Mineral Processing 374Assignment 1: Particle Size Distribution & Powder Sampling

One of the most important tasks of powder technology is the powder sampling. Sampling can be done from stored material and flowing streams. In 2 pages explain typical sampling devises and strategies.

Often in industry estimates of batch characteristics have to be made from an examination of a small portion of the overall population. This process is not exclusive to powder technology but the equipment used is quite different to other industries. If samples are not taken carefully and are non-representative of the bulk, samples can result in process failures and products that don’t meet customer standards. To ensure this does not happen there are a wide variety of procedures which should aim to meet the two golden rules of powder sampling; a powder should be sampled when in motion and the entire stream should be taken for multiple short increments of time.

Powder sampling can be taken from both stored material and flowing streams, with flowing streams being a far more accurate representation of the entire material. In the case of stored material sampling, a sample has to be combined from smaller incremental samples and a lower efficiency is to be expected. Due to different sizes of particles when they are placed in a heap they are no longer homogeneous due to separation, resulting in any sample taken being not accurate. It’s not possible or practical to have a guide on how to extract samples due to the large number of situations that are all different. The main two scenarios are whether or not the powder was mixed before storage which determines whether or not the particles are segregated into subsections.

Surface sampling is the most common due to its simplicity. This basically involves scooping a sample from the top by assuming it represents the entire pile due to a homogeneous mix. It is usually done at multiple locations of the pile and tested separately to make sure the variation is at an acceptable level. A second method which further improves accuracy is to use a sampling spear known as a thief. Three types of thief samples are available; the first consists of an inner and outer tube with one closed end and a window that runs the length of the spear which generates a core sample. Type 2 features a small chamber at the end which creates a spot sample and is typically used for compact powders. Usually spot samples are taken at different depths and are blended together as a composite sample. Type 3 includes several chambers down the length of the pipe to generate several samples simultaneously and is also best used for compacted powders.

Self-burrowing probes are another sampling device for stored material; however its lengthy process doesn’t gain any further accuracy when compared to scoop of thief. It involves coning or quartering a sample into 4 segments, recombining two opposite quadrants and repeating until a small enough sample has been created. This is based on the assumption that the heap is symmetrical, which is often not the case, so the generated sample usually isn’t representative of the entire batch. These issues with accuracy can be solved by one simple solution, take a sample when the powder is free flowing.

It is almost impossible to obtain a fair sample from stored material, so the easiest way to avoid this is by sampling from flowing streams. Powder systems are often moved via a flowing stream at some point during their manufacture. Some examples include screw and belt conveyors exiting hoppers or through pipes between processes. If none of these are viable options, samples can be taken during the filling and emptying of storing containers.

Sampling from conveyor belts has its own unique process to maximise accuracy by extracting the sample at the end of the line where the material is falling off the belt. If for some reason this zone is out of reach the next best option is to collect it straight off the belt. However the particles at the edge of the belt are most likely different to those in the centre, likewise for top and bottom, so an entire section across the belt needs to be collected. If the belt can be stopped then there exists a simple method to gather this sample, a scoop the same width as the belt consisting of two parallel plates at the rear that trap a full segment. This operation is hazardous if attempted while the belt is moving so it is highly recommended to be done when stopped. Sampling from a stream can be done continuously or intermittently. Continuous sampling involves a flowing stream being split off and then regularly being subdivided. In intermittent sampling the entire stream is diverted for a short period of time at

fixed intervals. As with most other procedures, the increments are compounded and the samples are analysed as a whole.

Belt conveyors can be set up to have automatic samplers. Samples can be extracted from the product stream by a tube being placed into the flow, with its nozzle or opening facing the incoming material. The powder proceeds to fill up the tube and the sampling head is shortly removed from the stream. There exists different types of samplers for different stream compositions. The snorkel type is used for vertical or inclined applications but is only accurate with a homogeneous stream. Like all automated samplers it can be pre-programmed to have a particular sampling frequency. A second type is the auger sampler which features a slot inside the stream which can be rotated to capture cross sections which fall down due to gravity into a container. This type however is only useful for homogeneous streams and it has the disadvantage that it obstructs the flow.

Sampling from falling streams requires great care when putting the sampler in and out to minimise the effects of segregation. Each sample must be taken from the whole stream for a short amount of time and inserted in the correct manner. The ideal way to put the sampling container in is by smoothly pushing it into the stream from the front, keeping it stationary in the middle before moving it through and out the other side. However if the stream has a high flow rate the best method may be to move the container from one side to the other at a consistent speed. There are several different types of collecting containers that are used depending on the material being collected, but typically for powders a ladle is used, which is a wide open bucket of certain dimensions. A stream sampling cup is used for a stream that features a variety of sized particles, with the rectangular opening at the top being at least 3 times the size of the biggest particle to allow for fair collection. As with most sampling containers it is vital these don’t fill up during the collection process, as this will lead to an overflow and a higher ratio or finer particles that stay on the pile, while the coarse material flows over.

