑ni=1 Ai(x, . . .)

x2(37)

where Ai is the adhesion force caused by a particular binding mechanism and x is therepresentative size of the particles forming the agglomerate.

Substituting Equation (36) into Equation (37), the following relation is obtained:

σt = 1− εε

∑ni=1 Ai(x, . . .)

x2(38)

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Handling and Processing of Food Powders and Particulates 125

Table 17 Geometric Arrangement, Porosity, and Coordination Number ofPackings of Monosized Particles

Geometric arrangement Porosity (ε) Coordination number (π/ε) k

Cubic 0.476 6.59 6Orthorhombic 0.395 7.95 8Tetragonal–spheroidal 0.302 10.39 10Rhombohedral (pyramidal) 0.260 12.08 12Rhombohedral (hexagonal) 0.260 12.08 12

(a) (b)

(c) (d)

(e) (f)

Figure 28 Packings of monosized spherical particles: (a) cubic, (b) and (c) orthorhombic,(d) tetragonal–spheroidal, (e) rhombohedral (pyramidal), (f) rhombohedral (hexagonal).

A further simplification results because many binding mechanisms are a function ofthe representative particle size x and thus:

σt = 1− εε

∑ni=1 Ai(x, . . .)

x(39)

The three dots in parentheses in Equations (37), (38), and (39) indicate that Ai is alsoa function of other, unknown, parameters.

When liquid bridges form at the coordination points, Ai depends on the bridge volumeand the wetting characteristics represented by the wetting angle. There are models availablefor predicting adhesion forces of various types (Pietsch, 1991), but Ai might be of differ-ent magnitude at each of the many coordination points, due to roughness or microscopicstructure of particulates forming the agglomerates.

The representative particle size most appropriate to describe the agglomerationprocess is the surface equivalent diameter, xsv, because porosity is surface dependant.Such diameter is the size of a spherical particle, which, if the powder consists of onlythese particles, would have the same specific surface area as the actual sample. When

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126 Enrique Ortega-Rivas

determining the specific surface area, methods must be chosen that only measure the outerparticle surface excluding the accessible inner surface due to open particle porosity.

From the previous paragraphs, it can be gathered that the strength of agglomer-ate structures held together by bonding mechanisms is highly dependent on porosity andparticle size, or, more properly, specific surface area. The relationship would be inverselyproportional in both cases, that is, higher strength at lower porosities and lower surface areas.

Agglomerates that are completely filled with liquid obtain strength from the negativecapillary pressure in the structure. A relationship for this case is:

σt = c1− εε

α1

xsv(40)

where c is a correction factor, α is the surface tension of the liquid and xsv is the surfaceequivalent diameter of the particle. In order to apply Equation (40), there must be a completewetting of the solids by the liquid.

For high-pressure agglomeration and the effect of matrix binders general formulashave not yet been developed. It can be considered, however, that the effects of variableswould follow the trend described before, with porosity, particle surface, contact area, andadhesion, all playing an important role. For nonmetallic powders, the following equationcan be used to evaluate the needed applied pressure p to agglomerate:

log p = mVR + b (41)

where VR represents the relationship V/Vs, V being the compacted volume at a givenpressure and Vs the volume of the solid material to be compacted; m and b are constants.

2. Agglomeration Methods

With few exceptions, agglomeration methods can be classified into two groups:tumble/growth agglomeration and pressure agglomeration. Also, agglomerates can beobtained using binders or in a binderless manner. The tumble/growth method producesagglomerates of approximate spherical shape by buildup during tumbling of fine particulatesolids, the resulting granules are at first weak and require binders to facilitate formation, andposttreatment is needed to reach final and permanent strength. On the other hand, productsfrom pressure agglomeration are made from particulate materials of diverse sizes, and areformed without the need of binders or posttreatment, and acquire immediate strength.

The mechanism of tumble/growth agglomeration is illustrated in Figure 29. As shown,the overall growth process is complex and involves both disintegration of weaker bonds andreagglomeration by abrasion transfer and coalescence of larger units (Cardew and Oliver,1985). Coalescence occurs at the contact point when, at impact, a binding mechanismthat is stronger than the separating forces develops. Additional growth of the agglomeratemay proceed by further coalescence, or by layering, or both. The most important andeffective separation force counteracting on the bonding mechanism is the weight of thesolid particle. For particles below 10 µm approximately, the natural attraction forces, suchas molecular, magnetic, and electrostatic, become significantly larger than the separationforces due to particle mass and external influences. In such a way, natural agglomerationoccurs.

The conditions needed for tumble/growth agglomeration can be provided by inclineddisks, rotating drums, any kind of powder mixer, and fluidized beds (Figure 30). In generalterms, any equipment or environment creating random movement is suitable for carryingout tumble/growth agglomeration. In certain applications, very simple tumbling motions,such as on the slope of storage piles or on other inclined surfaces, are sufficient for the

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Handling and Processing of Food Powders and Particulates 127

+ +

+ + +

(a)

+

+ +

(b)

+

+

+

(c)

+ +

+

(d)

Figure 29 Kinetics of tumble/growth agglomeration: (a) nucleation, (b) random coalescence,(c) abrasion transfer, (d) crushing and layering.

Binder

Feed

Product

Binder

FeedProduct

Feed

Binder

ProductAir

Feed

Binder

Product

(a) (b)

(c) (d)

Figure 30 Equipment for tumble/growth agglomeration: (a) inclined rotating disk, (b) inclinedrotating drum, (c) ribbon powder blender, (d) fluidized bed.

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128 Enrique Ortega-Rivas

formation of crude agglomerates. The most difficult task of tumble/growth agglomeration isto form stable nuclei due to the presence of few coordination points in small agglomerates.Also, since the mass of particles and nuclei are small, their kinetic energy is not highenough to cause microscopic deformation at the contact points, which enhances bonding.Recirculation of undersized fines provides nuclei to which feed particles adhere more easilyto form agglomerates. In the whole process, tumble/growth agglomeration renders first weakagglomerates known as green products. These wet agglomerates are temporarily bondedby surface tension, and by capillary forces of the liquid binder. This is the reason why, inmost cases, tumble/growth agglomeration requires some sort of posttreatment. Drying andheating, cooling, screening, adjustment of product characteristics by crushing, rescreening,conditioning, and recirculation of undersize material, are some of the processes, which havebeen used as posttreatment in tumble/growth agglomeration. Sometimes, a large percentageof recycle must be rewetted for agglomeration and needs to be processed again, causingeconomical burden to this technology (Pietsch, 1983).

In contrast to tumble/growth agglomeration where no external forces are applied, inpressure agglomeration pressure forces act on a confined mass of particulate solids, which isthen shaped and densified (Engelleitner, 1994). Pressure agglomeration is normally carriedout in two stages. The first one comprises a forced rearrangement of particles due to a littleapplied pressure, while the second step consists of a steep pressure rise during which brittleparticles break and malleable particles deform plastically (Pietsch, 1994). The mechanismof pressure agglomeration is illustrated in Figure 31. There are two important phenomena,which may limit the speed of compaction and, therefore, the capacity of the equipment:compressed air in the pores and elastic springback. Both can cause cracking and weakeningwhich, in turn, may lead to destruction of the pressure-agglomerated products. The effectof these two phenomena can be reduced if the maximum pressure is maintained for sometime, known as dwell time, prior to its release.

Elasticspringback

Compacted

(Plastic)(Brittle)

Bulk Densified

Time

Pre

ssur

e

Figure 31 Mechanism of pressure agglomeration.

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Handling and Processing of Food Powders and Particulates 129

Pressure agglomeration can be carried out in different types of equipment.Generally, low- and medium-pressure agglomeration is achieved in extruders includingthe screen extruder, the screw extruder, and the intermeshing gears extruder. On the otherhand, high-pressure agglomeration is performed in presses such as the punch-and-diepress, the compacting roller press, and the briquetting roller press. Low- and medium-pressure agglomeration yield relatively uniform agglomerates of elongated spaghetti-likeor cylindrical shape, whereas high-pressure agglomeration produces pillow or almond-like shapes. Figure 32 presents the equipment used for low- and medium-pressureagglomeration, while Figure 33 illustrates some common machinery for high-pressureagglomeration.

3. Applications

Agglomeration has many applications in food processing. In the context of instantizing,tumble/growth agglomeration is used in the food industry to improve reconstitutability ofa number of products including flours, cocoa powder, instant coffee, dried milk, sugar,sweeteners, fruit beverage powders, instant soups, and diverse spices. With regard to

(a.3)

(b.3)

(a.1) (a.2)

(b.1) (b.2)

Figure 32 Equipment used for (a) low- and (b) medium-pressure agglomeration: (a.1) screenextruder, (a.2) basket extruder, (a.3) cylindrical-die screw extruder, (b.1) flat-die extruder,(b.2) cylindrical-die extruder, (b.3) intermeshing-gears extruder.

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130 Enrique Ortega-Rivas

(a) (b)

Feed

Screw

Roll

Product

Screw

RollFeed

Product

Figure 33 Equipment used for high-pressure agglomeration: (a) compacting roller press,(b) briquetting roller press.

shaping, extrusion has been extensively used in grain process engineering to obtain anarray of products from diverse cereals, principally ready-to-eat breakfast cereals.

C. Mixing

The unit operation in which two or more materials are interspersed in space with oneanother is one of the oldest and yet one of the least understood of the unit operationsof process engineering. Mixing is used in the food industry with the main objective ofreducing differences in properties such as concentration, color, texture, taste, and so on,between different parts of a system. Since the components being mixed can exist in any ofthe three states of matter, a number of mixing possibilities arise. The mixing cases involvinga fluid, for example, liquid–liquid and solid–liquid, are most frequently encountered, sothey have been extensively studied. Despite the importance of the mixing of particulatematerials in many processing areas, fundamental work of real value for either designersor users of solids mixing equipment is still relatively sparse. It is through studies in veryspecific fields, such as powder technology and multiphase flow, that important advances inthe understanding of mixing of solids and pastes have been made.

Mixing is more difficult to define and evaluate with powders and particulates than itis with fluids, but some quantitative measures of dry solids mixing may aid in evaluatingmixer performance. In actual practice, however, the proof of a mixer is in the propertiesof the mixed material it produces. A significant proportion of research efforts in the foodindustry is directed toward the development of new and novel mixing devices for foodmaterials. These devices may be effective for many applications since they deliver a mixedproduct with the required blending characteristics. Due to the complex properties of foodsystems, which can themselves vary during mixing, it is extremely difficult to generalizeor standardize mixing operation for wider applications of mixing devices, either novel ortraditional. Developments in mathematical modeling of food-mixing processes are scarceand there are no established procedures for process design and scale-up. As a result, it is

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Handling and Processing of Food Powders and Particulates 131

virtually impossible to devise relationships between mixing and quality (Niranjan, 1995),especially for blending of food powders. With reference to solid foods, Niranjan and deAlwis (1993) mentioned as characteristic features of food mixing, the fragile and differentlysized nature of food products, as well as the segregating tendency of blended food systemson discharge. These characteristics, along with some others like cohesiveness and stickiness,makes food particulate mixing a complicated operation.

1. Mixing Mechanisms

Three mechanisms have been recognized in solids mixing: convection, diffusion, and shear.In any particular process one or more of these three basic mechanisms may be responsiblefor the course of the operation. In convective mixing masses or group of particles transferfrom one location to another, in diffusion mixing individual particles are distributed overa surface developed within the mixture, whereas in shear mixing groups of particles aremixed through the formation of slipping planes that develop within the mass of the mixture.Shear mixing is sometimes considered as part of a convective mechanism. Pure diffusion,when feasible, is highly effective, producing very intimate mixtures at the level of individualparticles but at an exceedingly slow rate. Pure convection, on the other hand, is much morerapid but tends to be less effective, leading to a final mixture that may still exhibit poormixing characteristics on a fine scale. These features of diffusion and convective mixingmechanisms suggest that an effective operation may be achieved by a combination of both,in order to take advantage of the speed of convection and the effectiveness of diffusion.

Compared with fluid mixing, in which diffusion can be normally regarded as beingspontaneous, particulate systems will only mix as a result of mechanical agitation providedby shaking, tumbling, vibration, or any other mechanical mean. Mechanical agitation willprovide conditions for the particles to change their relative positions either collectively orindividually. The movement of particles during a mixing operation, however, can also resultin another mechanism, which may retard, or even reverse, the mixing process and is knownas segregation. When particles differing in physical properties, particularly size and/ordensity are mixed, mixing is accompanied by a tendency to unmix. Thus, in any mixingoperation, mixing and demixing may occur concurrently and the intimacy of the resultingmix depends on the predominance of the former mechanism over the latter. Apart from theproperties already mentioned, surface properties, flow characteristics, friability, moisturecontent, and the tendency to cluster or agglomerate, may also influence the tendency tosegregate. The closer the ingredients are in size, shape, and density, the easier the mixingoperation and the more the intimacy of the final mix. Once the mixing and demixingmechanisms reach a state of equilibrium, the condition of the final mix is determined andfurther mixing will not produce a better result.

A general theory of segregation, regardless of the particular circumstances in whichthe operation takes place, has not yet been offered to explain the segregation phenomena inparticulate systems. In any blending operation the mixing and demixing mechanisms willbe acting simultaneously. The participation of each of these two sets of mechanisms will bedictated by the environment and by the tendency of each component to segregate out of thesystem. Since these two mentioned sets of mechanisms will be acting against each other,an equilibrium level will be obtained as the final state of the mixture.

2. Degree of Mixing

Over the years many workers have attempted to establish criteria for the completeness anddegree of mixture. In order to accomplish this, very frequent sampling of the mix is usuallyrequired and, tending to be statistical in nature, such an exercise is often of more interest

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132 Enrique Ortega-Rivas

to mathematicians than to process engineers. Thus, in practical mixing applications, anideal mixture may be regarded as the one produced at minimum cost and which satisfiesthe product specifications at the point of use.

Food mixing is a complicated task not easily described by mathematical modeling.Mixture quality results from several complex mechanisms operating in parallel, which arehard to follow and fit to a particular model. Dankwertz (1952) has defined the scale andintensity of segregation as the quantities necessary to characterize a mixture. The scale ofsegregation is a description of unmixed components, while the intensity of segregation isa measure of the standard deviation of composition from the mean, taken over all pointsin the mixture. In practice it is difficult to determine these parameters, since they requireconcentration data from a large number of points within the system. They provide, however,a sound theoretical basis for assessing mixture quality. Taking into account the complexityof components and interactions in food solids mixing, it would be rather difficult to definea unique criterion to assess mixture quality. A mixing endpoint or optimum mixing timecan also be considered a very relative definition due to the segregating tendency of foodpowder mixing. The degree of uniformity of a mixed product may be measured by analysisof a number of spot samples. Food powder mixers act on two or more separate materials tointermingle them. Once a material is randomly distributed through another, mixing may beconsidered to be complete. Based on these concepts, the well-known statistical parameters,mean and standard deviation of component concentration, can be used to characterize thestate of a mixture. If spot samples are taken at random from a mixture and analyzed, thestandard deviation of the analyses s, about the average value of the fraction of a specificpowder x is estimated by the following relation:

s =√∑N

i=1 (xi − x)2

N − 1(42)

where xi is every measured value of fraction of one powder and N is the number of samples.The standard deviation value on its own may be meaningless, unless it can be checked

against limiting values of either complete segregation s0, or complete randomization sr.The minimum standard deviation attainable with any mixture is sr and it represents the bestpossible mixture. Furthermore, if a mixture is stochastically ordered, sr would equal zero.Based on these limiting values of standard deviations, Lacey (1954) defined a mixing indexM1 as follows:

M1 = s20 − s2

s20 − s2

r

(43)

The numerator in Equation (43) would be an indicator of how much mixing hasoccurred, while the denominator would show how much mixing can occur. In practice,however, the values of s, even for a very poor mixture, lie much closer to sr than to s0. Pooleet al. (1964), suggested an alternative mixing index, that is:

M2 = s

sr(44)

Equation (44) clearly indicates that for efficient mixing or increasing randomizationM2 would approach unity. The values of s0 and s can be determined theoretically. Thesevalues would be dependent on the number of components and their size distributions.Simple expressions can be derived for two-component systems, while for a binary multisized

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Handling and Processing of Food Powders and Particulates 133

particulate mixture Poole et al. (1964) demonstrated that:

s2r =

pq[w/(q(

∑fawa)p + p(

∑fawa)q)

] (45)

where p and q are the proportions by weight of components within a total sample weight wand fa is the size fraction of one component of average weight wa in a particle size range. Fora given component in a multicomponent and multisized particulate system, Stange (1963)presented an expression for sr, as follows:

s2r =

p2

w

{[1− p

p

]2

· p(∑

fawa

)p+ q

(∑fawa

)q+ r

(∑fawa

)r+ · · ·

}(46)

Equations (43) and (46) can be used to calculate mixing indices defined byEquation (42). Another suggestion for the characterization of the degree of homogeneityin mixing of powders, has been reviewed by Boss (1986), with the degree of mixing M3defined as:

M3 = 1− s

s0(47)

Some other mixing indices have been reviewed by Fan and Wang (1975).McCabe et al. (1992), presented the following relationship to evaluate mixing time t

for solids blending:

t = 1

kln

1− 1/√

n

1− 1/M2(48)

where k is a constant and n is the number of particles in a spot sample. Equation (48) canbe used to calculate the time required for any required degree of mixing, provided k isknown and the segregating forces are not active. Mixing times should not be very long dueto the unavoidable segregation nature of most food solids mixtures. Instead of improvingefficiency, long mixing times often result in poor blending characteristics. A graph of thedegree of mixing versus time is recommended to select the proper mixing time quantitat-ively. Most cases of mixing of powders will attain maximum degree of homogeneity in lessthan 15 min when the proper type of machine and working capacity have been chosen.

3. Powder Mixers

In general terms, mixers for dry solids have nothing to do with mixers involving a liquidphase. According to the mixing mechanisms previously discussed, solids mixers can be clas-sified into two groups: segregating mixers and nonsegregating mixers. The former operatemainly by a diffusive mechanism while the latter practically involve a convective mech-anism. Segregating mixers are normally nonimpeller type units, such as tumbler mixers,whereas nonsegregating mixers may include screws, blades, and ploughs in their designs,and examples include horizontal trough mixers and vertical screw mixers. Food powderscan also be mixed by aeration using a fluidized bed. The resulting turbulence of passingair through a bed of particulate material causes material to blend. Mixing times required influidized beds are significantly lower than those required in conventional powder mixers.Van Deemter (1985) discussed different mixing mechanisms prevailing in fluidized beds.

Tumbler mixers operate by tumbling the mass of solids inside a revolving vessel.These vessels take various forms, such as those illustrated in Figure 34, which may befitted with baffles or stays to improve their performance. The shells rotate at variable speedshaving values up to 100 r/min with working capacities around 50 to 60% of the total. They

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134 Enrique Ortega-Rivas

(a) (b)

(c) (d)

Figure 34 Tumbler mixers used in food powder blending: (a) horizontal cylinder, (b) double cone,(c) V-cone, (d) Y-cone.

are manufactured using a wide variety of materials, including stainless steel. This type ofequipment is best suited for gentle blending of powders with similar physical characteristics.Segregation can represent a problem if particles vary, particularly in size and shape.

Horizontal trough mixers consist of a semicylindrical horizontal vessel in which oneor more rotating devices are located. For simple operations single or twin screw conveyorsare appropriate and one passage through such a system may be good enough. For moredemanding duties a ribbon mixer, like the one shown in Figure 35, may be used. A typicaldesign of a ribbon mixer will consist of two counteracting ribbons mounted on the sameshaft. One moves the solids slowly in one direction while the other moves it quickly inthe opposite direction. There is a resultant movement of solids in one direction, so theequipment can be used as a continuous mixer. Some other types of ribbon mixers operateon a batch basis. In these designs troughs may be closed, as to minimize dust hazard, ormay be jacketed to allow temperature control. Due to small clearance between the ribbonand the trough wall, these kinds of mixers can cause particle damage and may consumehigh amounts of power.

In vertical screw mixers a rotating vertical screw is located in a cylindrical or cone-shaped vessel. The screw may be mounted centrally in the vessel or may rotate or orbitaround the central axis of the vessel near the wall. Such mixers are schematically shownin Figure 36(a) and 36(b) respectively. The latter arrangement is more effective and stag-nant layers near the wall are eliminated. Vertical screw mixers are quick, efficient, andparticularly useful for mixing small quantities of additives into large masses of material.

4. Applications

Applications of powder mixing in food systems are diverse and varied and includeblending of grains prior to milling, blending of flours and incorporation of additives to

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Handling and Processing of Food Powders and Particulates 135

Feed

Product

Figure 35 Plain view of an open ribbon mixer.

(a) (b)

Figure 36 Vertical screw mixers: (a) central screw, (b) orbiting screw.

flours, preparation of custard powders and cake mixes, blending of soup mixes, blending ofspice mixes, incorporation of additives in dried products, preparation of baby formula, etc.

