Asst. Prof. Jewel A. CapunitanDepartment of Chemical EngineeringCollege of Engineering and Agro-Industrial TechnologyUniversity of the Philippines Los Baños

ChE 154 - Transfer Operations II1st sem. 2015-2016

PROPERTIES OF SOLIDS

MIXTURE OF PARTICLES

HOMOGENEOUS MIXTURE

mixture consisting of uniform particles.

the uniformity of the particles in the mixture must be

described by the following properties:

1. DENSITY (ρp

: same all throughout)

2. SHAPE (Φs : same all throughout)

3. PARTICLE SIZE

HOMOGENEOUS MIXTURE

4. NUMBER OF PARTICLES (N)

N =

where : mt= total mass of sample

mρ

= mass of 1 particle

ρp

= density of 1 particle

Vp

= volume of 1 particle

m t

mρ

=mt

ρp v p

HOMOGENEOUS MIXTURE

5. TOTAL SURFACE AREA (A)

A = NSp

=

where Sp

=surface area of 1 particle

6m t

φs ρ p D p

HETEROGENEOUS MIXTURE

mixture of particles having various sizes and densities

sorting is done in order to separate the particles (i.e.

screening)

properties are not described by a single value but a

range or distribution of values due to the non-

uniformity of the particles present in the mixture.

HETEROGENEOUS MIXTURE

HETEROGENEOUS MIXTURE

1. PARTICLE SIZE DISTRIBUTION

shows the proportionate fraction of each size of

individual particles in the mixture

assumes that size is constant per fraction

Two methods of analysis:

a. Differential / Fractional Analysis

b. Cumulative Analysis

HETEROGENEOUS MIXTURE

Example of PSD

HETEROGENEOUS MIXTURE

Differential/Fractional Analysis

plot of mass fraction vs. average particle size

consists of a histogram along with a continuous curve

showing the distribution of the particles

The plot shows the intermediate fraction that has the

highest composition in the feed.

HETEROGENEOUS MIXTURE

Example of Differential/Fractional Plot

HETEROGENEOUS MIXTURE

Cumulative Analysis

plot of the cumulative sums of mass fractions versus thecorresponding particle size

consists only of a continuous curve

does not require the computation of the average screendiameter but the addition of fractions passing through thescreens

can be done in two ways:

a. Cumulative mass fraction larger than Dpi vs Dpi

b. Cumulative mass fraction smaller than Dpi vs Dpi

HETEROGENEOUS MIXTURE

Example of Cumulative Plot

HETEROGENEOUS MIXTURE

2. TOTAL SURFACE AREA

sum of the surface area of each fraction

where: Ai = area of each fraction

n = number of fractions

HETEROGENEOUS MIXTURE

2. TOTAL SURFACE AREA

For each fraction:

HETEROGENEOUS MIXTURE

3. NUMBER OF PARTICLES

sum of the number of particles in each fraction

particle

HETEROGENEOUS MIXTURE

4. SPECIFIC SURFACE, AW

sum of the surface area of the particles in a fraction

equivalent to the total surface of the particles in a

fraction divided by the total mass of the fraction

HETEROGENEOUS MIXTURE

5. AVERAGE PARTICLE SIZE

a. Volume-Surface Mean Diameter,

aka Sauter Mean Diameter

parameter mostly applied in chemical engineering

when surface area per unit volume is important such

as packing materials in gas absorption and

adsorption.

HETEROGENEOUS MIXTURE

5. AVERAGE PARTICLE SIZE

a. Volume-Surface Mean Diameter,

obtained by measuring the volume and area of

entire sample and getting their ratio

HETEROGENEOUS MIXTURE

5. AVERAGE PARTICLE SIZE

b. Arithmetic Mean Diameter or

Mean Length Diameter,

summation of all particle dimensions divided by the

total number of measurements.

HETEROGENEOUS MIXTURE

5. AVERAGE PARTICLE SIZE

c. Mass Mean Diameter,

can be determined by taking the sum of all the

weighted mass of the particles and dividing it by the

total mass of particles

HETEROGENEOUS MIXTURE

5. AVERAGE PARTICLE SIZE

d. Volume Mean Diameter,

gives the average volumes of the particles in the

mixture

can be obtained by getting the total volume of the

particles and dividing it by the total number of

particles

HETEROGENEOUS MIXTURE

6. SPECIFIC NUMBER OF PARTICLES IN THE MIXTURE, NW

summation of the number of particles in a fraction

per total mass of particles

assumes that each particle has the same shape and

density

where a = is the volume shape factor:

HETEROGENEOUS MIXTURE

Example 3 (McCabe et al., 1993)

The screen analysis shown in Table 3 is applicable to a

sample of crushed quartz. The density of the particles is

2650 kg/m3 and the shape factors are a=2 and Φs=0.571.

(a) Based on Table 3, construct differential and cumulative

plots.

(b) For the material between 4 mesh and 200 mesh in

particle, calculate the specific surface in mm2/g, the

specific number of particles in particles per gram, volume

mean diameter, Sauter mean diameter, and number of

particles for the fraction at mesh 150/200.

HETEROGENEOUS MIXTURE

Given PSD for Example 3

Solution

Solution

(a) Differential & Cumulative Plots

Solution

(a) Differential & Cumulative Plots

Solution

(b) Specific surface, AW

Solution

(b) Specific number of particles, NW

Solution

(b) Volume mean diameter

Solution

(b) Sauter mean diameter

Solution

(b) Number of particles for the fraction at mesh 150/200

METHODS OF DETERMINING PARTICLE SIZE

method to be used depends on (a) size range, (b) physicalproperties of the particles and (c) moisture content of theparticles.

1. Microscopic Method

Particles are enlarged under the microscope and are directlymeasured (ex. Putting scale on top of the particles image)

Usually used in determining effectiveness of air bag filters andmeasuring dust particles in the air

Disadvantages:

a. Collection of sufficient data to ensure adequate precision

b. Operator fatigue

METHODS OF DETERMINING PARTICLE SIZE

2. Sedimentation Method

Done by mixing a sample of solid in water and then shaking

The size can be determined by making use of the settling

velocity equations, which is a function of Dp

3. Screening Method (use of standard sieves)

Can be done by either mounting the screens on a vibrator

(horizontal and/or vertical shaking) or may be hand shaken

END OF LECTURE

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