Traversing cutters, with the help of a second sampling device, are a way to further reduce larger samples that were taken from a conveyor. Usually the traversing cutter is the primary sampler and then the second device takes a smaller portion from it. This equipment is quite efficient however it does have certain limitations, for example it is difficult and expensive to install into an existing plant due to its space requirements. Also the quantity of sample obtained is proportional to the flow rate which can cause issues if the stream is subject to wide variations. Lastly it is rather difficult to enclose the sample to prevent the escape of dust and fumes when dealing with fine powders.

Sampling dusty materials requires much more care due to the small particle size that can be easily blown away by air movement. There are a few variations but the typical process is similar in all cases. The stream which flows in a sheltered environment, either through a pipe or along a conveyor with an enclosure, is diverted briefly by a mechanical arm of some form. The style used depends on the material being moved but it involves diverting the flow into a container and then the removal to return the flow to normal. One example is the slide-valve sampler which is initially covering a second pipe pointing downwards and when it’s opened the material naturally falls down into it instead of passing over the top when it is closed.

Often the sample collected from a flowing stream is far too large to be handled easily and has to be reduced. This is treated in more or less a similar fashion to sampling from stored material. To avoid negating the steps already taken to achieve a fair sample it must be certain the mixture is homogeneous before taking a portion. To obtain the most accurate results it should first be pre-mixed, commonly done by emptying into a hopper. When pouring into the hopper it is essential to not just dump it in the centre all at once as this will cause segregation. The walls of the hopper should be steep, at least 70°, and then move the pouring point around so the surface is horizontal. There are several sample-dividing devices which all have their own advantages and disadvantages and need to be chosen based on the requirements of the sample.

The main five sampling devices are cone and quartering, scoop, table, chute splitting and spin riffing. Quartering and coning is best for powders with poor flow characteristics but it is very operator-dependant. As described previously it is a method that relies on the assumptions that a heap will be symmetrical around its centre. If the sample is flattened and divided by a cross shaped cutter it is assumed each quadrant is equal in nature however this is almost always not the case. It relies heavily on the skill of the operator and is therefore

not a recommended procedure. If quartering is possible it means the heap is a relatively small size and should therefore be fed into a hopper with a spinning riffler. Quartering and Coning’s relative standard deviation (RSD) in terms of reliability when compared with the others is the worst at roughly 6.81%. Scoop sampling should only be used for homogeneous, non-flowing powders but it still has a pretty poor reliability of 5.14%. Table sampling relies heavily on the initial feed but it is able to separate a large quantity of material and it is cheap and simple. Chute splitting can greatly reduce the powder sample size but operator bias is a big factor. The most reliable process was spin riffing, with only a 0.125% RSD with its only downfall being its inability to handle large sample sizes. Spin riffing follows the two golden rules of sampling; a powder should be sampled when in motion and the entire stream should be taken for multiple short increments of time. This process involves the sample going in to the top of a hopper, where it falls down onto a vibratory feeder which provides a constant flowrate towards the spinning collection containers at the end of the feed. (T Allen, 2003)

Write a short report on different particle size distribution functions with special attention to the model (function) parameters. Clear comments on applicability of each correlation, along with corresponding parameters are expected.

More than a dozen methods of plotting the particle size distribution (PSD) are known. The two most common are the Gates-Gaudin-Schuhmann (GGS) and the Rosin-Rammler (RR). These methods are used for non-uniform size distributions and are derived from attempts to represent PSD curves by means of equations. A few other, lesser used equations are the normal distribution (Gaussian), Gaudin-Meloy, Bergstrom, log-hyperbolic and the log normal distribution functions.

Since 1940 the metalliferous mining industry has favoured the use of the GGS equation due to its simplicity. It can be defined by Y=¿ where Y is the fraction of the sample finer than size X, X is the particle diameter, K is the maximum particle diameter of the distribution and m is the distribution modulus. If the logarithm of Y is plotted versus log X a relatively straight line is produced with a slope of m, with the expressionlog Y=m log X−m log K . If the material fits the GGS model then the log-log line will be linear. GGS plotting is often preferred over RR method in mineral processing but a 1971 study by CC Harris suggested that the RR is actually a better method.

The Rosin-Rammler distribution function (sometimes known as Weibull distribution) is used to describe the particle size distribution of powders of various types and sizes. In particular it is suited to represent powders created through the means of grinding, milling and crushing. It was originally developed for the use in coal-preparation studies but has since expanded due to experiments suggesting it is a far better method. The

general expression can be written as Y=1−e−( X

P )n

where Y is the

distribution function, X is the particle size in millimetres, P is the mean particle size (mm) and n is a measure of the spread of particle sizes. P and n are adjustable parameters of the distribution. The expression can also be written in the form: ln {−ln [1−Y ] }=n ln X−n ln P and a plot of the first term of this expression against the natural log of X will result in a straight line of slope n if the material fits the RR model. The application of this function to a specific distribution and the calculation of its parameters are often done via linear regression of data.