D. Cyclonic Separations

Separation techniques are involved in a great number of processing industries and repres-ent, in many cases, the everyday problem of a practicing engineer. In spite of this, thetopic is normally not covered efficiently and sufficiently in higher education curricula ofsome engineering programs, mainly because its theoretical principles deal with a numberof subjects ranging from physics principles to applied fluid mechanics. In recent years, sep-aration techniques involving solids have been considered in the general interest of powderand particle technology, as many of these separations involve removal of discrete particlesor droplets from a fluid stream.

Separation techniques are defined as those operations, that isolate specific ingredientsof a mixture without a chemical reaction being carried out. Several criteria have been usedto classify or categorize separation techniques. One such criteria consists in grouping themaccording to the phases involved, that is, solid with liquid, solid with solid, liquid withliquid, etc. A classification based on this criterion is shown in Table 18. Dry separationtechniques would, therefore, constitute all those cases in which the particle to be isolatedor segregated from a mixture is not wet, and would include particular examples of thesolid mixtures and gas–solid mixture cases listed in Table 18. The most important dryseparation techniques in processing industries have been reviewed by Beddow (1981). Infood processing, there are important applications of dry separation techniques, such as theremoval of particles from dust-laden air in milling operations or the recovery of the driedproduct in spray dehydration.

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136 Enrique Ortega-Rivas

Table 18 Classification of Separation Techniques According toPhases Involved

Type of mixture Technique

Liquid–Liquid DistillationExtractionDecantationDialysis and electrodialysisParametric pumping

Solid–Solid ScreeningLeachingFlotationAir classification

Solid–Gas CycloningAir filtrationScrubbingElectrostatic precipitation

Solid–Liquid SedimentationCentrifugationFiltrationMembrane separations

In many processes of food and related industries, separating solids from a gas streamis very important. A typical example is one of the risk of dust explosion in the dry millingindustry. It has been found that not only in this industry, but also in many others theatmosphere may become dust-laden with particles from different sources representing evena health risk. In other cases the suspension of particles in a gas stream has been promoted,as in pneumatic conveying or spray drying, but at the end of the process there is the need toseparate the phases. Separation of solids from a gas is accomplished using many differentdevices. Perhaps the devices most commonly used to separate particles from gas streamsare cyclones.

1. Operating Principles

Cyclones are by far the most common type of gas–solids separation device used in differentindustrial processes. They have no moving parts, are inexpensive compared to other sep-aration devices, can be used at high temperatures, produce a dry product, have low energyconsumption, and are extremely reliable. Their primary disadvantage is that they have relat-ively low collection efficiency for particles below about 15 µm. As illustrated in Figure 37,a cyclone consists of a vertical cylinder with a conical bottom, a tangential inlet near thetop, and outlets at the top and the bottom respectively. The top outlet pipe protrudes intothe conical part of the cyclone in order to produce a vortex when a dust-laden gas (normallyair) is pumped tangentially into the cyclone body. Such a vortex develops centrifugal forceand, because the particles are much denser than the gas, they are projected outward to thewall flowing downward in a thin layer along this wall in a helical path. They are eventuallycollected at the bottom of the cyclone and separated. The inlet gas stream flows downwardin an annular vortex, reverses itself as it finds a reduction in the rotation space due to theconical shape, creates an upward inner vortex in the center of the cyclone, and then exitsthrough the top of the cyclone. In an ideal operation, in the upward flow, there is only gaswhereas the downward flow has all the particles fed with the stream. Cyclone diameters

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Handling and Processing of Food Powders and Particulates 137

Dustdischarge

Feed

Gasoutlet

Figure 37 Schematic diagram of a cyclone.

range in size from less than 0.05–10 m, feed concentrations cover values from 0.1 to about50 kg/m3, while gas inlet velocities may be in the order of 15–35 m/sec.

A cyclone is in fact a settling device in which a strong centrifugal force operates,acting radially, instead of the relatively weak gravity force that acts vertically. Due to thesmall range of particles involved in cyclone separation (the smallest particle that can beseparated is about 5 µm), it is considered that Stokes’ law primarily governs the settlingprocess. The common form of Stokes’ law is:

u t = x2(ρs − ρg)g

18µg(49)

where u t is the terminal settling velocity, x is the particle diameter, ρs is the solids densityρg is the gas density, and µg is the gas viscosity.

Cyclones can generate centrifugal forces between 5 and 2500 times the force ofgravity, depending on the diameter of the unit. When particles enter into the cyclone body,they quickly reach their terminal velocities corresponding to their sizes and radial positionin the cyclone. The radial acceleration in a cyclone depends on the radius of the path beingfollowed by the gas and is given by the equation:

g = ω2r (50)

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138 Enrique Ortega-Rivas

where ω is the angular velocity and r the radius. Substituting Equation (49) intoEquation (50):

vt = x2(ρs − ρg)ω2r

18µg(51)

where vt is the terminal velocity of the particle.Also, the centrifugal acceleration is a function of the tangential component of the

velocity vtan = ωr, and thus, considering this, Equation (51) becomes:

vr = x2(ρs − ρg)v2tan

18µgr(52)

Multiplying Equation (52) by g/g, the resultant equation gives:

vt =[

x2(ρs − ρg)g

18µg

]v2

tan

gr= (ut)

v2tan

gr(53)

where ut is the terminal settling velocity defined by Equation (49). As can be implied,according to Equation (53), the higher the terminal velocity the easier it is to “settle” aparticle within a cyclone.

For a given particle size, the terminal velocity is a maximum in the inner vortex, wherer is small, so the finest particles separated from the gas are eliminated in the inner vortex.They migrate through the outer vortex to the wall of the cyclone and drop, passing thebottom outlet. Smaller particles, which do not have time to reach the wall, are retained bythe air and carried to the top outlet. Although the chance of a particle to separate decreaseswith the square of the particle diameter, the fate of a particle also depends on its positionin the cross section of the entering stream and on its trajectory in the cyclone. Thus, theseparation according to size is not sharp. A specific diameter, called the cut diameter or cutsize, can be defined as that diameter for which one-half of the inlet particles, by mass, areseparated while the other half are retained by the gas. The cut size is a very useful variableto determine the separation efficiency of a cyclone. Since a given powder to be separatedin a cyclone would have an extremely fine half of its distribution, such half may not beeasily separated using conventional pressure drops. Therefore, it is advisable to make it thecut size to coincide with the mean size of a powder particle size distribution to guaranteeseparation of the coarse part of such distribution, as the fine one may unattainable due tothe small range involved.

2. Dimensionless Scale-up Approach

Experience and theory have shown that there are certain relationships among cyclone dimen-sions that should be observed for efficient cyclone performance (Geldart, 1986), and whichare generally related to the cyclone diameter. There are several different standard cyclone“designs” and a very common one is called the Stairmand design, whose dimensions areshown in Figure 38. Using standard geometries of cyclones is much easier to predict effectson variables changes and scale-up calculations are greatly reduced. Such calculations maybe carried out by means of dimensionless relationships. Selection and operation of cyclonescan be described by the relationship between the pressure drop and the flow rate, and therelationship between separation efficiency and flow rate (Svarovsky, 1981). The pressuredrop versus volumetric flow rate relationship is usually expressed as Eu = f (Re), where Euis the Euler number and Re is the Reynolds number. The Euler number is in fact a pressureloss factor, easily defined as the limit on the maximum characteristic velocity v obtained by

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Handling and Processing of Food Powders and Particulates 139

Dc /3

0.5Dc

0.5Dc

Dc

1.5Dc

2.5Dc

0.5Dc

Figure 38 Dimensions of a Stairmand standard cyclone.

a certain pressure drop �P across the cyclone. It can be expressed as:

Eu = 2�P

ρgv2(54)

where, as previously defined, ρg is the gas density.The Reynolds number defines flow characteristics of the system and, in the case of

cyclones, the characteristic dimension may be taken as the cyclone body diameter Dc. TheReynolds number for this case is, therefore, represented by:

Re = Dcvρg

µg(55)

where, as already defined, µg is the gas viscosity.The relationship between separation efficiency and flow rate is not significantly influ-

enced by operational variables, so it is commonly expressed in terms of cut size x50. The useof cut size to define efficiency of cyclones is of utmost importance since their performanceis highly dependent on particle size. Considering that cut size implies the size of particlesto be separated it follows that such particles must be influenced by forces exercised on thesuspension. The forces developed in a cyclone can be analyzed by sedimentation theory, anda dimensionless group thus derived, the Stokes number Stk, will include the cut size. TheStokes number is a very useful theoretical tool and, for the case of cyclones, its derivationmay be carried out as follows.

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140 Enrique Ortega-Rivas

The radial settling velocity in a cyclone is due to the centrifugal acceleration, which isproportional to the square of the tangential velocity of the particle and indirectly proportionalto the radius of the particle position. As the tangential motion of the particle is unopposed,the tangential particle velocity can be taken as equal to the tangential component of the fluidvelocity at the same point. For the same flow regime, the velocities anywhere in the flow ina cyclone are proportional to a characteristic velocity v, function of the cyclone cylindricalgeometry, called also the body velocity. The position radii are proportional to the cyclonediameter Dc. Under such assumptions, Equation (52) can be approximated to:

v = x2(ρs − ρg)v2

18µgDc(56)

Reexpressing Equation (56) in dimensionless form, the Stokes’ number Stk is obtained as:

Stk = x2(ρs − ρg)v

18µgDc(57)

Since the value of the gas density, usually air, is negligible in comparison with thesolids density, Equation (57) can also take the following form:

Stk = x2ρsv

18µgDc(58)

Furthermore, if the dimension x is replaced by the specific cut size x50:

Stk50 = x250ρsv

18µgDc(59)

Equations (54), (55), and (56), defining Euler Eu, Reynolds Re, and Stokes Stk50numbers respectively, are related by specific functions, which can be plotted as shown inFigure 39 and Figure 40, for a given cyclone geometry. The cyclone inside diameter Dc, isthe one shown in Figure 38 and, as previously mentioned, all geometrical proportions arerelated to it. In the case of scale-up procedures, proportions must be maintained. The cyclone

104

103

102

101

106105104103102

Reynolds number

Eul

er n

umbe

r

Figure 39 A typical plot of Eu versus Re for cyclones.

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Handling and Processing of Food Powders and Particulates 141

1000

500

100

10–310–4

Stk50

12Eu =

Stokes number

Eul

er n

umbe

r

Figure 40 A typical plot of Eu versus Stk50 for cyclones.

body velocity v is the characteristic velocity which can be defined in various ways, but thesimplest one is based on the cross section of the cylindrical body so that:

v = 4Q

πD2c

(60)

where Q is the gas flow rate.

3. Applications

As mentioned before, cyclones are extensively used in the food industry to reduce particleload to safe levels in dry milling, as well as in classification of particles in closed circuitgrinding operations. They are also employed in recovering fines from spray drying andfluidized bed drying processes. Another important application is in pneumatic conveyingof diverse food products, such as grains and flours.

V. CONCLUSIONS

Powder technology is of dynamic significance to the world economy with a broad range ofindustries taking advantage of the rapidly growing knowledge in this discipline. Researchwithin universities and similar institutions, coupled with the vested interest from the indus-trial community, has stimulated relevant results that have been applied to make a numberof processes more efficient. Periodical meetings and specialized publications are spreadingthe most relevant and recent advances in diverse topics such as materials handling, particleformation, mixing, grinding, and separation. As mentioned at the beginning of this chapter,there has been a rapid growth of adapting knowledge of particle technology worldwide inrecent years.

In the case of the application of particle technology principles to biological materials,specifically food powders and particulates, there is much to be done as very few researchgroups can be identified in this particular field around the globe. Since many strategic foodindustries, such as those based on grain processing, rely heavily on a firm understandingof powder technology, there is a lot of potential for research and development in the yearsto come.

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142 Enrique Ortega-Rivas

Food powder processing encompasses subjects of established disciplines such asparticle technology, as well as food and chemical engineering. There are a lot of activitiesin fundamental and applied research, to provide the food industry with theoretical tools toincrease competitiveness in a great number of processes, which involve food powders.

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REVIEW PAPER

Bulk Properties of Food Particulate Materials: An Appraisal

of their Characterisation and Relevance in Processing

Enrique Ortega-Rivas

Received: 20 September 2007 /Accepted: 4 June 2008 /Published online: 3 July 2008# Springer Science + Business Media, LLC 2008

Abstract The food industry is one of the largest commer-

cial enterprises in the world today representing important

contributions of the gross national product of many

countries. Numerous raw materials and products in this

industry are in powdered or particulate form, and their

optimum characterisation for processing purposes, rely

heavily in a deep knowledge of particle technology.

Characterisation of the main bulk properties affecting

processing, such as failure properties, bulk density and

compressibility, are discussed in this article. Testing of

these properties is far from standardised so the different

manners of measurement are reviewed along with theoret-

ical considerations, operating principles, and applications.

The food industry should make more efficient use of its

many processes involving powders and particulates in order

to provide high quality products. In this sense, future

competitiveness may be critically dependent on knowledge

originated by research activities in particle technology

applied to food materials.

Keywords Food powders . Bulk density . Compaction .

Failure properties . Reconstitution

Introduction

There is a relatively new branch of science and engineering

known as Particle Technology. Such discipline deals in the

broader sense with the systematic study of particulate

systems. For the case of food products and materials,

some important applications of particle technology can

be mentioned. For example, particle size in wheat flour is

an important factor in functionality of food products

(McDonald 1994), attrition of instant powdered foods

reduces their reconstitutability (Hogekamp and Schubert

2003), and uneven powder flow in extrusion hoppers may

be considered one of the factors affecting the rheology of a

paste (Pordesimo et al. 2007).

Particle characterisation, i.e., description of primary

properties of food powders in a particulate system, under-

lies all work in particle technology. Primary particle

properties such as particle shape and particle density,

together with the primary properties of a fluid (viscosity

and density), and also with the concentration and state of

dispersion, govern the secondary properties such as settling

velocity of particles or rehydration rate of powders. As

many relationships in powder technology are rather

complex and often not yet available in many areas, particle

properties are mainly used for qualitative assessment of the

behaviour of suspensions and powders, for example, as an

equipment selection guide. Since a powder is considered to

be a dispersed two-phase system consisting of a dispersed

phase of solid particles of different sizes and a gas as the

continuous phase, complete characterisation of powdered

materials is dependent on the properties of a particle as an

individual entity, the properties of the assembly of particles,

and the interactions between those assemblies and a fluid. It

is mainly for this reason that bulk properties have important

effects on many processes and unit operations dealing with

powders and particulates.

The objective of this review article is to discuss the main

techniques used in characterisation of food powders and

particulates, as well as the critical issues of such charac-

terisations in their further handling and processing.

Food Bioprocess Technol (2009) 2:28–44

DOI 10.1007/s11947-008-0107-5

E. Ortega-Rivas (*)

Postgraduate Programme in Food Science and Technology,

Autonomous University of Chihuahua,

University Campus I,

CP 31170 Chihuahua, Chih., México

e-mail: eortegar@uach.mx

Particle Size

There are several single particle characteristics that are very

important to product properties. They include particle size,

particle shape, surface, density, hardness, adsorption prop-

erties, etc. Amongst these mentioned features, particle size

is the most essential and important one. The term size of a

powder or particulate material is very relative, and it is

often used to classify, categorise or characterise a powder.

The selection of a relevant characteristic particle size to

start any analysis or measurement often poses a problem

(Kaye 1997). In practice, the particles forming a powder

will rarely have a spherical shape. Many industrial powders

are of mineral (metallic or non metallic) origin and have

been derived from hard materials by size-reduction pro-

cesses. They are generally known as inert powders and their

comminuted particles resemble polyhedrons with nearly

plane faces, in a number of 4 to 7, and sharp edges and

corners (McCabe et al. 2005). The particles may be

compact, with length, breadth and thickness nearly equal

but, sometimes, they may be plate-like or needle-like. As

particles get smaller, and by influence of attrition due to

handling, their edges may become smoother, and thus, they

may be considered close to a spherical shape. The term

diameter is, therefore, often used to refer to the charac-

teristic linear dimension, and a variable defining how

particles approximate to a spherical shape is known as

sphericity. This variable, described thoroughly in the

literature (Kaye 1994, 1997; Allen 1997; McCabe et al.

2005), takes values of unity for perfect spheres and 0.7–0.8

for most crushed materials.

Particle size, as an independent property is useless

because there is no particulate material having a single

particle size. Any powder would consist of a population of

particles of the same chemical composition, but with a wide

range of individual sizes. Particle size distribution mea-

surement is a common method in any physical, mechanical

or chemical process because it is directly related to material

behaviour and/or physical properties of products. Foods are

frequently in the form of fine particles during processing

and marketing (Schubert 1987). The bulk density, com-

pressibility and flowability of a food powder are highly

dependent on particle size and its distribution (Barbosa-

Cánovas et al. 1987). Segregation will happen in a free-

flowing powder mixture because of the differences in

particle sizes (Barbosa-Cánovas et al. 1985). Size distribu-

tion is also one of the factors affecting the flowability of

food powders (Peleg 1977). For quality control or system

property description, the need to represent the particle size

distribution of food powders becomes paramount and also

proper descriptors in the analysis of the handling, process-

ing and functionality of each food powder. There are many

different types of instruments available for measuring

particle size distribution, but most of them would fall into

four general methods: sieving, microscope counting tech-

niques, sedimentation, and stream scanning. In particle size

measurement, two most important decisions have to be

made before a technique is to be selected for the analysis;

these are concerned with the two variables measured, the

type of particle size and the occurrence of such size.

Particle size was previously discussed, and emphasising

what was already presented, is important to bear in mind

that great care must be taken when making a selection of

particle size, as an equivalent diameter, in order to choose

the most relevant to the property or process which is to be

controlled. The occurrence of amount of particle matter

belonging to specified sizes may be classified or arranged

by diverse criteria as to obtain tables or graphs. In powder

technology, the use of graphs is convenient and customary

for a number of reasons. For example, a particular size

which is to be used as the main reference of a given

material is easily read from a specific type of plot.

Particle Shape

All geometrical features of individual powders’ particles are

related to the intimate structures of their forming elements,

whose arrangements are normally symmetrical with definite

shapes like cubes or octahedrons for inert powders. On the

other hand, powdered food materials would be mostly

organic in origin, and their individual grain shapes could

have a great diversity of structures, since their chemical

compositions would be more complex than those of

inorganic industrial powders. Shape of food powders vary

from extreme degrees of irregularity (ground materials like

spices and sugar), to an approximate spherical shape (starch

and dry yeast) or well-defined crystalline shapes (granulated

sugar and salt). General definitions of particle shapes are

listed in Table 1. It is obvious that such simple definitions

are not enough to do the comparison of particle size

measured by different methods or to incorporate it as

Table 1 General definitions of particle shape (Adapted from Barbosa-

Cánovas et al. 2005)

Shape name Shape description

Acicular Needle shape

Angular Roughly polyhedral shape

Crystalline Freely developed geometric shape in a fluid medium

Dentritic Branched crystalline shape

Fibrous Regularly or irregular thread-like

Flaky Plate-like

Granular Approximately equidimensional irregular shape

Irregular Lacking any symmetry

Modular Rounded irregular shape

Spherical Global shape

Food Bioprocess Technol (2009) 2:28–44 2929

parameters into equations where particle shapes are not the

same (Herdan 1960; Allen 1997). Shape, in its broadest

meaning, is very important in particle behaviour, and just

looking at the particle shapes, with no attempts at

quantification, can be beneficial. Shape can be used as a

filter before size classification is performed. For example,

as shown in Fig. 1, all rough outlines could be eliminated

by using the ratio: perimeter/convex perimeter or all

particles with an extreme elongation ratio. The earliest

methods of describing the shape of particle outlines used

length L, breadth B and thickness T, in expressions such as

the elongation ratio (L/B) and the flakiness ratio (B/T). The

drawback with simple, one number shape measurements is

the possibility of ambiguity; the same single number may

be obtained from more than one shape. Nevertheless, a

measurement of this type which has been successfully

employed for many years is the so-called sphericity,

previously mentioned.

Due to the great variability of shape of food powders’

particles, interactions between assemblies of particles and

fluid may become more complex in food powders than in

inert powders. Bulk property determinations may be

considered, therefore, it is a very critical issue for food

powder characterisation, as well as for evaluating their

effects on processing.

Failure Properties

Basic Concepts of Powders Flow

Powder flow is defined as the relative movement of a bulk

of particles among neighbouring particles or along the

container wall surface (Peleg 1977). The practical objective

of powder flowability investigations is to provide both

qualitative and quantitative knowledge of powder behav-

iour, which can be used in equipment design and in

equipment performance prediction (Sutton 1976). The flow

characteristics of powders are of great importance in many

problems encountered in bulk material handling processes

in the agricultural, ceramic, food, mineral, mining and

pharmaceutical industries because the ease of powder

conveying, blending and packaging depends on flow

characteristics (Chen 1994). In designing plants involving

handling and processing of food powders, diverse difficul-

ties may arise that can cause severe operating problems.

Flow problems related to food powders, such as arching,

ratholing and erratic flow are thoroughly described and

reviewed by Marinelli (2005).

The common flow problems in hoppers and silos can be

summarised as follows: (a) no flow, (b) segregation, (c)

flooding and (d) structural failure. Lack of discharge in the

no flow situation can be attributed to the formation of a

stable arch over the outlet or a stable cavity called a

“rathole” (Marinelli and Carson 1992). With regard to

segregation, many materials experience separation of fine

and coarse particles (Carson et al. 1986), and such

separation can seriously compromise the quality of the

final product as well as the efficiency of the process.

