chapter 2 particle size characterization

8/19/2019 Chapter 2 Particle Size Characterization

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CHAPTER 2

PARTICLE SIZE CHARACTERIZATION


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1. In many powder handling and

processing operations, particle sizeand size distribution play a key role indetermining the bulk properties of thepowder.

2. Example of regular-shaped particles.

3. In practice, it is important to use themethod of size measurement, whichdirectly gives the particle size, which isrelevant to the situation, or process of

interest.

2.1 INTRODUCTION TO PARTICLE SIZE AND SHAPE

Source: http://blog.skylighter.com/fireworks/2007/11/how-particle-size-shape-is-defined.html


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4. methods of measurement

EQUIPMENT

LASERDIFFRACTION

ELECTROZONESENSING

SIEVESEDIMENTATION

MICROSCOPY


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1. Laser Diffraction

Malvern Mastersizer S(Malvern Instrument Inc.)

• Refer textbook section 1.8.6 (pg 16)• Light passing through a suspension• Diffraction angle is inversely proportional to theparticle size• An instrument would consist of a laser source anddetector• Diffraction angle relate with particle sizing -Farunhaufer theory and Mie theory.• This method give volume distribution


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2. Electrozone sensing

• Refer text book section 1.8.5• Particle in suspension in a dilute

electrolyte which is drawn through atiny orifice with a voltage appliedacross it

• As particles flow through the orifice avoltage pulse is recorded

• The amplitude of the pulse can berelated to the volume of the particlepassing the orifice

• It will give a number of distribution ofthe equivalent volume spherediameter

• Can detect 0.3-1000 mm


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3. Sieve

• Refer text book section 1.8.1• Dry sieving using woven wire

sieves is a simple and cheapmethod for particles size greaterthan 45mm.

• It gives mass distribution and a sizeknown as sieve diameter

• Sieve diameter is dependant onthe maximum width and maximumthickness of the particle.

• If standard procedures arefollowed and care is taken, sievinggives reliable and reproducibleanalysis


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4. Sedimentation

• Refer text book section 1.8.3• The rate of sedimentation of particles in

liquid is followed• Suspension is dilute and the particles

are assumed to fall at their singleparticle terminal velocity in the liquid

• Stoke’s law is assumed to apply (Re


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5. Microscopy

• Optical microscopy can be used to measure

particle sizes down to 5mm .• Coupled with image analysis, the optical

microscope or electron microscope can readily givenumber distributions of size and shape. Various

diameters can be calculated from the projectedimages (Martin’s, Feret’s , shear, projected area)


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2.2 SAMPLING METHOD

1. Most laboratory tests use only a small sample and this hasto be taken from a production stream or from an existing,stored material. This sample has to be the representative ofthe whole material.

2. Powders are unlike fluid where the properties change easilyunder applied load.3. They may consolidate with time, and attrition and

segregation may occur in transfer.

4. Sampling is an important element of powder handling suchthat it demands careful scientific design and operation ofthe sampling system.


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5. The purpose is to collect a manageable mass ofmaterial (=sample), which is representative of thetotal mass of powder from which it was taken.

6. This is achieved by taking many small samples fromall parts of total which, when combined, will

represent the total with an acceptable degree ofaccuracy.

7. This means that all particles in the total must havethe same probability of being included in the final

sample.


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8. To satisfy the above requirements, thefollowing basic‘golden’ rules of samplingshould be followed wherever practicable.

– Sampling should be made preferably from amoving stream (this applies to both powders andsuspensions) but powder on a stopped belt alsocan be sampled.

– A sample of the whole of the stream should betaken for many (equal-spaced) periods of timerather than part of the stream for the whole of thetime.

9. Re-combined primary sample taken from thewhole is too large for most powder test andso that, it need to be sub-divided intosecondary or tertiary sub-sample.


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• Allen (1981) reviewed and tested mostmethods available for sampling splittingand found the best is equipment called

spinning riffler (Figure 1).• In spinning riffler, the sample is slowly

conveyed by a vibratory feeder fromthe feed hopper to the rotating

carousel where it is divided into manycontainer ports via a machined rotaryhead

• The sub-samples are collected in this

depending on how many samples arerequired.• Feed rate is controlled by varying the

gap under the hopper and varying thevibration of the feeder.