The few other methods which are not commonly used each have their own purpose. The normal distribution

method or Gaussian distribution as it’s known in other applications has the equation dΦdD

= 1σ √2π

e−[

( D−D50)2

2σ 2 ]

where Φ refers to the cumulative fraction between 0 and D, σ is the standard deviation and D50 is the median diameter. This is heavily used in statistics and probability but can be used similarly for PSD. The log-normal distribution is often used to approximate the PSD of aerosols, aquatic and pulverised material. Its main form is Y=∑ e−log ( Xu) ×2¿¿ ¿¿¿ but it also

has the form q¿ where σg is the geometric standard deviation. Each have their respective uses in industry but are evidently not as simple as the previously described functions above. Figure 2: Log-normal plot example

Figure 1: PSD function plot example

Two others that are worth mentioning are the Gaudin-Meloy which has the form Y=1−(1− XX0 )

r

and the

BergstromY=[1−(1− XX0 )

r ]q

. Particle size distribution has a direct influence on material physical properties

such as reactivity, stability in suspension, texture, appearance, flow ability, viscosity and packing density. Measuring PSD and understanding how they affect your processes is critical to the success of the product.

Size of particles with non-spherical shape can be reported in different ways such as Stokes, Martin diameters. Write an essay on definition of different particle diameters, for at least 8 definitions. The estimation formula can clarify the concepts.

Particle size data is essential to treat powders. Expressing the size of a single particle is a challenging task when it is non-spherical. For irregular particles, it is desirable to quote the size of a particle in terms of a single quantity and the expression most often used is the equivalent diameter. This refers to a spherical particle that would behave in the same manner as the particle when put into a system. When a particle is circumscribed by a rectangular prism with length l, width w, and height t, its size is expressed by the diameter obtained from the three dimensions. Equivalent diameters usually depend on the method of measurement; hence the particle-sizing technique should duplicate the process needing to be controlled. The Stokes diameter is measured by sedimentation and elutriation techniques; the projected area diameter is measured microscopically and the sieve aperture diameter is measured by means of sieving. Data from size analysis should always be accompanied by an approximate shape of the particle, such as granular or acicular. There are many ways to describe the diameters, some of which are listed below.

Martin Diameter: Length of a chord dividing the particle silhouette into two equal areas in some fixed

direction. Stokes Diameter: Diameter of the sphere having the same gravitational settling velocity as that of

particle obtained by gravitational or centrifugal sedimentation and impactor. Feret Diameter: Distance between pairs of parallel tangents to the particle silhouette in some fixed

direction. Unrolled Diameter: Chord length through the centroid of the particle silhouette. Heywood diameter: Diameter of the circle having same area as projection area of particle,

corresponding to diameter obtained by light extinction. Equivalent light-scattering diameter: Diameter of the sphere giving the same intensity of light

scattering as that of a particle, obtained by the light-scattering method. Aerodynamic Diameter: Diameter of the sphere having unity in specific gravity and the same

gravitational settling velocity as that of a particle obtained by the same methods as above.

Sieve Diameter: Openings of sieves a1 and a2. 12 (a1+a2 ) or √a1 a2

Equivalent surface area diameter (specific surface diameter): Diameter of the sphere having the same surface as that of a particle. ¿

Equivalent volume diameter: Diameter of the sphere having the same volume as that of a particle, corresponding to diameter obtained by electrical sensing zone method. ¿

*Definitions and images obtained above from Powder Technology Handbook 3rd edition 2

As can be seen there are many different ways to measure the diameter of a non-spherical particle. The particular method chosen must represent the process being controlled in order to maximise accuracy. The way the diameter is measured is significantly different in each method so it is vital to understand each definition in order to pick the correct one.

Figure 3: Powder sampling

References:

1. Allen, Terrence. 2003. Powder Sampling and Particle Size Determination. Netherlands: Elsevier. 2. Higashitani, Ko, Hiroaki Masuda and Hideto Yoshida. 2006. Powder Technology Handbook. USA:

Taylor & Francis.3. Macias-Garcia, A. 2004. “Application of the Rosin-Rammler and Gates-Gaudin-Schuhmann models to

particle size distribution analysis of agglomerated cork”. Science Direct. doi.org/10.1016/j.matchar.2004.04.007

4. Particle Sciences, Inc. 2011. “Technical Brief Volume 5”. Drug Development Services 5: http://www.particlesciences.com/docs/technical_briefs/TB_2011_5.pdf.

5. Wills, Barry A. 2006. Wills’ Mineral Processing Technology - An Introduction to the Practical Aspects of Ore Treatment and Mineral Recovery (7th Edition). Elsevier.

Figures:

1. http://en.wikipedia.org/wiki/File:Bahco_Example.JPG2. https://www.iso.org/obp/ui/?_escaped_fragment_=iso:std:iso:9276:-3:ed-1:v1:en3. http://www.particlesciences.com/news/technical-briefs/2011/sampling-of-powders.html