Flooding can be caused by the collapse of a rathole in a bin

containing fine powder, resulting in uncontrollable flow of

material, loss of product and clouds of dust (Royal and

Carson 1993), among other problems. Pertaining to

structural failure, each year over 1,000 silos, bins and

hoppers fail in North America alone. Most of these failures

could have been prevented with proper and careful design,

in which the loads imposed by the bulk solid being stored,

had been well considered. The design of bins, hoppers and

silos has never been given the attention it deserves.

Approaches using properties such as angle of repose or

angle of spatula in design considerations are ineffective

because the resulting values bear no relation to the design

parameters needed to ensure reliable flow, since particulate

solids tend to compact or consolidate when stored. The

attempt of trying to model bulk solids as fluids also leads to

a bottleneck, due to the fact that flowing bulk solids

generate shear stresses and are able to maintain these

stresses even when their flow rate is changed dramatically.

It is also improper to consider bulk solids as having

viscosity since almost all bulk solids exhibit flow properties

that are flow-rate independent. The systematic approach for

designing powder handling and processing plants started in

the mid-1950s by the pioneering work of Andrew W.

Jenike. His concept was to model bulk solids using the

principles of continuum mechanics. The resulting compre-

hensive theory (Jenike 1964) describing the flow of bulk

solids has been applied and perfected over the years, but is

(a) (b)

Fig. 1 Relation between: a perimeter, and b convex perimeter of a

particle

30 Food Bioprocess Technol (2009) 2:28–44

generally recognised worldwide as the only scientific guide

to bulk solids flow.

Practically, for all fine powders, the attractive forces

between particles are large when compared with the weight

of individual particles, so they are said to be cohesive and

normally present flow problems (Adhikari et al. 2001).

Cohesion occurs when interparticle forces play a significant

role in the mechanics of the powder bed. Flow problems

occur in any kind of cohesive powder, but may be more

serious with food powders because they are more sensitive

to physical and physicochemical phenomena which may

affect their composition and properties (Fitzpatrick 2005).

The most common effects of such phenomena in food

powders lead to situations which aggravate flow properties,

as they normally relate to releasing of sticky substances or

to the presence of hygroscopic behaviour. Cohesive

powders are, normally, also adhesive. In cohesion, the

contact surface is similar (particle–particle), while in

adhesion, the contact surface is different (particle—any

surface material). For example, adhesion takes place

between drying droplets and the drying wall of a spray

dryer, whereas cohesion is responsible for caking of the

powder during processing and storage. In food powder,

processing cohesion is also termed caking, and adhesion is

also referred as stickiness.

Stickiness is a prevalent situation that can cause

problems in operation, equipment wear and product yield

(Adhikari et al. 2001). Interaction of water with solids is the

prime cause of stickiness and caking in low-moisture food

powders. Water provides the necessary plasticity to food

polymeric systems, to reduce viscosity and promote

molecular mobility. Chemical caking is caused by chemical

reactions in which a compound has been generated or

modified, as in hydration, recrystallisation or sublimation.

Plastic-flow caking occurs when the particles’ yield values

are exceeded, and they stick together or merge into a single

particulate form, as in amorphous materials like gels, lipids

or waxes. Melting and solidification of fats may also cause

solid bridges and enhance caking in food powders. In this

case, an increase in temperature causes solid fats to melt

producing a liquid that can redistribute itself among the

particles. If the temperature is subsequently reduced, the

liquid fat will solidify and form solid bridges between

the particles.

In general terms, the condition of the surrounding

atmosphere affects secondary properties of powders, such

as flowability, causing diverse type of problems. Small

differences in factors like moisture content, particle size,

storage time and temperature, can make a significant

difference in flowability. If relative humidity increases,

any kind of powder tends to absorb water that may form

liquid bridges between particles reducing flowability. Inert

powders, however, would desorb water with a decrease in

the surrounding relative humidity, so liquid bridges will

disappear, and flowability may turn back to normal. Food

powders are predominantly soluble, so solid bridges may

remain even after humidity decrease, causing the powder to

cake and aggravating flow problems. Furthermore, due to

their chemical composition, food powders are normally

more sensitive to all the ambient factors previously

described and physicochemical changes largely depend on

their temperature–moisture histories. For instance, increas-

ing the temperature of a food powder increases dissolution

of particles, facilitating changes in crystalline form that may

also result in caking and flow problems (Teunou and

Vasseur 1996).

Determination of Failure Properties

To assure steady and reliable flow, it is crucial to accurately

characterise the flow behaviour of powders. Obtaining

useful reproducible data has always been a difficult task

since, as previously discussed, it is not just a powder to be

tested, it is also a powder/air mixture, and the method of

packing, consolidating and shearing will greatly affect the

measurements (De Silva 2000). The forces involved in

powder flow are gravity, friction, cohesion (interparticle

attraction) and adhesion (particle–wall attraction). Further-

more, particle surface properties, particle shape and size

distribution, and the geometry of the system, are factors

affecting the flowability of a given powder. It is, therefore,

quite difficult to have a general theory applicable to all food

powders in all possible conditions that may develop in

practice (Peleg 1977). The first requirement is to identify

the properties which characterise the flowability of a

particular material and to specify procedures for measuring

them. The common belief that the flowability of a powder

is a direct function of the angle of the repose is misleading

and should be avoided because, as stated earlier, most

industrial powders show different grades of cohesiveness.

The angle of repose of a cohesive material is indeterminate,

being dependent on the previous story of a given sample,

and is irrelevant to the flow behaviour of the material in any

particular situation (Jenike 1964). The important feature of

a particulate material is the way its shear strength varies

with the consolidating stress, and the properties used to

identify and quantify such interactions are commonly

known as the failure properties of a powder.

Failure properties can be determined using a shear cell.

Two basic types of shear cells are available for powder

testing: the Jenike shear cell, also known as the transla-

tional shear box, and the annular or ring shear cell, also

called the rotational shear box. The Jenike shear cell is

circular in cross-section, with an internal diameter of

95 mm. As shown in Fig. 2 (Thomson 1997), it consists

of a base and a ring, which can slide horizontally over the

Food Bioprocess Technol (2009) 2:28–44 3131

base. The ring and base are filled with the powder, and a lid

is placed in position. By means of a weight carrier, a

vertical compacting load can be applied to the powder

sample (Fig. 2). The lid carries a bracket with a projecting

pin, and a measured horizontal force is applied to such

bracket, causing the ring and its content along with the lid,

to move forward at a constant speed. The shear force

needed to cause the powder to flow can thus be obtained.

The actual steps to carry out a test in a translational shear

box are: (a) a standardised procedure is used to fill the shear

cell with a powder specimen consolidated in some

reproducible manner, (b) a vertical load is applied in the

lid, (c) the horizontal force is applied to the bracket pushing

forward the upper part of the cell, and the maximum shear

force needed to initiate movement is measured, (d) the cell

is emptied, and a new sample is formed by the same

procedure as in the first step, (e) a different vertical load is

applied to the lid, (f) the procedure described in the third

step is repeated. Five or six different incremental vertical

loads are applied to a set of identical samples, and the shear

force needed to initiate flow is found in each case. The

forces are divided by the cross-sectional area of the cell to

give stresses, and the shear stress is plotted against the

normal stress. The resulting graph of plotting shear stress

against normal stress for the incremental vertical loads is

known as the yield locus as shown in Fig. 3 (Wilms 1999),

and it is a line which gives the stress conditions needed to

produce flow for the powder when compacted to a fixed

bulk density. A yield locus represents the result of a series

of tests on samples which have the same initial bulk

density. If the material being tested is cohesive, the yield

locus is not a straight line and does not pass through the

origin. It can be shown that the graph when extrapolated

downwards cuts the horizontal axis normally. As shown in

Fig. 3, the intercept T is known as the tensile strength of the

powder, and the intercept C is called the cohesion of the

powder; the yield locus ends at the point A. More yield loci

can be obtained by changing the sample preparation

procedure, and in this way a family of yield loci can be

obtained. This family of yield loci contains all the

information needed to characterise the flowability of a

particular material. For many powders, yield locus curves

can be described by the empirical Warren–Spring equation

(Chasseray 1994):

t

C

� �n

¼s

T1 ð1Þ

where t is the shear stress, C the material’s cohesion, σ the

normal stress, T the tensile strength, and n the shear index

(1<n<2).

The Jenike method for testing flowability of powders has

been successful because it couples a flow theory for bulk

Fig. 2 Diagram of Jenike’s

shear cell: a cell components, b

testing steps

32 Food Bioprocess Technol (2009) 2:28–44

solids to a practical technique for measuring their flow

properties (Wright 1999), resulting in the prediction of the

minimum acceptable values of the important hopper and

silo design parameters. Correct choice of these parameters

ensures collapsing of any cohesive arch at any container’s

hopper outlet, under its own weight. There are, however,

some disadvantages of the method, such as laborious

sample preparation prior to testing, unequal stress distribu-

tion causing progressive failure and inaccuracy of the

method at low loads due to tilting of the lid (Wright 1999).

Some of the difficulties of the translational shear tester

described above can be overcome by the use of a ring shear

tester. Ring, or annular, shear testers have been used in bulk

solids technology for an extended period of time (Carr and

Walker 1967; Münz 1976; Gebhard 1982; Höhne 1985)

with an increasing range of applications (Schulze 1994a, b).

In annular shear cells, the shear stress is applied by rotating

the top portion of an annular shear, as represented in Fig. 4.

A shear cover with concentric cutting edges connected by

cross ribs is used to determine the inner flow properties.

When the lid is placed in position, the cutting edges force

their way into the product making it possible to carry out

shearing in it. During the measurement, the lower shear

trough rotates, so the shear forces are measured via a lever

arm resting against a force transmitter, with the top shear lid

being arrested. These devices provide much larger shear

distances to be covered both in sample preparation and its

testing allowing a study of flow properties after testing, but

their geometry creates some problems. The distribution of

stress is not uniform in the radial direction but, for the ratio

of the inner and outer radii of the annuli greater than 0.8,

the geometrical effects are often considered negligible.

Rotational shear cells are said to have the advantages of

nearly unlimited shear deformation, possibility of mea-

surements at very low consolidation stresses, ease of

operation and possibility of time consolidation measure-

ments using a consolidation bench (Schulze 1996; Schulze

and Wittmaier 2007).

Another important failure property, the failure function,

can be measured using a split cylindrical die as shown in

Fig. 5. The bore of the cylinder may be about 50 mm, and

its height should be just more than twice the bore. The

cylinder is clamped so that the two halves cannot separate,

and it is filled with the powder to be tested, which is then

scraped off to be at al level with the top face. By means of a

plunger, the specimen is subjected to a known consolidat-

ing stress. The plunger is then removed, and the two halves

of the split die are separated, leaving a free standing

cylinder of the compacted powder. A plate is then placed on

top of the specimen, and an increasing vertical load is

applied to it until the column collapses. The stress at which

this occurs is the unconfined yield stress, i.e., the stress that

has to be applied to the free vertical surface on the column

to cause failure. If this is repeated for a number of different

compacting loads and the unconfined yield stress is plotted

against the compacting stress, the failure function of the

powder will be obtained. Although the results of this

method can be used for monitoring or for comparison, the

failure function obtained will not be the same as that given

by shear cell tests, due to the effect of die wall friction

when forming the compact. A method of correcting for

friction has been described (Williams et al. 1971).

The failure function, also referred as the flow function, is

a measure of how the unconfined yield strength developed

within the powder, varies with maximum consolidation

stress. This variation is illustrated in Fig. 6 and forms the

basis of the Jenike classification of powders. Jenike used

the inverse slope of the failure function, known as flow

index or flow factor ff, to classify powder flowabilty.

According to the value of the flow index, powders are

categorised as very cohesive (ff<2), cohesive (2<ff<4),

easy flow (4<ff<10) and free flow (10<ff).

Consolidatedsample

Lid

Trough

Normal load

Fig. 4 Diagram of an annular shear cell

Normal stress

Sh

ear

str

ess

A

C

T

Fig. 3 The Jenike yield locus

Food Bioprocess Technol (2009) 2:28–44 3333

Stickiness can be evaluated by several methods includ-

ing the Jenike shear method previously described, but since

shear cell methods are normally used for studying the flow

behaviour of powders through chutes and hoppers, they

have limited applications to characterise the stickiness of

food powders (Bhandari and Hartel 2005). Other available

methods for stickiness measurement are the propeller-

driven method, the optical probe method, the blow test

and the fluidisation method. The propeller driven method,

originally developed by Lazar et al. (1956), basically

comprises a test tube containing powder with known

moisture content. The test tube is immersed in a water bath,

and a machine-driven impeller stirs the powder. The tem-

perature of thewater bath is slowly risen to record amaximum

force of stirring at a point known as the sticky point.

The optical probe method is based on the changes in

optical properties of a free-flowing powder (Lockemann

1999). The motion of a food powder in a constantly rotating

tube is observed with a fibre-optic sensor. Both tube and

sensor are immersed in an oil bath to maintain the

temperature. A sharp increase in reflectance of a free-

flowing powder is observed at its sticky point. The method

seems appropriate for coloured foods, but has not been

applied to food materials tending to be transparent on

softening or melting. It seems to be a promising technique

for evaluation of already dried powders (Bhandari and

Hartel 2005).

A blow test method proposed by Paterson et al. (2001)

measures the velocity of air needed to blow a channel into a

pack bed of powder and the stickiness is based on the air

velocity range. The blow test apparatus consists of a multi-

segmented circular distributor where the preconditioned

sample is packed. Air, at a given temperature and humidity,

is blown from a 45° angle onto each segment with

increasing flow rate to a maximum of 22 l/min, until a

channel is formed. The result from this method would

represent further the caking behaviour of food powders, but

is physically demanding and several steps are required

before each measurement.

The fluidised method, described by Bloore (2000),

comprises a small fluidised bed set-up to study the

stickiness property of a powder at different temperature

and humidity conditions. The positive feature of this

method, compared to other tests, is that the powder is in a

dynamic condition, closer to spray drying and fluidised bed

drying situations. The stickiness observed by this method is

governed by the cohesive properties of the particles, and is

useful to represent conditions in spray and fluidised bed-

drying processes.

No flow

Easy flow

More

difficult

to flow

Maximum consolidating stress

Un

co

nfi

ned

yie

ld s

tren

gth

Fig. 6 The failure function of a food powder

(a)

(d) (e) (f)

(b) (c)

Fig. 5 Device for direct mea-

surement of failure function:

a mounted measuring device,

b securing halves and filling

with sample, c compacting with

plunger, d separating halves and

stable column of powder,

e application of normal force,

f collapsing of material

34 Food Bioprocess Technol (2009) 2:28–44

Factors Influencing Food Powder Flowability

Food powder flowability has been characterised as a

function of some of the factors affecting it previously

described. Particle size has a major influence on powder

flowability. From a critical size of about 200 μm and

downwards, flowability is seriously affected (Fitzpatrick

2005). A noticeable change in capacity to flow is observed

if the size is reduced by an order of magnitude, for example

from 100 to 10 μm. This reduction in flowability may be

attributed to the increase surface area per unit mass of

solids, as the particle becomes smaller. There is more

surface area or surface contacts available for cohesive

forces, in particular, and frictional forces to resist flow. The

particle size distribution also has an impact of flow

possibility. A significant amount of fines in the distribution

will aggravate flow problems and powder flowability may

be worse that that expected from the mean size of the

powder. Pertaining to particle shape, there is a dearth of

information in the literature on this aspect. Bumiller et al.

(2002) described studies of particle shape influence on

hopper angle and outer size requirements for mass flow.

Storage conditions including storage temperature, expo-

sure to air humidity, storage time and consolidation, all play

an important role in food powder flowability. Powders in

confinement tend to consolidate, which often leads to

increased strength within the powder and increase adhesion

between the powder and the hopper wall. Teunou and

Fitzpatrick (2000) reported effects of storage time and

consolidation on flowability of flour, tea and whey

permeate. In agreement with other reports (Walker 1967;

Goelema et al. 1993; Fitzpatrick et al. 2004; Barbosa-

Cánovas and Juliano 2005a), they found that the ability to

flow was reduced with consolidation time. For typical food

powders, the unconfined yield strength increases with

consolidation time for a given maximum consolidating

stress, as shown in Fig. 7.

Effects of relative humidity have also been investigated

(Teunou and Fitzpatrick 1999; Heng and Stainforth 1988;

Tomas and Schubert 1982). Generally, in bulk materials,

moisture absorption causes an increase in cohesion, with a

consequent decrease in flowability. Normally, local mois-

ture content is the direct cause of cohesion. For instance,

crystalline products can cake significantly when exposed to

humid conditions due to formation of liquid bridges

between particles, followed by drying. By a mechanism of

dissolution of soluble material and the transport of water

vapour away from solid surfaces, new crystal structures are

formed between particles (Johanson 2005). The effect of

different moisture levels on flowability of food powders

will generally follow the trend illustrated in Fig. 8.

In general, varying the storage temperature form above

freezing to 30–40°C does not have a major impact on

powder flowability, provided no melting of components

occurs, or no component exceeds its glass transition point

temperature. Some food powders undergo a glass transition

at elevated temperatures, where they change from crystal-

line material to an amorphous solid (Aguilera et al. 1995;

Bhandari and Hartel 2005). Amorphous particles become

soft, and solid contact pressures cause particles to bind

together, affecting thus flowability. Glass transition tem-

perature can characterise the stickiness during powder

storage (Roos and Karel 1991). Many food powders will

normally show an effect of temperature in flow capacity as

presented in Fig. 9. The presence of glassy low-molecular-

weight materials (glucose, fructose and sucrose) in spray-

dried fruit powders makes them particularly prone to

0

0.5

1

1.5

2

2.5

3

1.5 2 2.5 3 3.5 4 4.5

Maximum consolidated stress (kPa)

Un

co

nfi

ned

yie

ld s

tren

gth

(kP

a)

RH = 20%

RH = 44%

RH = 76%

Fig. 8 Effect of moisture content on flowability of self-rising wheat

flour (adapted from Teunou and Fitzpatrick 1999)

0

2

4

6

8

10

12

14

5 10 15 20 25 30

Maximum consolidated stress (kPa)

Un

co

nfi

ned

yie

ld s

tren

gth

(kP

a)

1 day

3 days

7 days

Fig. 7 Effect of consolidation time on flowability of self-rising wheat

flour (adapted from Teunou and Fitzpatrick 2000)

Food Bioprocess Technol (2009) 2:28–44 3535

stickiness, due to their elevated hygroscopic behaviour and

the chemical reactions occurring at elevated temperatures.

Bulk Density and Porosity

Definitions of Bulk Density

When a powder just fills a vessel of known volume V, and

the mass of the powder is m, then the bulk density of the

powder is m/V. However, if the vessel is tapped, it will be

found in most cases that the powder will settle, and more

powder needs to be added to have once more a complete

fill. If the mass now filling the vessel is m′ then the bulk

density is m′/V>m/V. Clearly, this change in density just

described has been caused by the influence of the fraction

of volume not occupied by a particle, known as porosity

(Barbosa-Cánovas et al. 2005). The bulk density is,

therefore, the mass of particles that occupies a unit volume

of a bed, while porosity or voidage is defined as the volume

of the voids within the bed divided by the total volume of

the bed. These two properties are, in fact, related via the

particle density in that, for a unit volume of the bulk

powder, there must be the following mass balance:

rb ¼ rs 1� "ð Þra" ð2Þ

where ρb is the powder bulk density, ρs is the particle density,

ε is the porosity and ρa is the air density. As the air density is

small relative to the powder density, it can be neglected, and

the porosity can thus be calculated simply as:

" ¼rs � rbð Þ

rs

ð3Þ

Porosity, as defined above can also be termed voidage,

but it may be confused with the void ratio often used in soil

mechanics. The void ratio VR, defined as the ratio between

volume of voids and volume of solids, gives another form

of mass balance for a given unit volume of solids as

follow:

VRþ 1ð Þrb ¼ rb þ raVR ð4Þ

and if ρa is again neglected, VR can be calculated from:

VR ¼rs � rbð Þ

rb

ð5Þ

As can be seen by comparison with Eq. 3, this equation

has the bulk density in the denominator instead of the

particle density as in the case of porosity. The relationship

between void ratio and porosity is from Eqs. 3 and 5 and is

as follows:

VR

"

¼rs

rb

ð6Þ

One fundamental difference between void ratio and

porosity is that the latter can never be greater than unity,

while the former can be as high as 1.3 in some cases (oats

for example). It is preferable to use porosity whenever

possible because its definition is more logical and less

prone to confusion (as a volume fraction of the whole).

Definitions and relationships between different types of

densities are still confusing, and differences among mea-

suring techniques can lead to considerable errors when

determining them (Fasina 2007). Over the years, in order of

increasing values, three classes of bulk density have

become conventional: poured, aerated and tap (Barbosa-

Cánovas and Juliano 2005b). Each of these depends on the

treatment to which the sample was subjected, and although

there is a move towards standard procedures, these are far

from universally adopted. There is still some confusion in

the open literature as to how these terms are interpreted.