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• Some common diameters used in microscopy analysis are: – Equivalent circle diameter –

Martin’s diameter – Ferret diameter – Shear diameter

• , d v and d sv can be calculated exactly for geometrical shapes

such as cuboids, rings etc.


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• According to Geldart (1989), in practice, value of for a specific material can be obtained as follows;1. Sieve out a narrow size fraction of the powder, usually

the middle of the size range or the coarser material, soas to obtain at least 0.5 – 1 kg.

2. Split this down using a riffler to obtain a few hundredsparticles.

3. Count the exact number (n) and weight them (M).Knowing the particle density, ρ p, calculate theequivalent sphere volume diameter, d v from


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4. Put the 0.5 – 1 kg of powder in a circular tube50 – 75 mm diameter and measure the

pressure drop, P, across the bed at a variety oflow flowrates.

5. The Carman-Kozeny equation relates pressuredrop to particle size, d sv, voidage, ε and beddepth, L at low Reynolds number.

6. Thus, d sv can be calculated from pressure dropdata.

7. From equation above, calculate .

23

21150

svd

U

L

P

(2.4)


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• For irregular particles: – Particles more than 75 m: sieving method – Particles less than 75 m: Laser diffraction technique: e.g.

Malvern Mastersizer, Coulter Counter etc.

• Different measurement techniques give different sizes ifthe particles are non-spherical, which is usually the case.

• dsv

and dv are generally considered to be the most useful

sizes where fluid/particle interactions are involved. (eg.Flow thru’ fixed and fluidized bed, pneumatic conveyingetc.) and they are related to each other thru’ the particlesphericity, .

• Malvern Master Sizer S: it measures d v if sphericity isknown, than d sv can be estimated.

• Other way to find d sv is by using Ergun equation.


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• According to Abrahamsen & Geldart (1980): – For quartz: = 0.8 – dv = 1.13d p (2.5)

• The average sphericity for regular figures:

• Thus, for non-spherical particles,d sv 0.87d p (2.7)

• For spherical or near-spherical particles;dv = dsv = dp (2.8)


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Example 2.1• Calculate the equivalent volume sphere diameter d v

and the surface volume equivalent sphere, d sv of acuboid particle of side length 1, 2 and 4 mm.


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Example 2.2• Particle (density=2000kg/m 3) with sphericity of 0.9

are poured into a container. A sample of 2000particles taken from the powder weighed 1000 mg.Determine volume diameter and surface/volumediameter


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2.3.2 Mean size and size distribution

• No industrial powder is monosized and it is usually necessary

to characterize the powder by both the size distribution and amean size .

• If a powder of mass M has a size range consisting of N p1 of sized1, Np2 of size d 2 and so on, the mean surface/volume size is

expressed by:

• where x is the weight fraction of particles in each size range.


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• When sieving is used, d 1, d 2,… are replaced by the arithmeticaverages of adjacent sieve apertures , d pi and the equation

becomes:

• and d p is mean particle size and not directly related to the d sv .• Mean particle size , d p: emphasis to the important influence

which small proportions of fines have.• Equation (2.11) should not be used if the powder has an

unusual distribution, for example bi- or tri-modal or has anextremely wide size range.


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• This type of powder will not behave in a homogeneous way and

cannot be characterized by a single number .

• Refer to Table 1 for example.

• The British Standard Sieve series is arranged in multiples of 2 1/4 ,

and this is used as a basis in Table 2.

• This will give an idea of relative spread as judged from the number

of sieves. (Refer Table 2).

• It is always advisable to first plot the size distribution of powder as

a weight fraction , or percentage in a size range , against the

average size , i.e. x vs. d pi because a plot of cumulative percentage

undersize can conceal peculiarities of distribution.