Some consider the poured bulk density as loose bulk

density, while others refer to it as apparent density. Aerated

density can also be considered to be a quite confusing term.

Strictly speaking, aerated should mean that the particles are

separated from each other by a film of air and not being in

direct contact with each other. Some authors interpret the

term as meaning the bulk density after the powder has been

aerated. Tap density, the bulk density after a volume of

powder has been tapped or vibrated under specific

conditions, can also be regarded as compact density.

Measurement of Bulk Density

Poured density is widely used and would simply mean to

determine the mass–volume ratio of a powder sample by

weighing a container of known volume without the sample

and then with the freely poured powder. The measurement

is often performed in a manner found suitable for the

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1.5 2 2.5 3 3.5

Maximum consolidated stress (kPa)

Un

co

nfi

ne

d y

ield

str

en

gth

(k

Pa

)

T = 40°C

T = 30°C

T = 5°C

Fig. 9 Effect of temperature on flowability of self-rising wheat flour

(adapted from Teunou and Fitzpatrick 1999)

36 Food Bioprocess Technol (2009) 2:28–44

requirements of the individual company or industry. In

some cases, the volume occupied by a particular mass of

powder is measured, but the elimination of operation

judgment, and thus possible error, in any measurement is

advisable. To achieve this, the use of a standard volume and

the measurement of the mass of powder to fill it are needed.

Certain precautions which should be taken are clear, e.g., it

is better to use a density cylinder with a 2:1 length to

diameter ratio, the powder should always be poured from

the same height, and the possibility of bias in the filling

should be made as small as possible. Although measuring

of poured bulk density is far form standardised, many

industries use a sawn-off funnel with a trap door or stop, to

pour the powder through into the measuring container.

The aerated bulk density is, in practical terms, the

density when the powder is in its most loosely packed form,

while the tap bulk density, as is implied by its name, is the

bulk density of a powder, which has been settled into a

closer packing than existed in the poured state by tapping,

jolting or vibrating the measuring vessel. Aerated and tap

bulk densities can both be determined by use of a powder

tester. A commonly used tester, which has been designed in

compliance by norms established by the American Asso-

ciation of Testing and Materials (ASTM) is the Hosakawa

powder tester.

For determination of the aerated bulk density, a loosely

packed form can be achieved by dropping a well-dispersed

cloud of individual particles down into a measuring vessel.

The structure within the vessel is held by the cohesive

forces between the particles and can be extremely fragile.

Levelling off the surface of the powder at the top of the

vessel is difficult to achieve without causing particle

movement leading to error, as some structure collapses.

As shown in Fig. 10 (Abdullah and Geldart 1999), the

Hosakawa powder tester comprises an assembly of screen

cover, a screen, a spacer ring and a chute attached to a

mains-operated vibrator of variable amplitude. A stationary

chute is aligned with the centre of a pre-weighed 100 ml

cup. The powder is poured through a vibrating sieve and

allowed to fall a fixed height of 25 cm approximately

through the stationary chute into the cylindrical cup. The

amplitude of the vibration is set so that the powder will fill

the cup in 20 to 30 s. The excess powder is skimmed from

the top of the cup using the sharp edge of a knife or ruler,

without disturbing, or compacting, the loosely settled

powder.

For measuring the tap bulk density, as with poured bulk

density, the volume of a particular mass of powder may be

observed, but it is generally better to measure the mass of

powder in a fixed volume. Although tapping can be done

manually, it is better to use a mechanical tapping device so

that the conditions of sample preparation are more

reproducible. The version of the Hosokawa powder tester

to determine tap bulk density includes a standard cup

(100 ml) and a cam-operated tapping device which moves

the cup upward and drops it periodically (once in every

1.2 s). A cup extension piece has to be fitted and powder

added during the sample preparation so that, at no time, the

powder packs below the rim of the cup. After the tapping,

excess powder is scraped from the rim of the cup and the

bulk density determined by weighing the cup.

Approximate values of poured bulk density of different

food powders are given in Table 2. As can be seen, with

very few exceptions, food powders have poured bulk

densities in the range of 300 to 800 kg/m3. The solid

density of most food powders is about 1,400 kg/m3, so

these values are an indication that food powders have high

porosity, which can be internal, external or both. There are

Standard

100 cc cup

Scoop

Screen cover

ScreenSpacer ring

Vibrating

chute

Stationary

chute

Air-borne

fines

Cup

location

Fig. 10 Determination of aerated bulk density

Food Bioprocess Technol (2009) 2:28–44 3737

many published theoretical and experimental studies of

porosity as a function of the particle size, distribution and

shape. Most of them pertain to free-flowing powders or

models (e.g., steel shots and metal powders), where

porosity can be treated as primarily due to geometrical

and statistical factors only (Gray 1968; McGeary 1967).

Even though in these cases porosity can vary considerably,

depending on factors such as the concentration of fines, it is

still evident that the exceedingly low density of food

powders cannot be explained by geometrical considerations

only. Most food powders are known to be cohesive, and

therefore, an open bed structure supported by interparticle

forces is very likely to exist (Moreyra and Peleg 1981;

Scoville and Peleg 1980; Dobbs et al. 1982). Since the bulk

density of food powders depends on the combined effect of

interrelated factors, such as the intensity of attractive

interparticle forces, the particle size and the number of

contact points (Rumpf 1961), it is clear that a change in any

of the powder characteristics may result in a significant

change in the powder bulk density. For example, in Table 3,

variations in poured and tap density of three food powders

are presented (Teunou and Fitzpatrick 1999). As can be

seen, significant difference exists in the values of the two

types of density measured for the three powders tested. The

magnitude of change in bulk density of food powders

cannot always be anticipated. There is an intricate relation-

ship between the factors affecting food powder bulk

density, as well as surface activity and cohesion.

With regard to the moisture factor, also included in

Table 2, moisture sorption is generally associated with

increased cohesiveness mainly due to interparticle bridges.

Many food powders are highly hygroscopic, and therefore,

high moisture contents would result in lower loose bulk

densities. However, this decrease would only be detected in

freshly sieved or in flowing powders, where the same

interparticle forces are not allowed to cause caking of the

mass. Whereas sugar and salt are examples of powders

which lower their densities as a result of increasing

humidity, fine powders which are very cohesive even in

their dry form (baby formula and coffee creamer) do not

present such a trend. For these powders, it appears that the

bed array has reached maximum voidage at low moisture

contents, and further lowering of the density becomes

impossible. It is also worthwhile to remember that

excessive moisture levels, especially in powders containing

soluble crystalline compounds, may result in liquefaction of

the powder with the consequent increase in its density.

Anticaking agents, also known as flow conditioners, are

supposed to reduce interparticle forces, and as such, they

are expected to increase the bulk density of powders (Peleg

and Mannheim 1973). It has been observed that there may

be an optimal concentration beyond which the effect will

diminish or will be practically unaffected by the anticaking

concentration (Hollenbach et al. 1982). It can also be

observed that, for a noticeable effect on the bulk density

(i.e., an increase in the order of 10% or more), the agent

and host particles must have surface affinity. If this is not

the case, the conditioner particles may segregate and,

instead of reducing interparticle forces, will only fill

interparticle space. Examples of effects of moisture and

anticaking agents on the bulk properties of selected food

powders are given in Tables 4 and 5.

Compressibility

In most cases, a material’s bulk density varies continuously

as a function of the consolidating pressure acting on it. As a

result, it is not sufficient to describe a material simply as

Table 2 Approximate bulk density and moisture of different food

powders (adapted from Barbosa-Cánovas et al. 2005)

Powder Poured bulk

density (kg/m3)

Moisture

content (%)

Baby formula 400 2.5

Cocoa 480 3–5

Coffee (ground and roasted) 330 7

Coffee (instant) 470 2.5

Coffee creamer 660 3

Corn meal 560 12

Corn starch 340 12

Egg (whole) 680 2–4

Gelatin (ground) 680 12

Microcrystalline cellulose 610 6

Milk 430 2–4

Oatmeal 510 8

Onion (powdered) 960 1–4

Salt (granulated) 950 0.2

Salt (powdered) 280 0.2

Soy protein (precipitated) 800 2–3

Sugar (granulated) 480 0.5

Sugar (powdered) 480 0.5

Wheat flour 800 12

Wheat (whole) 560 12

Whey 520 4.5

Yeast (active dry baker’s) 820 8

Yeast (active dry wine) 8

Table 3 Comparison of two types of bulk density for different food

powders (adapted from Teunou and Fitzpatrick 2000)

Powder Poured bulk

density (kg/m3)

Tap bulked

density (kg/m3)

Self-rising wheat flour 601 695

Fine tea powder 617 913

Wheat-permeate powder 516 622

38 Food Bioprocess Technol (2009) 2:28–44

loose or compacted. Instead, the bulk density-to-pressure

relationship can be often expressed as a straight line on a

log–log plot as illustrated in Fig. 11. Food powders can be

compacted by tapping or by mechanical compression.

These processes can occur either unintentionally as a result

of handling or transporting or intentionally as when

tabletting or agglomerating. In the food industry, uninten-

tional compression is normally undesirable, while opera-

tions aimed at obtaining defined shapes are usually required

in some processes. Theoretical and empirical considerations

of vibratory compaction have been mainly focused to

nonfood powders (Hausner et al. 1976). Sone (1972)

reported the following relationship for food powders:

gn ¼V0 � Vn

V0

¼abn

1þ bnð7Þ

Table 4 Effect of moisture

content on mechanical charac-

teristics of some food powders

(adapted from Barbosa-

Cánovas et al. 2005)

Powder Moisture (%) Poured bulk

density (kg/m3)

Compressibility

(b in Eq. 9)

Cohesion

(g/cm2)

Glass beads Dry 1,720 ∼0 ∼0

(175 μm) 1.0 1,200 0.23 15

Powdered salt Dry 1,260 0.02 ∼0

(100/200 mesh) 0.6 780 0.12 50

Powdered sucrose Dry 620 0.152 ∼10

(60/80 mesh) 0.1 500 0.185 ∼14

Starch Dry 810 0.12 ∼6

18.5 690 0.15 ∼13

Powdered onion Dry 510 0.03 5

(80/120 mesh) 5.2 510 0.05 15

Baby formula Dry 520 0.08 37

(commercial) 2.7 410 0.08 Too cohesive

Coffee creamer Dry 460 0.08 49

(commercial) 7.0 450 0.19 32

Active dry 5.2 520 0.05 ∼0

Baker’s yeast 8.4 520 0.08 14

13.0 490 0.26 Too cohesive

Table 5 Effect of anticaking

agents on bulk density and

compressibility of selected

food powders (adapted from

Barbosa-Cánovas et al. 2005)

Powder Agent Concentration Poured bulk

density (kg/m3)

Compressibility

(b in Equation 9)

Sucrose (powdered) None – 700 0.066

Calcium stearate 0.5 870 0.039

Silicon oxide 0.5 750 0.052

Tricalcium phosphate 0.5 760 0.044

Salt (powdered) None – 1,010 0.080

Calcium stearate 0.1 1,140 0.032

Silicon oxide 0.1 1,100 0.045

Tricalcium phosphate 0.1 1,160 0.025

Soup mix None – 700 0.27

Aluminium silicate 2.0 750 0.15

Calcium stearate 2.0 630 0.27

Gelatin (powdered) None – 680 ∼0

Aluminium silicate 1.0 700 0.016

Microcristalline cellulose None – 350 0.017

Aluminium silicate 1.0 360 0.030

Corn starch None – 620 0.109

Calcium stearate 1.0 590 0.099

Silicon oxide 1.0 670 0.077

Tricalcium phosphate 1.0 610 0.062

Soy protein None – 270 0.040

Calcium stearate 1.0 270 0.041

Silicon oxide 1.0 270 0.036

Tricalcium phosphate 1.0 310 0.024

Food Bioprocess Technol (2009) 2:28–44 3939

where γn is the volume reduction fraction, V0 is the initial

volume, Vn is the volume after n taps, and a and b are

constants.

The applicability of Eq. 7 was tested through its fit to the

following linear form:

n

gn

¼1

abþ

n

að8Þ

The constant a in Eqs. 7 and 8 represents the asymptotic

level of the volume change (the level obtained after a large

number of tapings or a long time in vibration). The constant

b is representative of the rate at which this compaction is

achieved, i.e., 1/b is the number of vibrations necessary to

reach half of the asymptotic change. In general, this form of

data presentation is very convenient for systems com-

parisons, since it only involves two constants.

A very common undesirable aspect of compressibility is

its negative influence on flowing capacity. In powder

technology, great attention has been paid to the general

behaviour of powders under compressive stress (Peleg

1977; Barbosa-Cánovas and Juliano 2005a, b). It has been

observed that the compressive mechanisms in fine food

powders are different from those in food agglomerates

(Barbosa-Cánovas and Juliano 2005b). The first stage of

compression in fine powders involves the movement of

particles toward filling voids similar to or larger in size than

the particles themselves (Nyström and Karehill 1996). The

second stage involves filling of smaller voids by particles

that are deformed elastically and/or plastically, and eventu-

ally broken down (Kurup and Pilpel 1978; Carstensen and

Hou 1985; Duberg and Nyström 1986). Most of the organic

compounds show consolidation behaviour consisting on

particle fragmentation during the initial loading, followed

by elastic and/or plastic deformation at higher loads. In

food agglomerates, on the other hand, compression takes

place in three distinct stages: agglomerate particle re-

arrangement to fill the voids similar or larger in size than

the agglomerates, agglomerate deformation or brittle break-

down, and primary particle rearrangement, elastic/plastic

deformation and fracture (Mort et al. 1994; Nuebel and

Peleg 1994). Both compression mechanisms in fine and

agglomerated food powders are influenced by particle size

and size distribution, particle shape and surface properties.

If the material is packed in a loose state, considerable

compressibility is shown, and when compressive forces are

applied, they are transmitted at the contact points.

Compression tests have been used widely in food

powders, as a simple and convenient technique to measure

physical properties such as compressibility and flowability.

In order to get the pressure–density relationship for a given

powder, a set of compression cells (usually a piston in a

cylinder) is used. The tested powder is poured into the

cylinder and compressed with a piston attached to the cross-

head of a TA-XT2 Texture Analyzer or Instron Universal

Testing Machine. Normally, a force–distance relationship

during a compression test will be recorded by the

instrument. It is relatively easy to change this relationship

into a pressure–density relationship to get the com-

pressibility after data treatment, when the cross section

area of the cell and the initial powder weight are known.

The pressure–density for powders in a compression test at

low pressure range can be described by the following

equation (Barbosa-Cánovas et al. 1987):

r sð Þ � r0

r0

¼ aþ b log s ð9Þ

where ρ(σ) is the bulk density under the applied normal

stress σ, ρ0 the initial bulk density, and a and b constants.

The constant b represents, specifically, the compressibility

of a given powder. Compression tests are useful in

characterising the flowability of powders because the

interparticle forces that enable open structures in powder

beds succumb under relatively low pressures. As shown in

Eq. 9, the constant b representing the change in bulk

density by the applied stress is referred to as the powder

compressibility. It has been found that b can be correlated

with cohesion of a variety of powders and therefore could

be a simple parameter to indicate flowability changes

100

1000

0.1 1 10 100

Consolidation pressure (kPa)

Bu

lk d

en

sit

y (

kg

/m3) 500

Fig. 11 Bulk density of a food powder as a function of consolidation

pressure

40 Food Bioprocess Technol (2009) 2:28–44

(Peleg 1977). Generally, the higher the compressibility, the

poorer the flowability is, but if quantitative information

about capacity to flow is required, shear tests are necessary

(Schubert 1987).

One of the standard methods to evaluate the flowability

of a particulate system is to calculate the Hausner ratio after

tapping. This ratio is defined as the ratio of a powder

system’s initial bulk density to its tapped bulk density. It is

easy to calculate the Hausner ratio and evaluate the

flowability when the loose and tapped volumes of the test

material are known. For a Hausner ratio of 1.0∼1.1, the

powder is classified as free flowing; 1.1∼1.25, medium

flowing; 1.25∼1.4, difficult flowing and >1.4, very difficult

flowing (Hayes 1987). Flowability of food powders can be

improved by agglomeration followed by drying in an air

stream. Apart from improving flowability, agglomerated

powders may show better wettability and dispersibility in

liquids, and tend to be dust-free (Masters 1976).

Reconstitution Properties

Reconstitutability is the term used to describe the rate at

which dried foods pick up and absorb water reverting to a

condition which resembles the un-dried material, when put

in contact with an excessive amount of this liquid (Masters

1976). In the case of dried-powdered foods, a number of

properties may influence the overall reconstitution charac-

teristics (Hogekamp and Schubert 2003). For instance,

wettability describes the capacity of the powder particles to

absorb water on their surface, thus initiating reconstitution.

Such a property depends largely on particle size. Small

particles, representing a large surface area: mass ratio, may

not be wetted individually but may clump together sharing

a wetted surface layer. This layer reduces the rate at which

water penetrates into the particle clump. Increasing particle

size and/or agglomerating particles can reduce the inci-

dence of clumping. The nature of the particle surface can

also affect wettability. For example, the presence of free fat

in the surface reduces wettability. Another important

property is the sinkability, which describes the ability of

the powder particles to sink quickly into the water. This

depends mainly on the size and density of the particles.

Larger denser particles sink more rapidly than finer, lighter

ones. Particles with a high content of occluded air may be

relatively large but exhibit poor sinkability because of their

low density. Finally, dispersability describes the ease for a

powder to be distributed as single particles over the surface

and throughout the bulk of the reconstituting water, while

solubility refers to the rate and extent to which the

components of the powder particles dissolve in water.

Food dried powders and particulates are normally

reconstituted for consumption. For a dried product to

exhibit good reconstitution characteristics, there needs to

be a correct balance between the individual properties

discussed above. In many cases, alteration of one or two of

these properties can markedly change the rehydrating

behaviour. Several measures can be taken in order to

improve reconstitutability of dried food products. The

selected drying method and adjustment of drying conditions

can result in a product with good rehydration properties.

For example, it is well known that freeze drying consists of

production of ice crystals and their sublimation at very low

pressures (Heldman and Singh 1981). This procedure

results in food particles with an open pore structure which

absorb water easily when they are reconstituted. Another

alternative is the use of the so-called combined methods,

such as osmotic dehydration followed by conventional

drying. In osmotic dehydration, food particles are immersed

in a concentrated solution. By osmotic pressure, the water

inside the particles tends to migrate to the solution in order

to equate water activities on both sides of the cellular wall

(Monsalve-González et al. 1993). This partial dehydration

will aid in the final stage drying, and textural damage will

be minimised. In this sense, food materials dehydrated by

combined methods will also have an open pore structure,

and similar to freeze dried materials, will present good

reconstitution properties. Beltran-Reyes et al. (1996) devel-

oped an apple powdered ingredient by grinding dried

apples obtained by osmotic dehydration followed by

conventional heated air drying. They determined that the

firmness of the rehydrated mash was a direct function of the

particle size. For the same ingredient, it has been reported

(Ortega-Rivas and Beltran-Reyes 1997) that rehydration

improved as particle size decreased, as shown in Fig. 12.

The most efficient method to improve the rehydration

characteristics of dried food powders is probably the use of

agglomeration (Barletta and Barbosa-Cánovas 1993). In

order to improve wettability of food powders, their particles

can be increased in size by agglomeration. A critical size of

0

1

2

3

4

5

6

7

0.6 0.7 0.8 0.9 1 1.1

Particle size (mm)

Reh

yd

rati

on

rati

o

Fig. 12 Dehydration ratio as a function of particle size of a food

powder (adapted from Ortega-Rivas and Beltran-Reyes 1997)

Food Bioprocess Technol (2009) 2:28–44 4141

particles to get wet is about 100 μm. Generally, powders

with particle sizes below 100 μm are difficult to wet

because of their small inter-particulate space (Bhandari and

Hartel 2005). Thus, increasing median sizes to a larger

range between 500 and 3,000 μm will have a positive

impact in wettability. This agglomeration process is called

instantisation, and it is generally accepted that “instant”

powders will get wet quickly and will disperse in water

faster than “non-instant” powders. Instantisation can be

carried out by removing particles from a spray drier at high

moisture content (in thermoplastic state) and allow them to

stick in a fluidised bed at elevated temperature. Another

method of instantisation involves rewetting the surface of

individual particles allowing them to come in contact and

stick together, and then drying to remove water and cause

stuck particles to become stable agglomerates.

Wetting time is the most important variable in evaluating

instant properties. Standard procedures for measuring

instant properties need to consider a series of aspects such

as specific solvent temperature, liquid surface area, amount

of material to dissolve, method for depositing a certain

amount of material on the liquid surface, unassisted or

predetermined mixing steps, and timing procedure (Pietsch

1999). Different techniques have been reported to evaluate

food powder instant properties (Barbosa-Cánovas and

Juliano 2005b) and include the penetration speed test and

the standard dynamic wetting test. In the penetration test, a

cell with screen carrying a layer of agglomerates, retained

with a plexiglass cylinder, is placed into water. Penetration

time is measured until the entire material bed is submerged

(Pietsch 1999). The dynamic wetting test makes use of a

measuring cell attached to a weighing cell, which is placed

in contact with the liquid by tilting the cell onto its surface.

The force measured by the weighing cell is proportional to

the liquid volume absorbed due to capillary pressure, and is

plotted against time (Schubert 1980; Pietsch 1999).

Conclusions

Particle technology is of dynamic significance to the world

economy with a broad range of industries taking advantage

of the rapidly growing knowledge in this discipline.

Processing of food powders and particulates may be deeply

understood only when appropriate characterisation of their

properties are made. Secondary properties are crucial in

handling and processing because they consider the two-

phase nature of powders. For food powders, determination

of some of these bulk properties, represent a more

challenging task than the equivalent determinations for

inert powders. Food particulate materials tend to be soft and

friable, while their physicochemical nature may cause

release of sticky substances or tendency to absorb moisture.

Stickiness and caking are common problems prevailing in

food powder handling and processing, so their flowability

results are quite indeterminate. Reliable characterisation of

secondary properties would aid to understand better flow

behaviour of food powders under different conditions.

Notation

(Dimensions given in terms of mass, M, length, L, and

time, T)

a constant, asymptotic level of the volume change

b constant, rate at which compaction is achieved,

compressibility of given powder

C cohesion (ml−2)

n shear index, number of taps

T tensile strength (ml−1 t−2)

Vn volume after n taps (l3)

VR void ratio

V0 initial volume (l3)

Greek symbols

γn Volume reduction fraction

ε Porosity

ρa Air density (ml−3)

ρb Powder bulk density (ml−3)

ρs Particle density (ml−3)

ρ0 Initial bulk density (ml−3)

ρ(σ) Bulk density under applied normal stress (ml−3)

σ Normal stress (ml−1 t−2)

t Shear stress (ml−1 t−2)

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Home / Chemistry / Industrial Chemistry Ullmann's Encyclopedia of Industrial Chemistry Hydrocyclones Standard Article Enrique Ortega-Rivas1 1Food and Chemical Engineering Program, Autonomous University of Chihuahua; University Campus I, Chihuahua, Chih., 31170, Mexico Copyright © 2007 by Wiley-VCH Verlag GmbH & Co. KGaA. All rights reserved. DOI: 10.1002/14356007.c13_c02.pub2 Article Online Posting Date: July 15, 2007

Abstract Hydrocyclone technology has been suggested as a practical alternative for solid–liquid separations in many applications in diverse industries. The hydrocyclone is easy to install,test and operate, and requires very limited space. It represents an unsophisticated piece of equipment which runs in a continuous manner and it can be operated at lower costs thanmost of the solid–liquid separation devices. Hydrocyclones have been used in liquid–solid, liquid–liquid, or liquid–gas separations, and can perform varied duties in industries as diverse as mineral processing, chemical engineering, food processing, biotechnology, oil and gas.They have been used not only as separators, but also as clarifiers, classifiers, and in someother applications. This article reviews theoretical aspects of hydrocyclone operation andgives some insight into different applications of hydrocyclone technology.

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c© 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim10.1002/14356007.c13 c02.pub2

Hydrocyclones 1

Hydrocyclones

Enrique Ortega-Rivas, Food and Chemical Engineering Program, Autonomous University of Chihuahua;University Campus I, Chihuahua, Chih., 31170, Mexico

1. Introduction . . . . . . . . . . . . . . . 31.1. General Remarks . . . . . . . . . . . . 31.2. Principle of Operation . . . . . . . . . 32. Categories and Application . . . . . 42.1. Thickening . . . . . . . . . . . . . . . . 42.2. Clarification . . . . . . . . . . . . . . . 42.3. Classification . . . . . . . . . . . . . . . 42.4. Other Applications . . . . . . . . . . . 43. Theoretical Background . . . . . . . 43.1. Simultaneous Flow of Fluids and

Solids . . . . . . . . . . . . . . . . . . . . 43.1.1. Dynamics of Particles Submerged in

Fluids . . . . . . . . . . . . . . . . . . . . 53.1.2. Rheology of Suspensions . . . . . . . . 63.1.3. Flow of Suspensions . . . . . . . . . . . 73.2. Flow Patterns in Hydrocyclones . . 83.3. Mechanisms of Particle Separation 93.3.1. Equilibrium-Orbit Theory . . . . . . . 103.3.2. Residence-Time Theory . . . . . . . . . 103.3.3. Crowding Theory . . . . . . . . . . . . . 103.3.4. Turbulent Two-phase Flow Theory . . 103.4. Characteristics of Performance of

Hydrocyclones . . . . . . . . . . . . . . 113.4.1. Separation Efficiency, Cut Size . . . . 11

3.4.2. Capacity, Pressure Drop . . . . . . . . . 164. Effect of Variables on Hydrocyclone

Performance . . . . . . . . . . . . . . . 164.1. Operation Variables . . . . . . . . . . 164.2. Design Variables . . . . . . . . . . . . . 175. Selection and Design of Hydrocy-

clone Systems . . . . . . . . . . . . . . . 175.1. Analytical Solutions . . . . . . . . . . 185.2. Graphical Solutions . . . . . . . . . . 185.3. Manufactures’ Choice . . . . . . . . . 185.4. Dimensionless Scale-Up of

Hydrocyclones . . . . . . . . . . . . . . 195.4.1. Introduction . . . . . . . . . . . . . . . . 195.4.2. Definition and Derivation of

Dimensionless Groups for Hydrocy-clones . . . . . . . . . . . . . . . . . . . . 19

5.4.3. Scale-Up at Low Concentrations . . . 205.4.4. Scale-Up at High Concentrations . . . 215.4.5. Considerations for non-Newtonian

Behavior . . . . . . . . . . . . . . . . . . 215.4.6. Empirical Models . . . . . . . . . . . . . 225.4.7. Practical Applications . . . . . . . . . . 236. References . . . . . . . . . . . . . . . . . 26

Notation(Dimensions given in terms of mass,M,length, L, time, T, and temperature,θ)

A arithmetic mean, acceleration (L/T2)A area (L2)Ai area of inlet nozzle of hydrocyclone

(L2)A1n parameter dependent on the flowbehav-

ior indexC volume fraction of solids in suspensionCD drag coefficientC′

n parameter dependant on the flowbehav-ior index

Cy50 dimensionless cyclone numberD pipe diameter (L)Dc hydrocyclone diameter (L)Di inlet diameter of hydrocyclone (L)

Do overflowpipe diameter of hydrocyclone(L)

Du underflow pipe diameter of hydrocy-clone (L)

Ep partial efficiencyEt total efficiencyE′

t reduced total efficiencyEu Euler numberf fanning friction factorf pv purely viscous fanning friction factorf (x) frequencyFc(x) cumulative percentage oversize of sep-

arated solidsFD drag force (MLT−2)Ff (x) cumulative percentage oversize of non-

separated solidsF(x) cumulative percentage oversize of feed

solids

2 Hydrocyclones

g acceleration due to gravity (L/T2)G(x) grade efficiencyG′(x) reduced grade efficiencyH height of liquid column or liquid head

(L)H i height of rectangular inlet channel of

hydrocyclone (L)H25/75 sharpness indexkp empirical constant for a family of geo-

metrically similar hydrocyclonesk1, k2 constantsK constant, correlation constant of the

power lawK ′ fluid consistency index (MTn/L2)l vortex finder length (L)L hydrocyclone length (L)L1 length of cylindrical part of hydrocy-

clone (L)m exponent, mass (M)M mass flows rate of solids in suspension

(M/T)Mc mass flows rate of separated solids

(M/T)Mf mass flows rate of nonseparated solids

(M/T)n exponent; slope of the curve repre-

senting the power lawnp empirical constant for a family of geo-

metrically similar hydrocyclonesn′ flow behavior indexN revolutions per minute or per second

(1/T)O volumetric flow rate of overflow sus-

pension (L3/T)P pressure (M/LT2)q volumetric flow rate per unit area (L/T)Q volumetric flow rate (L3/T)r parameter function of a log-ln plot in

the coarse regionR radius of rotation (L)Rav average radius of rotation (L)Re Reynolds numberRep particle Reynolds numberRe∗ Reynolds number for power-law fluidsRf underflow-to-throughput ratios parameter function of the slope of the

log-ln plot in fine size regionsStk50 Stokes numberStk′

50 Stokes number including the reducedcut size

Stk∗50 Stokes number for power-law fluids

Stk∗50(r) Stokes number for power-law fluids in-

cluding the reduced cut sizet time (T)td detention time (T)ts settling time (T)T temperature (θ)u fluid-particle relative velocity (L/T)ut terminal settling velocity under gravity

(L/T)U volumetric flow rate of underflow sus-

pension (L3/T)v linear velocity, hydrocyclone character-

istic velocity (L/T)vg terminal settling velocity under gravity

(L/T)vi inlet tangential velocity (L/T)vo maximum tangential velocity (L/T)vr radial settling velocity (L/T)vt tangential velocity (L/T)V volume (L3)w vertical velocity at cyclone wall (1/T)x particle size (L)xa arithmetic mean of particle size (L)xc cut size (L)xg geometric mean of particle distribution,

mass median size of particle (L)xm mode of particle size distributionxo maximum particle size in sample (L)xr constant function of particles size range

(L)x0 particle size with zero centrifugal effi-

ciency (L)x50 cut size (L)x′

50 reduced cut size (L)x98 approximate particle size fully sepa-

rated (L)Z acceleration factorZ i width of rectangular inlet channel of

hydrocyclone (L)Greek

α constantγ viscosity coefficient for power-law flu-

ids (M/LT2−n).γ shear rate (1/T)∆ differenceθ hydrocyclone cone angleµ liquid absolute viscosity (M/LT)µo viscosity of pure solvent (M/LT)ρ liquid density (M/L3)ρm slurry density (M/L3)ρs solids density (M/L3)σ standard deviation

Hydrocyclones 3

τ shear stress (M/LT2)τw shear stress at tube wall (M/LT2)φ volume fraction of spheres in suspen-

sionω angular velocity (1/T)

1. Introduction

1.1. General Remarks

Hydrocyclones have been less employed thancentrifuges to develop high centrifugal forcesand perform separation of solids. Althoughhydrocycloneswere first patentedmore than 100years ago, industrial use of them was practicallynonexisting until the late 1940s. Hydrocycloneswere early utilized in the paper and mineral in-dustries, to become later popular in a larger num-ber of factories from chemical, cement, and nu-clear to the food, pharmaceutical, and oil indus-tries. Although hydrocyclones continue findingnew applications, the dearth of specialized lit-erature about them is surprising. With only twoknown books written in English since the 1980sand some attention paid to them in the literature,there is more to learn about hydrocyclones thanabout other solid–liquid separation techniques.

1.2. Principle of Operation

A hydrocyclone is a sedimentation device,which employs enhanced gravity force to sep-arate solid from a carrying liquid. This men-tioned force is in fact the centrifugal field pro-duced when a fluid suspension is pumped tan-gentially into a cone-cylindrical body. As a vor-tex is created, coarse particles move towards thewall and fines towards the axis. Flow is at firstdown the innerwall of the cylindrical section andthe cone, as far as the stagnation point near thecone apex. There, because the opening is small,the downward primary vortex is forced to turnupwards again, thus forming the secondary vor-tex. Thus, at the bottomof the cone theflowsplitsinto two streams, the underflow containing mostof the coarse particles, and the overflow withmost of the fines in it. The overflow pipe gener-ally protrudes into the cylindrical body, to formwhat is known as the vortex finder. A diagram

of a hydrocyclone is shown in Figure 1. As canbe concluded, separation is based on differencein settling velocities, as in sedimentation. Thus,size, density and shape of particles play a roleimportant in the operation.

Figure 1. Diagram of a hydrocyclone

Figure 2. Nomenclature and dimensions of hydrocycloneDc: cyclone body diameter,Do: overflow pipe diameter,Di:inlet diameter, [(4HiZ i)/π]1/2 for rectangular inlet chan-nels, l: vortex finder length, L1: cylindrical section length,L: hydrocyclone length, θ: cone angle, Du: underflow ori-fice

Typical sizes of hydrocyclones range from10mm to 2.5m in diameter, capacities of sin-

4 Hydrocyclones

gle units go from 0.1 to 7200m3/h, and pressuredrops vary from 0.34 to 6 bar. The efficiency,reported as cut size, lies between 2 and 250µm.The main advantages of the hydrocyclone areits simple, compact, and inexpensive construc-tion, its ease of operation (no moving parts), itsshort residence time, and its manageability ofsizes finer than those treated in mechanical clas-sifiers. Some disadvantages are its high powerconsumption, its high wear, its inflexibility andits problem with blockage, especially in smallunits. Figure 2 presents typical dimensions andstandard nomenclature of hydrocyclones.

2. Categories and Application

Hydrocyclones are very versatile pieces ofequipment. They can be employed as thicken-ers, clarifiers, classifiers and even in liquid–liq-uid separations. A quite useful and up-to-dateguide of applications and models of hydrocy-clones is given in [1].

2.1. Thickening

For thickening proposes, hydrocyclones haveproved to be efficient, with underflow concen-tration as high as 50% obtained with some ma-terial. Thus, they can easily compete in this fieldwith gravity thickeners, with advantages of lessspace requirement. The main problem in the op-eration, however, is the risk of blockage, buthydrocyclones with variable underflow orificeare employed to avoid this difficulty.

2.2. Clarification

When used in clarification, small diameterhydrocyclones with parallel multicyclone ar-rangement are preferred. Multiple cyclone unitswith six to several hundredhydrocyclones in par-allel are available and have been successfullyused.

2.3. Classification

Since the principle of operation of hydrocy-clones is centrifugal, they can be used to separate

solids from solids in a suspension according toparticle size. Sometimes, either coarse or fineparticles may be removed from the product, andhydrocyclones have performed such operationsknown as degritting or refining, and deslimingor washing, respectively. This classifying char-acteristic of hydrocyclones is also employed toimprove the performance of other filtration orseparation equipments. The coarse and fine par-ticles separated from hydrocyclones normallyfollow different paths in a processing plant, be-ing sometimes fed into other units, to finish as adifferent product.

2.4. Other Applications

Ashydrocyclones have beenused either as thick-eners or as clarifiers, they have also performedboth functions in one operation. In order to doso, two or more units are connected in series.One of them functions as thickener and the oth-ers as clarifiers. A typical arrangement, whichoperates with the thickener at the first stage, fol-lowed by two clarification stages, and the un-derflow of them returned to the feed, has beenwidely described in [2]. Other arrangements thathave also maximized the overall performancehave been analyzed in [1]. The centrifugal fea-tures of hydrocyclones give them possibilities toperform separation of two immiscible liquids.Hydrocyclones have been applied in separationof oil from water, in dewatering of light oilsand in producing highly concentrated samplesof lighter dispersed phases. Other applicationssuch as countercurrent washing of solids andseparation of gas bubbles from feed liquids haveas well been tried, giving satisfactory results.

3. Theoretical Background

3.1. Simultaneous Flow of Fluids andSolids

As hydrocyclones are usually fed with a disper-sion of solids in liquid, a study of the principalcharacteristics of suspension is necessary. Sinceconcentration can be vary widely in hydrocy-clone operations, particle–fluid interaction, aswell as proper rheology of thewhole suspension,

Hydrocyclones 5

are of the utmost importance. For a detailed de-scription of fluid dynamics and rheology see →Fluid Mechanics.

3.1.1. Dynamics of Particles Submerged inFluids

If a particle moves relative to the fluid in whichit is suspended, the force opposing the motionis known as the drag force. Knowledge of themagnitude of this force is essential if the parti-cle motion is to be studied. Conventionally, thedrag force FD is expressed as:

FD = CDAρu2

2(1)

where u is the particle–fluid relative velocity, ρis the fluid density, A is the area of the particleprojected in direction of the motion, and CD is acoefficient of proportionality known as the dragcoefficient. Assuming the drag force is due to theinertia of the fluid,CD would be constant and di-mensional analysis shows that CD is generally afunction of the particle Reynolds number, i.e.:

Rep =uxρ

µ(2)

where x is the particle size and µ the mediumviscosity; the form of the function depends onthe regime of the flow. This relationship for rigidspherical particles is shown in Figure 3. At lowReynolds number under laminar flow conditionswhen viscous forces prevail, CD can be deter-mined theoretically from Navier–Stokes equa-tions (see → Fluid Mechanics, Section 3.2) andthe solution is known as Stokes’ law and repre-sented by:

FD = 3πµux (3)

Figure 3.Drag coefficient versus particle Reynolds numberfor spherical particles

This is an approximation, which gives thebest results forRep→0; the upper limit of its va-lidity depends on the error that can be accepted.The usually quoted limit for the Stokes region ofRep = 0.2 is based on an error of about 2% inthe terminal settling velocity. Equations 1, 2 and3 combined give another form of Stokes’ law asfollows:

CD =24Rep

(Rep<0.2) (4)

For Reynolds numbers > 1000 the flow isfully turbulent with inertial forces prevailing,and CD becomes constant and equal to 0.44 (theNewton region). The region in-between Rep =0.2−1000 is known as the transition region, andCD is either described in a graph or by one ormore empirical equations.

For a particle ofmassm under the influence ofa field of acceleration a, the equation of motionis:

m

[dudt

]= ma−ma

[ρ

ρs

]−FD (5)

where ρs is the density of the solids and t is thetime.

In applications of hydrocyclones concernedwith separation of fine particles, which are allmost difficult to separate, the Reynolds numbersare low, often less than 0.2, due to the low val-ues of x and u. Therefore, it is reasonable alsothat the time necessary for the particle velocityto reach values very close to the terminal set-tling velocity is very short and being the field ofacceleration gravity, Equation (5) can be solvedto give:

ut =x2 (ρs−ρ) g

18µ(6)

in which the acceleration due to gravity g has re-placed a and ut is known as the terminal settlingvelocity under gravity.

The radial settling velocity in a hydrocyclonevr is due to the centrifugal acceleration, whichis proportional to the square of the tangentialvelocity of the particle, and indirectly propor-tional to the radius of the particle position. Asthe tangential motion of particle is unopposed,the tangential particle velocity can be taken asequal to the tangential component of the fluid

6 Hydrocyclones

velocity at the same point. The inclusion of thecentrifugal terms in Equation (6) leads simplyto:

vr =x2 (ρs−ρ)Rω2

18µ(7)

where R is the radius of the particle position andω is the angular velocity.

As the concentration of the suspension in-creases, particles get closer together and inter-fere with each other. If the particles are notdisturbed uniformly, the overall effect is a netincrease in settling velocity because the returnflow caused by volume displacement predom-inates in particles-sparse regions. This is thewell-known effect of cluster formation, whichis significant only in nearly monosized suspen-sions. With most practical widely dispersed sus-pension, clusters do not survive long enoughto affect the settling behavior and, as the re-turn flow is more uniformly distributed, the set-tling rate steadily declines with increasing con-centration. This phenomenon is referred to ashindered settling and can be theoretically ap-proached in three differentmanners: as a Stokes’law correction by introduction of a multiply-ing factor; by adopting effective fluid propertiesfor the suspension different from these of thepure fluid; and by determination of bed expan-sion with a modified version of the well knowCarman–Kozeny equation. All the approachescan be shown to yield essentially identical re-sults. Some important correlations accountingfor the hindered settling effect have been re-viewed in [3]. It was shown that their differencesare minimal and, according to this, the Richard-son and Zakii equation is an obvious choice inpractice. Such relation can be expressed as:u

ut= (1−C)4.65 (8)

where u is the settling velocity at concentrationC and ut is the settling velocity of a single par-ticle.

The relationship above applies only to free,particulate separation unaffected by coagulationor flocculation, andwhere all particles are of uni-form density.

3.1.2. Rheology of Suspensions

The rheological properties of suspension havebeen studied since the beginning of the 20th

century. The first research was done by Ein-stein[4] in his classical study of the viscosityof dilute suspensions of rigid spheres. His ap-proach is purely hydrodynamic, and his modelconsists of an isolated sphere situated in a simpleshear flow field in an infinite fluid. A number ofworkers have been extendingEinstein’s analysis[3, 5]. Three approaches have been presented:the theoretical basis of viscosity computation,the effect of particle texture and shape, and theeffect of concentration. Several relations havebeen developed for suspensions in with nearestneighbor interactions cannot be neglected.Guthand Simha [6] considered the first order effect ofspheres interactingwith one another. They foundthat:µ

µo= 1+2.5ø+14.1ø2 (9)

where µ is the viscosity of the suspension, µois the viscosity of the pure solvent and φ is thevolume fraction of spheres in the suspension. Alater correction gave a value of 12.6 for the lastconstant [7].