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Table 1: Size Distribution of sieved sand

Sieve aperture,

m

Size d pi , m Wt % in range,

x i

Cum. %

undersize -600 + 500 550 0.50 100

-500 + 420 460 11.60 99.5

-420 + 350 385 11.25 87.9

-350 + 300 325 14.45 76.65

-300 + 250 275 20.80 62.2

-250 + 210 230 13.85 41.4

-210 + 180 195 12.50 27.55 -180 + 150 165 11.90 15.05

-150 + 125 137 3.15 3.15


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Table 2: Width of Size Distributions Based on Relative Spread

Number of sieves on

which the middle 70%(approx.) of the powder

is found

Type of distribution

1 0 Very narrow2 0.03 Narrow

3 0.17 Fairly narrow4 0.25 Fairly wide5 0.33

Wide6 0.41

7 0.48

9 0.60 Very wide11 0.70

> 13 > 0.80 Extremely wide

pmd


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• Other method of characterizing powder, the median, d pm :

corresponds to the 50% value on the graph of cumulativepercentage undersize versus size .

• There is no universally agreed way of comparing the width of the

size distribution of two powders having different mean sizes, norof defining how wide a distribution is.

• In order to compare the width of the size distribution of two

powders having different mean size or defining how wide adistribution is; relative spread , from cumulative percentage

undersize plot is used as suggested by Geldart (2003). pmd


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• Some of the central tendency expression which depending onthe particular application are as below:

– Mode : The most frequently occurring size in the sample.The mode has no practical significance as a measure ofcentral tendency and is rarely used in practice.

– Median : Easily read from the cumulative distribution asthe 50% size, which splits the distribution into two equalparts. Also has no special significance as a measure ofparticle size.


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• Many different means can be defined for a given sizedistribution. All the means below can be described by the

equation;

• where x is the mean and g is the weighting function , which isdifferent for each mean definition (refer Table 3)


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Table 3 Definition of means

g(x) Mean and notation

dp Arithmetic mean, d p,a

dp2 Quadratic mean, d p,q

dp3 Cubic mean, d p,c

Log d p Geometric mean, d p,g

1/ d p

Harmonic mean, d p,h


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• Equation (2.15) tells us that the mean is the area between thecurve and the cumulative distribution, F(x) axis in a plot of F(x)versus the weighting function g(x) (refer Figure 3).

Figure 3: Plot of cumulative frequency, F(x) vs. weighting function, g(x).

F (

x )


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• Each mean conserve two properties of original

population of particles.• Example 1: arithmetic mean of surface distribution

conserves the surface and volume of originalpopulation (see example 3.3). This mean is alsoknown as surface-volume mean or Sauter mean.

• Example 2: quadratic mean of number distributionconserves the number and surface or original

population and is known as number-surface mean.


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Figure 4: Comparison between measures of central tendency.


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Physical properties of particulate

1. Shape2. Size3. Density

4. Porosity5. Hardness6. Sphericity

7. Roughness


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Porosity

• Porosity is the ratio of porevolume to its total volume.

• Porosity is controlled by: rocktype, grain size, pore distribution,cementation, diagenetic historyand composition.

• Measurement: BET, mercuryporosimeter


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Hardness

•

is a measure of how resistantsolid matter is to various kindsof permanent shape changewhen a force is applied.

•

Macroscopic hardness -strongintermolecular bonds• different measurements of

hardness: scratch hardness,

indentation hardness, andrebound hardness


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Sphericity• is a measure of how spherical (round) an object is.• Wadell in 1935, the sphericity of a particle is: the

ratio of the surface area of a sphere (with the samevolume as the given particle) to the surface area of

the particle:• Measurement: image analysis


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Roughness

• Physical/Morphology of the surface of particulates• Determine the contact force (interparticle forces)• Explain/Show the particle interaction with other particles or

any environment


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(Atomic Force Microscopy)


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Particles Crystallinity

Crystal vs. Amorphous


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Definition of crystal

• Solid with short and long range order withatoms of molecules in a fixed latticearrangement

• The distinction between a crystal andamorphous solid is that between order anddisorder over large distances

• Internal structure of crystals accessible by x-ray diffraction analysis.


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chapter 2 particle size characterization

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