Several authors have made experimentalstudies of the effects of concentration on theviscosity of suspension of spheres. The datathey have proposed are considerably scattered.Thomas [8] has tried to find the sources of scatterin the data and found that scattering is causedin large part by variations in particle size. Forsmall particle sizes (diameters < 1–10µm) col-loidal forces become important and the viscos-ity begins to increase as particle size decreases.The viscosity is also shear rate-dependent in thiscase. For the particles larger than 1 to 10 µm,the particle Reynolds number becomes signifi-cant. The inertial effects results in an increase inrelative viscosity with increasing particle size.Thomas has developed a unique curve, by elim-inating diameter and shear rate effects. For lowconcentration data, such a graph can be repre-sented by:µ

µo= 1+2.5ø+11.4ø2 (10)

where all the components are already defined.The behavior of some specific systems has

also been reported in the literature. Lin andBrodkey [9] studied rheological properties of

Hydrocyclones 7

slurry fuel, concluding that they are shear-thinning under most conditions, but turn shear-thickening at extreme conditions. Griskey et al.[10] investigated the rheological behavior ofcornstarch dispersions and found that they gofrom dilatant (shear-thickening) behavior at lowshear rates to Newtonian behaviors at highershear rates. The effect of particle aggregationon suspension has also been studied. Devries[11] presented a number of experimental resultsconcerning the particle aggregation in polymerlattices induced or accelerated by simple shearflow. No stable flow is possible under these con-ditions, and the apparent viscosity is an increas-ing function of the time of shearing.

3.1.3. Flow of Suspensions

Some flow patterns of relative interest will be re-viewed. One of the most studied cases is that oftransport of suspensions such as slurries throughpipelines, due mainly to its occurrence in a widenumber of industrial processes. Most of the the-ory developed for flow through tubes applies tolaminar flow in smooth tubes. There are some re-lationships available for pressure-loss flow ratein purely viscous and viscoelastics flows. Re-lations for thixotropic and rheopectic systemsappear not to be available.

Under the assumptions that purely viscousbehavior prevails and that no slip occurs at thetube wall, the power-law equation for laminarflow is in the form [12]:

τw =D∆P

4L= K′

[8vD

]n′(11)

where τw is the shearing stress at the wall of thetube, D is the tube diameter, ∆P is the pressuredrop, L is the length of the tube, v the mean ve-locity, n’ is the slope of the line when the dataare plotted on logarithmic coordinates. For n’ =1, the fluid is Newtonian; for n’<1, pseudoplas-tic, or Bingham plastic if the curve does not gothrough the origin; and for n’ >1, dilatant. Theterm K’ is the consistency index; as the namesuggest, the larger its value the thicker or moreviscous the fluid.

The constant K’ may be related to the anal-ogous power-law constant K (see → Fluid Me-chanics, Section 4.1.2) as follows [13]:

K′ = K

[3n′+14n′

]n[8vD

]n−n′

(12)

if the fluid obeys the power-law, n = n’ and:

K′ = K

[3n+14n

]n

(13)

Since Equation (11) rigorously portrays thelaminar flow behavior of the fluid (provided n’and K’ are evaluated at the correct shear stress),one may use it to define a Reynolds number ap-plicable to all purely viscous fluids under lam-inar flow conditions. This dimensionless groupcan be derived simply by the substitution of(D∆P/4L) from Equation (11) into the usualdefinition of the fanning friction factor, i.e.:

f =D∆P/4Lρv2/2

(14)

such substitution leads to:

f =16γ

Dn′v2−n′ρ(15)

where γ = K ′8n′−1 and all the remaining com-ponent as already defined.

By letting f = 16/Re as for Newtonian flu-ids in laminar flow, the above mentioned gener-alized Reynolds number can be obtained as:

Re∗ = Dn′v2−n′

ρ

γ(16)

If the equation is desired in terms of K in-stead of K’, Equation (12b) may be substitutedinto Equation (15) and:

Re∗ = Dnv2−nρ

K8n−1[ 3n+1

4n

]n (17)

For Newtonian fluids n′ = 1 and K ′ = µ,so γ reduces to µ and Re∗ in Equation (16)transforms to the familiarDv/ρ/µ showing thatthis traditional dimensionless group is merely aspecial restricted form of the more general de-scribed here.

Non-Newtonian fluids in turbulent flow gen-erally show lower friction factors and, conse-quently, lower pressure drops than Newtonianfluids at corresponding Reynolds number. A de-tailed analysis of non-Newtonian flow at tur-bulent regime began with two papers publishedin 1959 byDodge andMetzner [14] and ShaverandMerril [15].Dodge andMetzner used solu-tions of carboxymethyl cellulose and carbopal (aB. F.Goodrich soluble thickener), aswell as clay

8 Hydrocyclones

suspensions. They presented a viscous correla-tion in terms of parameters from shear-stress–shear-rate data and concluded that except for thecarboxymethyl cellulose, the behavior of thesematerials could be correlated with the followinggeneralization of the Newtonian friction factor:√1f= A1nlog

[Re∗(f)1−0.5n′

]+C∗

n (18)

where A1n and C ′n are parameters dependent

on the flow-behavior index n. While the choiceof power-law equation in the derivation requiresthat the Reynolds number used in Equation (17)be the power-law special case of Equation (16),it has been shown [14] that any errors due tothis approximation are less important under tur-bulent flowconditions than in the laminar region.The utility of Equation (17) and of Reynoldsnumber outside the laminar region has beenshown diagrammatically in [14]. The authorsfound excellent agreement between experimen-tal and extrapolated data. Furthermore, devia-tions from smooth curves were no greater forthose fluids, which did not obey the power law,than for those which did. The parameters A1n

and C ′n in Equation (17) must be evaluated em-

pirically, just as in the simpler case ofNewtonianbehavior.

By far, most of the study of the flow behav-ior of non-Newtonian suspensions has been de-voted to monosized and monoshaped systems,mainly of spherical particle geometry. In real-ity, however, solid–liquid mixtures usually con-sist of dissolved solids with a variety of particlesizes, shapes, and concentrations. The availabletheory for the behavior of non-Newtonian sus-pensions is, therefore, of a limited application,and when dealing with real systems, empiricalcorrections are necessary to fully explain the sus-pension properties.

Studies of some real applications such asslurry transport are also encountered in the liter-ature. The slurry to be transported may have set-tling or nonsettling characteristics. Sand in wa-ter, salt in benzene, and clay in drilling mud aretypical examples of settling slurries, while pa-per pulp is a good example of nonsettling slurry.The law governing the settling rate of particles atlow Reynolds numbers is the well know Stokeslaw. Settling phenomena of slurries in pipelines,

as well as modifications of original Stokes lawfor flocculated suspensions and particles of oddshapes, have been studied by Thomas [16]. Theturbulent regime is sometimes preferred to trans-port slurries within pipe in order to prevent set-tling, and to provide high throughputs. In thiscase, the viscosity of the suspension has beennormally used to correlate the turbulence fric-tion factors.

The problem of distribution and mixing ofsolids in turbulent slurry flow has been stud-ied. The magnitude of flow velocity or Reynoldsnumber required for maintaining turbulent mix-ing of solid–liquid slurries, may be computedfrom the following equation:

ρv2

(ρs−ρ) gx= K′

[ρmvD

µ

]0.775 (19)

where ρ is the liquid density, ρs the solid density,ρm the slurry density, v the minimum standardvelocity, g the acceleration due to the gravity, Dthe mean particle diameter, µ the viscosity andK’ a constant. When densities of solids and liq-uids are known, along with the volume fractionof solids in the slurry, the density of the mixturemay be calculated by:

ρm = Cρs+(1−C) ρ (20)

where C is the volume fraction of solids in theslurry. Equation (18) is recommended for meandiameters between 50 and 500µm.

3.2. Flow Patterns in Hydrocyclones

The flow pattern in a hydrocyclone is com-plex. However, it is normally accepted that thehydrocyclone fluid flow consists of the three ve-locity components: tangential, vertical, and ra-dial. Figure 4 shows a diagrammatically repre-sentation of these three velocity distributionswithin a hydrocyclone. With respect to the tan-gential component vt, the linear velocity of thefeed stream at the inlet point is given by:

vt =Q

Ai(21)

whereQ is the volumetric flow rate and Ai is thearea of the inlet nozzle.

Hydrocyclones 9

Figure 4. Velocity distribution profiles within a hydrocy-clone

As the flow develops in a spiral manner to-wards the air core, the circular speed increases asthe diameter of rotationdecreases.Under no fric-tion loss conditions, the angular speed remainsconstant and is given by:

vtR = constant (22)

where R is any radius of rotation.In practical systems frictional losses result in

a progressive decrease in tangential speed, thusEquation [21] needs to be modified, e.g.:

vtRn = constant (23)

where: 0<n<1.Experience has shown that the value of n de-

creases with increasing solids contents, with amaximum value of about 0.3 for solids contentsof about 60wt%. For normal operating con-ditions of 15 to 25% of solids approximately,Trawinski[17] has suggested an average valueof 0.5.

The maximum tangential velocity will occurin the secondary vortex immediately adjacent to

the air core. Taking the proposed average valueof 0.5, this maximum velocity will be theoreti-cally described by:

vo = vt

[Di

Do

]1/2(24)

Practically, the limit on themaximum tangen-tial velocity is given by pressure drop across thehydrocyclone. Under ideal conditions of no fric-tion loss, the following relationship describesthis maximum velocity:

vo =[2∆P

ρm

]1/2(25)

where ∆P is the pressure drop and ρm is thedensity of the slurry. As can be seen from Figure4b, the profile of the vertical velocity componentshows a well-defined position of zero velocityoutside of which there is a low speed down-wards, and inside of which the flow is muchhigher and upwards. This locus of zero verti-cal velocity (LZVV) follows the profile of thecyclone.

The radial component of velocity is inward,and accurate measurement of it is difficult be-cause its magnitude is small. Apparently, suchspeed decreases proportionally to radius de-creasing, from a value that can be expressed by:

vr = wtan[θ

2

](26)

where w is the vertical velocity at the wall andθ is the angle of the cone.

The radial position at which this velocity fallsto zero is not known precisely. Figure 4c showsthe radial component of velocity.

3.3. Mechanisms of Particle Separation

According to the flow patterns just described,several models to explain the actual mecha-nism of particle separation have been devel-oped. Each model works well for particularhydrocyclones only, the models are not of gen-eral application, because every one relies on asingle dominant feature of the flow inside thehydrocyclone. There have been at least four ap-proaches to describe the behavior of particlesin a hydrocyclone: the equilibrium-orbit theory,the residence-time theory, the crowding theoryand the turbulent two-phase theory.

10 Hydrocyclones

3.3.1. Equilibrium-Orbit Theory

Anequilibriumorbit is proposed at a radius posi-tion, at which the inward drag on the particle dueto the inward radial velocity of the fluid counter-balances the outward force to the liquid rotation,i.e.:

πx3

6(ρs−ρ)

v2t

R= 3πµvrx (27)

or:

x2

18(ρs−ρ)

µ=

Rvr

v2t

(28)

where x is the particle diameter or size, and thedensities and velocities are as previously de-fined. If vt∼ (v/Rn) and vr∼ (v/Rm), wherev is the inlet velocity, then:

x2

18

[ρs−ρ

µ

]=

[K

v

]R1+2n−m (29)

For given inlet velocity and liquid, the radiusof the orbit is proportional to the particle size. IfR is greater than the radial position for zero ver-tical velocity, it is assumed that all particles willbe collected. If R is less than the radial position,all particles will be carried away in the under-flow. Thus, a particle will have a 50% chanceof removal if the radius of its equilibrium orbitis equal to that of the zero vertical velocity. Us-ing this approach,Bradley [7] derived a relationmaking assumptions to the position of the locusof zero vertical velocity profile.

3.3.2. Residence-Time Theory

This theory advocates the importance of the timespent in the hydrocyclone. Assuming the spiralhas a constant velocity equal to the average in-let velocity, and supposing the liquid follows Ncomplete spirals at an average radius Rav, theresidence time will be:

t =[2πRav

v

]N (30)

a particle of size x will travel a distance L in thistime t where:

L

t= v =

x2 (ρs−ρ)18µ

[v2

R

](31)

Combining Equations 30 and 31 the followingrelationship is obtained:

x2 =9µL

Nπv (ρs−ρ)(32)

This is a form similar to Equation 29 withoutthe dependence on radial positions.

Using direct analogy with gravity settling,Trawinski [22] proposed another simple ap-proach, which may be considered as a variationof the residence-time theory.He reported the fol-lowing equation:

xc =[

18µqg (ρs−ρ)Z

]1/2(33)

where xc is known as the cut point, q equals(Q/A) and Z is the acceleration factor. Includingfurther considerations, e.g., for capacity and theseparating area (surface of the cylinder formedby the air core), Trawinski [17] also proposed:

xc = k1

[18µ

(ρs−ρ) g

]1/2[DcDi

l

]1/2(H)−0.25 (34)

where k1 is a constant, H is the liquid head, andall the geometric characteristics are as definedin Figure 2.

3.3.3. Crowding Theory

Due originally to Fahlstrom [18], this theoryproposes that the cut size is a function of thecapacity of the underflow orifice and the par-ticle size distribution. The crowding effect canswamp the primary interaction to the extent thatthe cut size can be estimated from the mass re-covery to the underflow. The support to this the-ory has been given mainly by Bloor And Ing-ham [19], by means of the mathematical mod-els developed to describe the fluid mechanics ofhydrocyclones.

3.3.4. Turbulent Two-phase Flow Theory

This theory states the importance of the effectcaused by turbulent flow in hydrocyclones. Ac-cording to this, it is proposed that separationtakes place under the influence of the centrifu-gal field and the turbulent transport in the two-phase flow. The influence of turbulence can bedescribed by an eddy diffusion coefficient equalto, or smaller than the diffusion of the fluid parti-cles. The assessment of the influence of such dif-fusion on separation is very difficult in practice.

Hydrocyclones 11

Bloor and Ingham [19] have also contributed tothe theoretical background of this theory. Theyderived an analytical form of the radial velocityand found an analytical solution to the equationof motion for the tangential speed. They alsodeveloped a more elaborated and physically re-alistic model, for the eddy viscosity based on thePrandtl mixing theory, which greatly simplifiedthe equation of motion.

Schubert and Neesse [20] proposed a set ofequations and derived two models for turbulentcross-flow wet classification: the suspension-partition model and the suspension-tappingmodel. In the former the flow is divided intooverflow and underflow without changes in thetotal cross-section, whereas in the latter over-flow and underflow are tapped from the mainflow through small outlet openings. Accordingto them, the suspension-tapping model is analo-gously applicable to the separation in hydrocy-clones.

3.4. Characteristics of Performance ofHydrocyclones

The most important features of performance ofhydrocyclones are the particle cut size, the pres-sure drop and the volume throughput. Previouswork has established the cut size as the best wayto predict efficiency in hydrocyclones. In orderto understand and utilize the cut size concept, itis necessary to deal with at least two topics, i.e.,particle size analysis and efficiency of solid–liq-uid separation (see→ Particle SizeAnalysis andCharacterization of a Classification Process; →Solid–Liquid Separation, Introduction).

3.4.1. Separation Efficiency, Cut Size

The solid phase of suspensions to be treatedin solid–liquid separation equipment generallyconsists of an immense number of particles ofdiverse sizes and shapes. All this population ofparticles needs to be identified or characterized.The frequency of occurrence of particles of ev-ery size present, arranged and presented in a sta-tistical manner, is known as the particle size dis-tribution. The most common way of presentingsuch distributions as well as the types of distri-butions important to particles technology, can be

found in the specialized literature [21, 22] (see→ Particle Size Analysis and Characterizationof a Classification Process).

In solid–liquid separation it is important toknow the particle size distribution in order toidentify which part of it will be separated, andtransform this quantity in ameasure of efficiency(→ Particle Size Analysis and Characterizationof a Classification Process, Section 2.1). Thecommon way of presenting particle size data forsolid–liquid separation purposes is in form ofa plot. The most common ones are equivalentsphere diameters, equivalent circle diameter, andstatistical diameters. The equivalent sphere di-ameter is the diameter of a sphere which hasthe same property as the particle itself. Such aproperty could be the settling velocity. A diam-eter derived from the settling velocity is knownas Stokes diameter and is a very useful quantityfor solid–liquid separation, especially to thosetechniques in which the particle motion relativeto the fluid is the governing mechanism.

The amount of particle matter which belongsto specified size classes on the particle axis maybe also represented in several ways. Number ofparticles andmass of particles are the most com-mons ones, but surface area and volume are usedas well. For solid–liquid separation techniques,the most convenient form of expressing amountof particle matter is by mass, because the bal-ances necessary to define performance are nor-mally mass balances.

In general, particle size distributions can bepresented as frequencies, f(x), or cumulative fre-quencies, F(x), which are related to each otherby following equation:

f(x) =dF (x)dx

(35)

the graphical representation of a particle size dis-tribution is usually plotted in a cumulative form.In a typical cumulative plot, points are enteredshowing the amount of particulate material con-tributed by particles below or above a specifiedsize. Hence, the curve presents a continuouslyrising or deceasing character. These oversize andundersize distributions, as illustrated in Figure5, are simply related by:

F (x)oversize = 1−F (x) (36)

where F(x) is the cumulative fraction undersize.

12 Hydrocyclones

Figure 5. Relationship between frequency and cumulativedistributions

A cumulative plot will, therefore, include abroad range of particle sizes. It is often conve-nient, however, to refer to a single characteristicsize for system. Many characteristic sizes havebeen proposed, most of them involving a math-ematical formula. An important one, which canbe read off any cumulative plot of the particlesize data, is the median particle size. It is de-fined as that particle size for which the particleamount equals 50% of the total. If the parti-cle size is represented by number, such point iscalled the numbermedian size. If mass is used asthe measure of particle amount, this parameteris known as the mass median size. The distribu-tion between number and mass median is veryimportant, since they differ generally by a con-siderable amount. Such difference means thatnumber and mass cumulative plots do not agreefor the same system of particles. The weight of aparticle, which varies as the cube of its diameter,accounts for this mentioned disagreement.

For practical purposes, it is reasonable to fitan analytical function to experimental particlesize distribution data, and then handle this func-tion mathematically in further treatment. It is,for example, very much easier to evaluate meansizes from analytical functions from experimen-tal data. Several different distribution functionscan be found in the literature (→ Particle SizeAnalysis and Characterization of a Classifica-tion Process, Section 2.3). An exhaustive reviewof some of them has been presented [23].

The normal distribution is widely used inmost fields of science for the representation ofpopulations. The normal distribution function isgiven by:

y =1

σ√2πexp

[− (x−a)2

2σ2

](37)

where y is the probability density, x the diameterof the particle, a the arithmetic mean, and σ thestandard deviation. From the normal function,if the arithmetic mean a is zero, the probabilityof occurrence within the interval form the mean(zero) to the value x, i.e., F(x) is given by theerror function:

F (x) =1

σ√2π

x∫0

exp[− x2

2σ2

]dx (38)

where σ and x have the same meaning as de-scribed in the normal function.

Materials with a normal distribution of parti-cle size are relatively rare and are found chieflyamong the particulates produced by chemicalprocesses like condensation or precipitation.The importance of this function, however, is thatit provides an idealized error distribution builtupon the assumption that elementary errors orsmall causes combine at random to produce theobserved effect.

The log-normal distribution is probably themost widely used type of function; it is again atwo-parameter function, it is skewed to the rightand it gives equal probability to ratios of sizesrather than to size differences, as in the normaldistribution. Furthermore, the log-normal func-tion is the most useful one among the differenttypes of functions. It can be expressed in thefollowing form:

f(x) =1

xlnσg√2πexp

[− (lnx−lnxg)2

2ln2σg

](39)

where f(x) is the size distribution function forparticle size x, xg is the geometric mean of thedistribution, and σg the geometric standard de-viation of lnx.

The log-normal distribution has the importantadvantage of ease of conversion from one typeof size distribution to another. It can be shownmathematically that all four particle size distri-butions, by number, length, surface, and volume(mass), when plotted on log-probability paperare parallel lines with equal linear spacing.

The Rosin–Rammler distribution function isanother equation widely used in particle sizemeasurement. It is a two-parameter function,usually given as cumulative percentage oversize:

F (x) = exp[−

(x

xr

)n](40)

Hydrocyclones 13

where xr is a constant giving a measure of theparticle size range present and n is another con-stant characteristic of thematerial under analysisand gives a measure of the steepness of the cu-mulative curve. The frequency distribution is ob-tained by differentiation of Equation 40, whichcan be reduced to:

log[ln

1F (x)

]= nlogx−nlogxr (41)

which gives a straight line if log (ln 1/F/ (x))is plotted against lnx. This is the basis for theRosin–Rammler graph paper because it is thesize corresponding to 100/e = 36.8% and nis the slope of the line. Rosin–Rammler chartsfromGerman sources contain edge scales,whichwith the aid of a parallel rule allow direct estima-tion of n. For accuratework, the use of large sizes(32.4× 25.4 cm) charts designed by Harris [24]is recommended. The various mean sizes avail-able may be easily calculated from the Rosin–Rammler equation; they all involve mathemati-cal tables.

The Harris model is a three-parameter equa-tion, which is very versatile and fitsmany empir-ical size distributions. Harris [24] showed thatmost of the widely used two-parameter equa-tions are in fact special cases of the equation:

F (x) =[1−

(x

xo

)s]r

(42)

where F(x) is cumulative percentage oversize,xo is the maximum size in the sample, s is a pa-rameter concerned with the slope of the log–lnplot in the fine region and r is a parameter con-cerned with the shape of the log–ln plot in thecoarse region.

The ways for measuring particle size are di-verse and have been largely improved in re-cent years. Sieving and sedimentation are thetraditional ones, but microscopy, laser diffrac-tion, and stream scanning techniques are cur-rently spreading and finding applications. Sev-eral methods for analytical determination of par-ticle size analysis have been reviewed [23]. Al-though the most novel techniques have the ad-vantage of quick response, they have proved tobe very selective. Therefore, most of them areof quite limited application. A rule of thumbshould be to use the analytical technique whoseindirect measurement agrees, as much as pos-sible, with the specific application. For exam-ple, in solid–liquid separations one is concerned

with particles settling by gravitational forces, sotechniques using this sort of forces to evaluateparticle size distribution would be most appro-priate.

To evaluate the efficiency of separation it isnecessary to take into account that solid–liq-uid separation is basically an imperfect process.Whereas the underflow is always wet slurry, theoverflow can be considered as a turbid liquid.This general behavior is critic in hydrocyclones,as they always, despite the presence of solids inthe liquid, will split the flow into two streams.Therefore, the aim of operation of a hydrocy-clone will be not only to obtain the above-mentioned slurry, but also to deliver is as freefrom liquid as possible. Equally, for clarificationpurposes, the overflow should be drawn from thehydrocyclone with the least possible concentra-tion of solids. As Tenberger and Rietema [25]have stated, a single efficiency number can neverbe capable of fully describe the result of separa-tion, except when it is ideal.

The imperfection of solid–liquid separationhas caused the need to express efficiency by dif-ferent means. A good review of these mentionedefficiencies is presented in [26].

The first and most obvious definition of sep-aration efficiency is simply the overall mass re-covery as a fraction of the feed flow rate. Ac-cording to Figure 6:

Et =Mc

M(43)

where all the components are as defined in Fig-ure 6.

If there is no accumulation of solids in theseparator then:

M =Mc+Mf (44)

and there is a choice of three possible combi-nations of the material streams for the total ef-ficiency testing. It can be shown [3] that if allthe operating conditions are equal, the most ac-curate estimation of the local efficiency comesfrom the two leaving streams.

As has been already mentioned, hydrocy-clones act as flow dividers. Thus, they also splitthe solids in at least the same ratio, as is the ratioof underflow to throughput, Rf :

Rf =U

Q(45)

14 Hydrocyclones

Figure 6. Schematic diagram of a separator. M: mass flowrate of solids in the feed, Mc: mass flow rate of separatedsolids,Mf : mass flow rate of nonseparated solids, F(x): cu-mulative percentage oversize of feed solids, Fc(x): cumula-tive percentage oversize of separated solids, Ff (x): cumula-tive percentage oversize of nonseparated solids,Q: volumet-ric flow rate of feed suspension, U: volumetric flow rate ofunderflow suspension, O: volumetric flow rate of overflowsuspension

The total efficiency defined in Equation 43will thus include the effect of this flow split-ting known as dead flux. For this reason, a betterway of expressing efficiency of separators suchas hydrocyclones, is by means of a reduced ef-ficiency which has been defined as:

E′t = Et−Rf

1−Rf(46)

If complete separation is achieved, providingthat there is no accumulation of solids, the valueof the total efficiency from Equation 43 will bethe unit, and so will be the value of the reducedtotal efficiency. If, on the other hand, there is noseparation at all, Et will equal Rf in order to sat-isfy the requirements of an efficiency definition,leading to a value of zero in Equation 46.

The total efficiency defined by Equation 43includes all particle sizes present in the feedsolids. If only a narrow range of particle sizesis of interest, another efficiency of separationparticular to that range can be defined. A math-ematical expression of such partial efficiency is:

Ep =[Mc

M

]x1/x2

(47)

where x1 and x2 represent the particle size limitsof a definite range.

If the particle size range in Equation 47 be-comes infinitesimal, the obtained efficiency cor-responds to a single particle size x and it is knownas the grade efficiency, defined by:

G(x) =[Mc

M

]x

(48)

The grade efficiency has become a very use-ful definition, because most industrial powdersconsist of an infinite number of differently sizedparticles. Thus, a single particle size really corre-sponds to a range of particles having almost sim-ilar sizes. Therefore, the grade efficiency ofmostseparation equipments is a continuous functionof x. This function is seldom expressed analyti-cally but graphically. An S-shaped curve is usu-ally obtained for separators like hydrocyclones,in which inertial or gravity body forces performthe separation.

As the value of the grade efficiency has thecharacter of probability, plotting the probabilityfor any given size fraction against particle sizewould give a curve as known in Figure 7. Thissort of curve is normally called a grade efficiencycurve.

Figure 7. Grade efficiency and reduced grade efficiencycurve for hydrocyclones

A grade efficiency curve for hydrocyclone isderived from screen analysis data on the feed,overflow and underflow streams. As mentionedbefore, it is practically impossible to fractioncommon systems of particles in a finite num-ber of sizes. It can be shown [27] that a practi-cal grade efficiency curve is really derived froma stepwise calculation, drawing a line throughthe midpoints of size intervals. A curve thus de-rived does not pass through the origin. This canbe explained bearing in mind that, as has beenpreviously emphasized, a hydrocyclone is a flowdivider, so the underflow always contains a cer-tain quantity of very fine particles which simplyfollow the flow, and are split in the same ratioas the liquid. The apparently finite efficiency for

Hydrocyclones 15

fine particles is, therefore, equal to the underflowto throughput ratio Rf as shown in Figure 7. Areduced grade efficiency, similar to the reducedefficiency represented by Equation 46 can thenbe obtained as:

G′(x) =G(x)−Rf

1−Rf(49)

As can be seen in Figure 7, the correspondentcurve to this definition does cross the origin.

Hydrocyclones are among those equipmentswhose separation performance is highly depen-dent on particle size. Thus, according to this, anoverall efficiency of separation is not the bestway to evaluate their performance. For this rea-son, it is advisable to express their efficiency foreach size of particle in the range measured. Asexperience has shown, the only single number,which in some way gives the separation powerof a hydrocyclone, is the cut size x50 (for a def-inition of cut size see → Particle Size Analy-sis and Characterization of a Classification Pro-cess, Section 3.1.4). All particles above the cutsize will be generally going to the underflow,whereas those below the cut size will be nor-mally reported to the overflow.

As can be concluded, the cut size is derivedfrom a grade efficiency curve. As the calculationand plotting of a full grade efficiency curve is atime-consuming task, alternative ways of deter-mining the cut size have been proposed [28, 29].

The sharpness of separation can be relatedto the shape of the curve in a number of man-ners. Knowing the grade efficiency curve, com-parisons of classification sharpness of differentequipments can bemade by plottingG(x) againstthe dimensionless size x/x50, and comparing theresultant normalized curves. To define the curvesteepness, a ratio of two sizes corresponding totwo different percentages on the grade efficiencycurve on either side, and 50% equidistant, canbe used. This parameter is called the sharpnessindex and is represented by:

H25/75 =[x25

x75

](50)

It was previously stated that the grade effi-ciency curve does not go through the origin. Thecut size as has been defined is derived from thiscurve. If, in order to practically assess the per-formance of hydrocyclones, a reduced grade ef-ficiency curve is used, the particle size which

gives a 50% efficiency in such a curve is calledthe reduced cut size and is represented by x′

50.The maximum obtainable efficiency related

to particle size would be that minimum particlesize with 100% probability of being reported tothe underflow. Graphically, by extrapolating theend part of the curve to the horizontal axis, suchsize will be obtained. It has been proved thatin practice, the maximum of the efficiency isaround 98%, and the minimum size correspon-dent to this efficiency is represented by x98 andknown as the approximate limit of separation.

Several correlations have been proposed inliterature to evaluate the cut size. They are ei-ther empirical or theoretical, and are expressedin the traditional British System of units, as wellas in SI units, even in both. Perhaps the mostimportant criterion for classifying the proposedcorrelation for cut size, is by dividing them intotwo groups considering whether the feed con-centration has been taken into account. Themaincorrelations, which do not consider the feed con-centration as a variable, will be reviewed as fol-lows.

Bradley [2] proposed:

x50 =[18πµ(1−Rf)16LQ(ρs−ρ)

]1/2[2.3Do

Dc

]n [D2

i

α

](51)

where Q is the flow rate, Do, Dc and Di are thedimensions defined in Figure 2, and (and n areempirical constants depending on the cyclonedesign and the fluid properties.

Rietema [30] derived a dimensionless, char-acteristic cyclone number Cy50 represented by:

Cy50 = x250 (ρs−ρ)

L∆P

µρQ(52)

where ∆P is the pressure drop. Cy50 is deter-mined experimentally and is not directly relatedto the more important hydrocyclone variables.However, Rietema has demonstrated the use-fulness of the parameter and quotes a value of3.50 for optimal separation, corresponding tothe conditions: L/Dc = 5, Di/Dc = 0.28,Do/Dc = 0.34 and l/Dc = 0.4, where all thedimensions are as defined in Figure 2.

Dahlstrom [31] proposed:

x50 =C(DoDi)0.68

Q0.53

[1.73ρs−ρ

]1/2(53)

where C is a constant sensitive only to majorchanges in the cyclone dimensions. This equa-tion holds well for cyclones in which the length

16 Hydrocyclones

of the cylindrical section equals that of the cone,and has been shown to hold for diameters of 3to 14 inches (7.5 to 35 cm), for flows containingup to 20% solids by weight.

Yoshioka and Hotta [32] developed an equa-tion based on the orbital concept and equilibriumcone surface defined by the end of the vortexfinder and the cone apex. The equation is:

x50 = 0.2D0.1c D0.6

i D0.8o

[µ

Q(ρs−ρ)

]1/2(54)

which is expressed in SI units; the constant 0.2was experimentally evaluated.

De Gelder [33] has derived an equation,which does not include experimental values:

x0 = Do

[0.349Re(Dc−kDo)

Di

] [ρs

ρ−1

]1/2(55)

where Re is the Reynolds number, x0 is the di-ameter of particlewhich is just not collected, i.e.,with centrifugal efficiency of 0% and k is a con-stant, functionofD2

i /DoDc.AlthoughEquation55 was first developed for gas cyclones, it is saidto hold well for hydrocyclones.

Lynch and Rao [34] presented the followingempirical correlation:

logx′50 = Do

2.6−Du

3.5+∆P

10.7−Qlo

52+K (56)

where x∗50 is in micrometers, Do and Du are in

inches, ∆P is in pounds per square inch (psi),Qlo (mass flow rate of the liquid in the overflow)is in ton/h, and K is a function of the materialand the hydrocyclone (2.0 for silica and 2.5 forcopper ore).

3.4.2. Capacity, Pressure Drop

The capacity of a hydrocyclone can be evalu-ated in terms of the volume flow rate delivered,also known as throughput, which depends onthe available pressure drop. Thus, there is a lossof pressure across the unit. The pressure dropis an important variable and is more easily de-fined than efficiency. Relationships between Qand ∆P can be developed by means of estab-lished theory for the flow of liquids in pipes.There are a number of pressure drop correla-tions reported in the literature, some of whichwill be described.

Trawinski [35] proposed the correlation:

Q = KDiDo

[∆Pg

ρ

]1/2(57)

where K is a factor, which contains diameter ra-tios, fraction loss, and cone angle variables. Forθ = 15◦−30◦, K equals 0.5.

Bradley’s approach [2] leads to the follow-ing expression:

(∆P/ρ)(v2

i /2g)=

α2

n

[(Dc/Do)2n−1

](58)

where the left-hand side group is the pressuredifference in terms of inlet velocity heads and αis the inlet velocity loss coefficient vc/vi whereasn is the power from Equation 23.

4. Effect of Variables onHydrocyclone Performance

A single conclusion can be made from the pre-viously survey: the operation of hydrocyclonesis quite complex. There is not a unified theory tofully explain the mechanisms of flow and parti-cle separation inside a hydrocyclone. It is nor-mally accepted that the overall behavior of theparticles of solids inside a unit will depend onfactors contributed by the liquid, by the solid,and by the apparatus design. These factors maybe interrelated or independent of each other. Inorder to study the effect of such factors upon theperformance of hydrocyclone units, they havebeen usually divided into operational variablesand design variables.

4.1. Operation Variables

First of all, a pressure drop must exist in or-der to drive the feed suspension across the unit.An increment in this pressure drop will decreasethe cut size as well as increase the sharpnessof separation and flow rate. According to this,great mass recoveries could be obtained raisingthe pressure drop. Although such fact is literallytrue, it is normally an uneconomical measurebecause large pressure loss increases are nec-essary. As has been mentioned earlier, practicalvalues of pressure drop range between 0.34 and6 bar. However, for small cyclones, Trawinski[27] has suggested an upper limit of 4 bar. Asin other separation techniques, a finite density

Hydrocyclones 17

difference between the phases involved is essen-tially necessary.Without it, no separation can beachieved. As expected, experience has shown anincrease in separation efficiency as the densitydifference increases.

The effect of feed solids concentration onseparation performance is well recognized inpractice. Generally, increasing input concentra-tions reduces the total efficiency. Svarovsky andMarasinghe [36] have proposed a semiempiri-cal correlation,which allows scale-up predictionof performance with feed concentrations higherthan 8 vol%. Neesse et al. [37] compared di-lute flow (low solids concentration of the feed)and dense flow (high solids concentration of thefeed) separations, focusing their study on the ef-fect of turbulence.

Perhaps the least understood effect on per-formance of a hydrocyclone is that of the vis-cosity. Very little quantitative information existson the literature about it. It is normally acceptedthat viscosity has little effect on separation ef-ficiency. From simple theory it can be provedthat medium viscosity will only have an effectat low Reynolds numbers (i.e., laminar flow),but because turbulence is promoted by pumping,the effect of viscosity will only be appreciablewhen the flow is forced by static head or in verylarge units. Nappier-Munn [38] found concor-dance with theory about viscosity effects, whileWilliamson et al. [39] studied the effect of vis-cosity, along with pressure drop, in reducing theminimum cut size of particles that can be sepa-rated effectively. They found that cut size fallsas the pressure drop rises and as viscosity is re-duced.

The effect of less common variables has alsobeen studied.Fontein et al. [40] examined the in-fluence of some uncommon parameters such asthe roughness of the cyclone wall, as well as theshape of the solid particles on suspension. Theyfound that rough-walled cyclones show lower ef-ficiencies than smooth-walled ones. Accordingto them, this is mainly due to the fact the rotationflow is greatly retarded by the rough wall, thusdecreasing the centrifugal force, which affectsseparation.

4.2. Design Variables

Some modifications and recommendationsabout the geometry of hydrocyclones have ap-peared in the literature, mainly from manufac-tures.Despitemanyvariations in design and sug-gestions for varied configurations, the so-calledstandard cyclones, such as the Rietema cyclone,have proved the most efficient in separation andcapacity.

The most common materials of construc-tion are steel, aluminum oxide, ceramics,polyurethane, and other plastics. Sometimes theinner body is lined with hard materials in orderto minimize wear caused by operation. Soft rub-ber is popular and suitable where temperaturesdo not exceed 60◦C and where hydrocarbon oilsor solvents are absent. Ceramic liners can alsobe used. Wear-resistant metals are useful whenparticle sizes are above 100 µm or where trampmaterial is suspected, which could damage rub-ber linings.With temperatures above 60 ◦C or inpresence of hydrocarbons, neoprene or nitrile, aswell as polyurethane rubbers have been success-fully employed.

The effects of some geometry variables onhydrocyclone performance are shown in Table1.Table 1. Effects of some design variables on hydrocycloneperformance

Variable EffectCyclone diameter increases cut size increases, pressure drop

usually decreasesCyclone inlet diameter increases gravity force in cyclone

decreases, cut size increases,capacity falls, pressure dropdecreases

Overflow diameter increases cut size increases, risk of coarsesizes evident

Underflow diameter increases brings excess fines from liquidphase into underflow

Cyclone shape becomes longer decreases cut size sharpnessseparation

Cyclone wall become rougher capacity increases, efficiencydecreases

5. Selection and Design ofHydrocyclone Systems

Hydrocyclones differ from other solid–liquidseparation equipments as theyhave a broadnum-ber of variables involved in their operation. Theinfluence of some variables is not completelyunderstood, and their effect may be completely

18 Hydrocyclones

different from one unit to another. Theses aresome of the reasons why the task of selectinga hydrocyclone system is difficult to deal with.Generalizations of performance characteristicscan seldom be made, and the choice necessar-ily relies upon semiempirical relationships ormodels, which are, inevitably, of limited appli-cation. In selecting or designing hydrocyclonesfor a specific duty, the recommended way is ei-ther using manufactures catalogues or to makecalculations to obtain cut point and throughputs.

5.1. Analytical Solutions

The previously cited formulae for the computa-tion of cut points and capacities can be employedas a first approximation. The actual choice canbe mainly based on the function to be performedby the system. In classification applications, forinstance, the cut size is usually fixed and thedesign is simply based upon achieving that cutsize. On the other hand, in separation, a certaindegree of efficiency is normally required, andthe resulting design must be a compromise bet-ween technical and economical considerations.The adaptability to industrial scale can representa real problem.Moir [41] pointed out that someof the correlations for calculating cut points andthroughputs for cyclones might not be suitablefor industrial problems, since they were devel-oped using slurries with low solids contents andsmall units. An alternative to high capacities isuse of multiple hydrocyclone systems for indus-trial production. Gerrard and Liddle [42] have

described two methods for selection of units tobe used in parallel for a given duty. Many otherauthors have mentioned the advantage of usingmulticyclone systems.

5.2. Graphical Solutions

A series of charts or nomographs have beenalso developed for the estimation of effects ofchanges in operating variables on performanceof hydrocyclones. Zanker [43] presented a se-ries of equations incorporated into some nomo-graphs in order to make trial-and-error calcula-tions faster. Rao and Nageswararao [44] sim-plified the use of charts to just one nomograph.Again, combined with some calculations, theyclaimed such a graph to be a useful tool in select-ing hydrocyclones for specific duties. Anotherproposed graphical method is given in [45]. Theauthors emphasized, however, that applicationof the technique should be for guidance purposesonly.

5.3. Manufactures’ Choice

Several equipmentmanufactures have publishedliterature about selection of hydrocyclones inthe form of brochures, technical reports, andso on. In many International Conferences heldaround theworld somemanufactures present pa-pers about selection, innovations, etc., as wellas table-top exhibitions of their available equip-ment.

Table 2. Summary of some known hydrocyclone designs

Cyclone type and size ofhydrocyclone

Di/Dc Do/Dc l/Dc L/Dc θ Stk50Eu** Kp

∗∗ np∗∗

Rietema’s design* Dc =0.075 m

0.280 0.340 0.40 5.00 20◦ 0.0611 24.38 0.3748

Bradley’s designDc =0.038 m

0.133 0.200 0.33 6.85 9◦ 0.1111 446.5 0.3230

Mozley cyclone 1Dc = 0.022m

0.154 0.214 0.57 7.43 6◦ 0.1203 6381 0

Mozley cyclone 2Dc = 0.044m

0.160 0.250 0.57 7.71 6◦ 0.1508 4451 0

Mozley cyclone 3Dc = 0.022m

0.197 0.320 0.57 7.71 6◦ 0.2182 3441 0

Warman 3′′ model RDc =0.076 m

0.290 0.200 0.31 4.00 15◦ 0.1709 2.618 0.8000

RW 2515 (AKW)Dc = 0.125m

0.200 0.320 0.80 6.24 15◦ 0.1642 2458 0

* Optimum separation.** Optimum separation.

Hydrocyclones 19

5.4. Dimensionless Scale-Up ofHydrocyclones

5.4.1. Introduction

Because of the hydrocyclones’ inflexibility, themethods of selection just reviewed can be onlyused as an approximation. The correlations pro-posed are often derived from studies of effectsof geometrical proportions on capacity and sep-aration efficiency. In this sense, if literature onhydrocyclones is rigidly followed when design-ing a unit, it might lead to a unique hydrocyclonechoice, whose geometry could has been nevertested before, so reliable prediction of its per-formance may be misleading. Based on this andmany other facts and factors, a scale-up proce-dure to select hydrocyclones, attributed mainlyto Svarovsky [1] has been proposed. Themethodconsists of selecting a known design of hydrocy-clone and, by using a series of dimensionlessrelations, making the necessary predictions aschanges on fixed variables are introduced. Asummary of some known hydrocyclone designsis presented in Table 2.

As the performance characteristics ofhydrocyclones involve a great number of vari-ables, the use of dimensionless groups in thismethod is an obvious advantage. The basic con-cepts underlying dimensionless analysis andscale-up procedures have been used for longtime in classical mechanics principally. Perhapsthe most common method of dimensional anal-ysis is that attributed to Lord Rayleigh knownas the Pi theorem. The basic steps of dimen-sional analysis can be found in (→ Scale-Up inChemical Engineering) [43].

5.4.2. Definition and Derivation ofDimensionless Groups for Hydrocyclones

In the case of hydrocyclones, selection and op-eration is based on the relationships between thepressure drop and flow rate and the relationshipbetween separation efficiency and flow rate. Thepressure drop versus volumetric flow rate rela-tionship is usually expressed as Eu = f (Re),whereEu is the Euler number. These dimension-less groups are graphically related as shown inFigure 8. The Euler number is in fact a pres-sure loss factor, easily defined as the limit on the

maximum characteristic velocity v obtained bya certain pressure drop ∆P across the hydrocy-clone. It can be expressed as:

Eu =2∆P

ρv2(59)

where ρ is the density of the fluid.

Figure 8. A typical plot of Eu versus Re for hydrocyclones

The Reynolds number defines flow charac-teristic of the system and in the case of hydrocy-clones, the characteristic dimension may betaken as the cyclone body diameter Dc, i.e.:

Re =Dcvρ

µ(60)

where µ is the medium viscosity.The relationship between separation effi-

ciency and flow rate is not significantly influ-enced by operational variables, so it is com-monly expressed in terms of cut size x50. The useof the cut size to define efficiency of hydrocy-clone is of the utmost importance since, as hasbeen previously emphasized their performanceis highly dependent on particle size. Since cutsize implies size of particles likely to be sepa-rated, it follows that such particles must be in-fluenced by forces exercised on the suspension.The forces developed in a hydrocyclone can beanalyzed by sedimentation theory, and a dimen-sionless group thus derived, the Stokes number,will include cut size.

The Stokes number is a very useful theoret-ical tool and, for the case of hydrocyclones, itsderivation may be carried out as follows. Con-sidering a settling tank of length L and wide W,it would have a settling area of A= LW, and ifthe depth is H, then the retention volume is V =

20 Hydrocyclones

AH. With a flow through the tank of Q (m3/h),the detention time is given by:

td =V

Q(61)

Particles to be removed must settle, undergravity influence, through the depth H requir-ing ts, where:

ts =H

ut(62)

ut being the settling rate defined by Equation 6.Only particles for which ts is equal or less

than td will be removed. Hence, by equating tsand td a cut point or separation mesh is definedas:

H

ut=

V

Q(63)

transposing for ut:

ut =HQ

V=

Q

A(64)

If Equation 64 is then equated to Equation 6,the limiting size of particles to be settled can bederived giving:

x2 =18µQ

g (ρs−ρ)A(65)

For centrifugal systems the same replacementdone in Equation 6 leads to:

x2 =18µQ

Rω2 (ρs−ρ)A(66)

Since ω = vt/R, where vt is the tangential ve-locity of the particle, Equation 66 can also beexpressed as:

x2 =18µQR

v2t (ρs−ρ)A

(67)

The radial settling velocity in a hydrocycloneis due to the centrifugal acceleration, which isproportional to the square of the tangential ve-locity of the particle and indirectly proportionalto the radius of the particle position. As the tan-gential motion of the particle is unopposed, thetangential particle velocity can be taken as equalto the tangential component of the fluid veloc-ity at the same point. For the same flow regime,the velocities anywhere in the flow in a hydrocy-clone are proportional to a characteristic velocityv while the position radii are proportional to thecyclone diameter Dc. Under such assumptionsEquation 67 can be approximated to:

x2 =18µQDc

v2 (ρs−ρ)A(68)

Considering the superficial velocity in thehydrocyclone body as the characteristic veloc-ity, the volumetric flow rate equals

(vπD2

c

)/4,

also A = πD2c/4 for the cyclone body. Thus,

substituting Q and A into Equation 68:

x2 =18µDc

v (ρs−ρ)(69)

Rearranging Equation 69 to express it in termsof inertial forces and hydrodynamic forces; thedimensionless group known as Stokes numberis obtained, i.e.:

Stk =x2 (ρs−ρ) v18µDc

(70)

Furthermore, if the dimension x is replacedby the specific cut size, x50:

Stk50 =x250 (ρs−ρ) v18µDc

(71)

or:

Stk50(r) =x′250 (ρs−ρ) v

18µDc(72)

if the reduced cut size x′50 or x50(r) is incorpo-

rated.

5.4.3. Scale-Up at Low Concentrations

At low concentrations of the feed (less than 1vol%), the flow pattern in a hydrocyclone is notaffected by the presence of particles in the flowand particle—particle interaction is negligible.As only few particles report to the underflow, theunderflow-to-throughput ratio can be assumedto have no effect on the cut size. If this is thecase, the dimensional analysis gives two basicrelations between the three above described di-mensionless groups:

Stk50Eu = constant (73)

Eu = KpRenp (74)

where Kp and np are empirical constants for afamily of geometrically similar cyclones. Theproduct Stk50Eu depends on the cyclone de-sign, and on the underflow to throughput ratio.Its value range from 0.06 to 0.33. The value ofnp is usually between 0.0 and 0.4 [1].

Hydrocyclones 21

5.4.4. Scale-Up at High Concentrations

At higher concentrations, the feed concentra-tion as a fraction of volume C has to be in-cluded as an additional dimensionless group.The feed concentration of solids is a very impor-tant variable, which affects the separation effi-ciency and the pressure drop of a given hydrocy-clone. It has been alreadymentioned thedecreas-ing in efficiency as feed concentration increases.This means that the underflow-to-throughput ra-tio has to be increased (to allow greater volumeof separated solids to be discharged). For thisreason, most hydrocyclones are equipped witheither a continuously variable underflow orifice,or a series of replaceable nozzles.

Theoretical and empirical approaches of theeffect of feed solids concentration in hydrocy-clones have appeared in the literature.SvarovskyandMarasinghe [36] havedeveloped the follow-ing expression for the effect of high-feed solidsconcentration:

Stk50(r) = k1 (1−Rf) exp(k2C) (75)

where Stk50(r) includes the reduced cut size,as already defined, while k1 and k2 are empir-ical constants, which depend on the hydrocy-clone configuration as well as on solids proper-ties. The correlation has proved to hold well forconcentrations above 8 vol%, and the values ofthe constants k1 and k2 were found to be 9.05× 10−5 and 6.461, respectively, for limestoneand a hydrocyclone manufactured by AmbergerKaolinwerke (AKW).

5.4.5. Considerations for non-NewtonianBehavior

When fine powders are dispersed into liquids theresultant suspension is usually non-Newtonian.The non-Newtonian behavior of suspensions isnormally a direct function of concentration. Inthis sense, the viscosity of a dilute suspensionnearly equals that of the suspending liquid. Thus,when dealing with suspension of low solidscontents either the apparent suspension viscos-ity or the suspending liquid viscosity can beused for characterization purposes.However, formore concentrated suspensions non-Newtonianbehavior may be present and their viscositiescannot be considered constant anymore; their

flow behavior must, therefore, be evaluated byother means.

The point above mentioned, make neces-sary to include parameters that characterize non-Newtonian fluids in the previously developeddimensionless groups, if they are going to beused in scale-up of hydrocyclones dealing withsuspensions, whichmight be non-Newtonian. Inthis case, an approach similar to that employedin the derivation of Equation 17 may be carriedout. Firstly, in this type of fluid, the drag coeffi-cient, CD, for steady-state creeping flow past asphere based on a macroscopic momentum andenergy balance ofWasserman and Slattery [47]is:

CD =24Re∗ (76)

where Re* is a generalized Reynolds numberanalogous to that defined by Equation 17, be-ing its characteristic dimension x, i.e,. the parti-

cle diameter, and γ = K ′(3)n′−1. Also, K ′ =K[( 2n′+1)/3n′]n

′, for this case.

For Newtonian fluids, an approximation ofthe drag coefficient in Stokes and the intermedi-ate region [48] is:

CD =[ 24

Re

( 24Re+4.5

)]1/2 (Re<500) (77)

a modification of Equation 77 to better fit thedata is:

CD =[ 24

Reα1

( 24Reα2 +α3

)]1/2 (Re∗<500) (78)

where the alpha constants are α1 = 1.1, α2 =0.2, and α3 = 7.5.

By substitution of 24/Re* for 24/Re in Equa-tion 78 and modification of the constants to en-sure a friction factor of 0.44 at Re* = 500, theresultant non-Newtonian drag coefficient corre-lation is:

CD =[ 24

Re∗α1

( 24Re∗α2 +α3

)]1/2 (Re∗<500)(79)where the alpha constant values are as previouslynoted.

The terminal settling velocity for non-Newtonian fluids (Re<500) is found by equat-ing Relation (77) with the generalized form ofthe drag coefficient, i.e.:

4gx3u2

t

[ρs−ρ

ρ

]=

[24

Re∗α1

(24

Re∗α2+α3

)]1/2(80)

Substituting Equation 17 and eliminatingReynolds number, Equation 80 becomes:

22 Hydrocyclones

[gxn′+1 (ρs−ρ)

18γ

]2

= u2n′t +

α3

24

[ρxn′

γ

]α2

u2n′+α2(2−n′)t (81)

For small Reynolds numbers (Re∗<0.1), thesecond term of the right-hand side of Equation81 is negligible and the simplification leads to:

ut =[

gxn′+1(ρs−ρ)18γ

]1/n′(Re∗<0.1) (82)

For Newtonian fluids n′ = 1, γ equals µ, soEquation 82 becomes the familiar expression ofStokes law as described by Equation 6.

Following a similar procedure as when ob-taining Stokes’ number expression, Equation 82can be equated to Equation 6, i.e.:

Q

A=

[gxn′+1 (ρs−ρ)

18γ

]1/n′(83)

transposing for xn′+1:

xn′+1 =18γQn′

g (ρs−ρ)An′ (84)

Again, considering centrifugal acceleration:

xn′+1 =18γRQn′

v2t (ρs−ρ)An′ (85)

and, under the assumptions made before:

xn′+1 =18γQn′

Dc

v2 (ρs−ρ)An′ (86)

Substituting Q and A and rearrangingterms, the Stokes number expression for non-Newtonian systems is obtained, i.e.:

Stk∗ = xn′+1 (ρs−ρ) v2−n′

18γDc(87)

It can be noticed that, again, that for Newto-nian fluids this generalized Stokes number re-duces to the common expression represented byEquation 12.

Finally, since concentration is an importantfactor in this case, replacing the reduced cut sizefor the simple particle size, x:

Stk∗50(r) =

xn′+150 (r) (ρs−ρ) v2−n′

18γDc(88)

in which x50(r) is preferred to x′50 in order to

avoid confusion.

5.4.6. Empirical Models

An exhaustive study for concentrations up to 10vol% was carried out byMedroho [49] in orderto prove the applicability of Equations 73, 74and 75. He employed three geometrically sim-ilar hydrocyclones of Rietema’s [30] optimumgeometry and obtained the following relations:

Stk50(r)Eu = 0.047[ln(1/Rf)]0.74exp(8.96C) (89)

Eu = 71(Re)−0.116(Di/Dc)−1.3exp(2.12C) (90)

Rf = 1218(Du/Dc)−4.75(Eu)−0.30 (91)

where Rf is the underflow-to-throughput ratio,C is the volume fraction of solids, Di, Dc, andDu are the inlet, body, and underflow diame-ters of the hydrocyclone, respectively. Coveringalso the low feed concentration range (i.e. upto 10 vol%), Antunes and Medroho [50] de-veloped a set of equations bearing similarity tothose presented above, but for hydrocyclones ofBradley’s [2] geometry.

Ortega-Rivas and Svarovsky [51] have pro-posed a model for concentrated suspensions andaccounting for non-Newtonian behavior of thetreated slurries. They covered a feed concentra-tion range from 5 to 25 vol% and used geometri-cally similar hydrocyclones followingRietema’s[30] proportions. The relationships that they de-rived are presented below:

Stk∗50(r)Eu = 0.006[ln(1/Rf)]

2.37exp(6.84C) (92)

Eu = 1686(Re∗)−0.035exp(−3.39C) (93)

Rf = 32.8(Du/Dc)1.53(Re∗)−0.34exp(3.70C) (94)

where the dimensionless Reynolds and Stokesnumbers include the parameters of characteri-zation of non-Newtonian suspension previouslydescribed. Equations 92, 93 and 94 allow reli-able hydrocyclones design and scale-up at con-centrations up to 25 vol% of shear-thickeningsuspensions. They apply to Rietema’s geometry,but there is some evidence suggesting that theycould equally be employed to other geometries,because reasonable agreement has been foundwith previous models of hydrocyclone designand performance. The authors also claim that

Hydrocyclones 23

for the case of Newtonian suspensions, i.e., lowsolids contents, the above mentioned equationswould reduce to the common definitions so theyconclude their model is of wide applicability.

All the above described relationships havethe advantage of presenting graphical functions,such as the one shown in Figure 8. Those graphscan be handled for design purposes by manipu-lating variables and predict, in a practical man-ner, operation effects of hydrocyclone technol-ogy.

Figure 9. Hydrocyclone test rig

5.4.7. Practical Applications

In order to test the different models previouslydescribed in this article, experimental runs insmall hydrocyclone rigs are advised. Standardgeometries of cyclones, such as the Rietema’shydrocyclone, can be used to run tests at dif-ferent diameters and pressure drops. As previ-ously mentioned, many different design graphsdescribing the relationships between dimension-less groups may be available for variable manip-ulation and prediction of best performance vari-ables. A hydrocyclone test rig is shown in Fig-ure 9. The units are changeable and they maybe equipped with removable underflow nozzles

(Fig. 10.), in order to verify the effect that varia-tions in the underflow orifice diameter may havein the cut size. Once a number of tests have beenperformed, the possible scale-up to industrialsize may follow.

Figure 10. Rietema’s proportions hydrocyclone with re-placeable underflow spigots

Since cut size is a direct function of hydrocy-clone diameter, the best efficiency for a numberof useful applications would be given by smallunits. Cut sizes down to 2µmhave been reportedin 10mm diameter hydrocyclones [51]. On theother hand, also capacity is a direct function ofhydrocyclone diameter, so larger units will de-liver higher flow rates. Therefore, it would benecessary to reach a compromise between ef-ficiency and capacity for industrial operation.In this sense, a basic small geometry may bekept to cut as fine particles as possible, whileseries arrangements may be required to renderindustrial capacities. A number of arrangementshave been experienced, but probably the mostefficient is the radial (spider) arrangement withthe hydrocyclones axes horizontally placed likespokes in a wheel lying down. As shown in Fig-ure 11, one “wheel” or hydrocyclone deck ac-commodates a number of “spokes” or hydrocy-

24 Hydrocyclones

Figure 11. Diagram of radial (spider) arrangement of hydrocyclones for industrial scale

clone bodies. For cyclone cavities with a cylin-drical diameter of 10mm the diameter of thedeck is 300mm. The whole cyclone deck can bemolded by injection in one piece. The feed zoneis the annular space closest to the periphery. Theoverflow is through peripheral screw-in-vortexfinders. The underflow leaves via the central cir-cular space where the small apex openings enter.

The design feed flow per cyclone cavity isabout 250 L/h corresponding to a pressure dropof 600 kPa, approximately. A deck with 20 cy-clones in parallel consequently may have a ca-pacity of 5m3/h. This is, however, not the max-imum capacity. The cyclone cavities can be

closed off individually by insertion of a blindingdevice in order to control the capacity. For feedflows above 5m3/h, the decks can be stacked ontopof eachother andheld together by connectingrods through the inner annular space. There is alimit to the number of decks that can be stackedon top of each other. If the stack of decks be-comes too high, the pressure drop over the feedzonewill result in a lower inlet pressure to the cy-clones furthest downstream and, consequently,these cyclones will give lower throughputs andlower efficiency. Some other arrangements havebeen tested with different degrees of success.Some of them have been reviewed in [1].

Hydrocyclones 25

As has been discussed, hydrocyclone tech-nology has numerous applications in a wide va-riety of industries. Hydrocyclones have beenparticularly used for long time in mineral pro-cessing, as well as in the oil and gas industry.In these industries, many materials can be con-sidered inert powders, and thus the equationsof the dimensionless scale-up model proposedby Medronho and Svarovsky [49] can be em-ployed to carry out experimental tests, as sug-gested above. Hydrocyclones have been alsosuccessfully used in other industries, such as thefood and biochemical industry. Since most ma-terials in these industries may behave as non-Newtonian, the model suggested by Ortega-Rivas and Svarovsky [51] would be more suit-able for modeling purposes of processes involv-ing biological systems.

Some examples of application of the dimen-sionless scale-up model are given below.

Example 1. Predict the cut size obtained if1 L/s of a suspension containing 5 vol% of a2150 kg/m3 dolomite slurry in water, is going tobe separated in a 25.4mm diameter hydrocy-clone of Rietema’s geometry. The availablepressure is 2× 105 Pa and the underflow orificeis 5mm.

The relatively low concentration of suspen-sion would allow use of the density and viscos-ity of water as suspending medium properties.Also, since no temperature has been given, areasonable assumption for the water density is1000 kg/m3 and for the water viscosity 0.001 kgm−1 s−1. Thus, bearing inmind to use the super-ficial velocity in the cyclone body, [4Q/π(Dc)2]as the characteristic one, the following resultsare obtained:

The characteristic velocity is, firstly, ob-tained, as defined above, i.e.:

v =4 (0.001)m3/s

3.1416(0.0254)2m2= 1.97m/s (95)

Then, substituting into Equation 59, the Eulernumber is calculated as:

Eu =2

(2×105)

kg/s2·m(1000) kg/m3 (1.97)m/s

= 102.7 (96)

As stated before, due to the low suspension con-centration, the set of equations suggested forthis case [49] can be considered, and thus, usingEquation 91 the underflow-to-throughput ratiomay be obtained as:

Rf = 1218(0.005m0.0254m

)4.75(102.7)−0.3 = 0.1346 (97)

Equation 89 can then be employed to computethe value of the Stk50(r) group, i.e.:

Stk50 (r) =0.047[ln (1/0.1346)]0.74exp [8.96 (0.05)]

102.7= 0.0019 (98)

Finally, transposing the cut size from the defini-tion of the Stokes number given by Equation 72,the result is obtained as follows:

x′250 =

((0.0019) (18) (0.001) kg/m·s (0.0254)m

(2150−1000) kg/m3 (1.97)m/s

)

= 1.55×105 m (99)

The cut size calculated is approximately equalto 15µm.

Example 2. A slurry containing calcium car-bonate at a concentration of 15 vol% solids,is going to be clarified using hydrocyclonesof Rietema’s proportions. The slurry has beencharacterized being non-Newtonian in behav-ior, with values of the parameters n′ and K ′of 1.39 and 2× 10−5 kg m−1 · s−(2−n), respec-tively. The density of the slurry has been deter-mined as 1250 kg/m3. It is required to clarify8 L/s of slurry, counting on a maximum pump-ing capacity of 315 kPa. Find out the optimumcyclone diameter and the number of units, ifnecessary, in order to obtain a cut size of 8µm.Small scale experimentation has determined val-ues of some dimensionless relationships as fol-lows: Stk50Eu = 0.0625, and Eu = 720. The cal-cium carbonate density has been determined as2800 kg/m3.

The value of the parameter n corresponds toa shear-thickening fluid, while the requirementof using Rietema’s cyclones makes it possibleto use the model suggested by Ortega-Rivasand Svarovsky [51]. The maximum pumpingcapacity would produce a pressure drop of thesame value (315 000N/m2), because the leav-ing streams discharge at atmosphere conditions.Substituting the definition of superficial veloc-ity in the cyclone body, as used in the previousexample, into Equation 59, and considering thedensity of the slurry due to its high concentra-tion, the following relation is obtained:

26 Hydrocyclones

Dc = 4

√(Q2) (Eu) (ρm)(1.23) (∆P)

(100)

Substituting, also, the same characteristic veloc-ity in Equation 88 and transposing for the re-duced cut size:

xn′+1

50 (r) = (101)

(Stk∗50) (18) (3)

n′−1 (K′) [(2n+1) / (3n)]n′(Dc)5−2n′

(1.27Q)2−n′(ρs−ρ)

As previously stated, the cut size is directly pro-portional to the hydrocyclone diameter, whilethis diameter is inversely proportional to theflowrate. It would be, therefore, necessary to verifywhether the required cut size could be obtainedin a single hydrocyclone, whose diameter wouldmatch the capacity needed. If both variables donot coincide (cut size and flow rate with a singleunit), iterations would be needed until a numberof units is found, each of them separating therequired size, while processing the appropriatefraction of the total capacity. A first approxima-tion would consist in calculating the hydrocy-clone diameter, using the first equation derivedabove, which will handle the 8 L/s of slurry to betreated. Once having that diameter, with the sec-ond equation, the cut size that the single unit sep-arates, will be known. If such diameter is widerthan 8µm, the volumetric flow rate will be frac-tioned in equal parts to recalculate hydrocyclonediameter until a match of number of units andcut size is found. The first approximation leadsto the following values:

Dc = (102)

4

√(0.008)2m6/s2 (720) (1250) kg/m3

(1.23) (315000) kg/s2·m = 0.11m

and:

x∗50 = (103)

2.39

√(8.68×10−5

)(18) (1.53)

(2×10−5

)kg/m·s2−n (0.872) (0.007445)m5−2n

(0.0608) (m3/s)2−n (1800) kg/m3

x∗50 = 15 µm (104)

So it is found that a 0.11m diameter hydrocy-clone will separate particles much coarser thanthe required cut size. By doing iterations, whenfractioning the rate four times, i.e., when Q= 0.002m3/s, a diameter of hydrocyclone Dc= 0.055m and a cut size of 7.8× 10−6 m arefound. Therefore, the election would be the useof four units, 5.5 cm in diameter, to handle thecapacity required and obtain the cut size needed.

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