Particle Size FAQs

F A Q’s on Particle Size Analyzing
1. What is a particle?
A particle is a minute object with a certain size and shape. Macroscopically it is very small, but
microscopically, a particle contains numerous molecules and atoms.
2. What is particle size?
Although this simply implies particle size is the size of an individual particle, determining
absolute particle size can be difficult.
3. What is particle size distribution?
The number of particles that fall into each of the various size ranges given as a percentage of the
total number of all sizes in the sample of interest.
4. How to express particle size distribution?
1) Table: percentage of particles from the total within a size range; it includes differential
distribution and cumulative distribution.
2) Figure: particle distribution by histogram and curves, etc.
3) Function: particle distribution functionally including R-R distribution and normal
distribution.
5. What is particle diameter?
It is the diameter of a particle normally expressed either in microns (10^-6m) or nanometers
(10^-9m).
6. What is equivalent particle diameter?
For certain physical characteristics a particle will have equivalent properties to a spherical particle,
hence, equivalent diameter. Equivalent diameter can be divided into following measurements:
1) Equivalent Volumetric Diameter: diameter of a spherical particle having the same
constitution and volume as the particle tested. Particle diameter obtained by laser methods
is generally recognized as equivalent volumetric diameter.
2) Equivalent Sedimentation Speed Diameter: diameter of a spherical particle having the same
constitution and sedimentation speed as the particles to be tested. Diameter measurements
obtained by gravity sedimentation or centrifugal sedimentation belong under this category,
also known as Stokes diameter.
3) Equivalent Resistance Diameter: Diameter of a spherical particle having the same
constitution and resistance as the particle to be tested. Diameter measurements obtained by
Coulter methods are consider equivalent resistance diameters.
4) Equivalent Projection Area Diameter: Diameter of a spherical particle having the same
constitution and projected area as the particle to be tested. Image analysis is an equivalent
projection area measurement.
FAQ on Particle Size Analyzing
Beatop (Zhuhai) Instruments Limited http://www.beatop.com 1/8

7. Why introduce equivalent particle diameter?
In practice, particles are not uniformly shaped therefore they are difficult to define in a single
number. By correlating the particle to a sphere, one number can describe the size of a
geometrically complicated particle.
8. What is D50?
Also known as the median diameter or the medium value of the particle size distribution, it is the
value of the particle diameter at 50% in the cumulative distribution. It is one of an important
parameter for representing particle size. For example, if D50=5µm, then 50% of the particles in
the sample are larger than 5µm, and 50% smaller than 5µm.
9. What is average diameter?
It is the weighted average of particle size.
10. What is D97? What is the purpose of it?
It is the particle diameter value where 97% of the sample is smaller than that value. It is useful for
determining the upper limit to the particle size distribution.
11. What are frequently used methods to test particle size?
There are microscope imaging methods, sieve analysis, gravity sedimentation, centrifugal
sedimentation, Coulter (resistance) analysis, laser diffraction/scattering methods, electron
microscope, ultrasonic, gas sorption, etc.
12. Advantages & disadvantages of the above methods:
1) Microscope Imaging:
• Advantage: simple, direct test procedure, shape analysis available.
• Disadvantage: long test cycle, relatively poor representation, testing of ultra fine particles
not possible.
2) Sieve Analysis:
• Advantage: simple, direct test procedure, low cost.
• Disadvantage: samples smaller than 40µm can not be tested; test results are subject to
deformation of sieve meshes.
3) Sedimentation (including gravity sedimentation & centrifugal sedimentation):
• Advantage: low price, continuous operation, high degree of accuracy and repeatability,
relatively broad test range.
• Disadvantage: long test cycle.
4) Coulter:
• Advantage: easy operation, short testing cycle, relatively high accuracy.
• Disadvantage: narrower size range, easily blocked apertures, electric conductivity of
medium necessary.
5) Laser methods:
• Advantage: easy operation, broad test range, high degree of accuracy and repeatability,
on-line test and dry test available.
• Disadvantage: test results are subject to distribution pattern, high cost of instrument.

6) Electron Microscope:
• Advantage: capable of measuring particles of nanometer size, high resolution.
• Disadvantage: possible alteration of particles during sample prep, small representation of
overall sample, and high cost.
7) Ultrasonic:
• Advantage: direct test on highly concentrated liquid.
• Disadvantage: low resolution.
8) Gas absorption:
• Advantage: low cost of instrument, sample dispersion not an issue, testing on magnetic
powders capable.
• Disadvantage: only average particle size available, particle size distribution unobtainable.
13. What are differential distribution and cumulative distribution?
Differential distribution is the percentage of particles from the total that are within a specified
sized range; for example, 30% within 1-10um range, 50% within 10-20um range, and 20% within
20-30um range. Cumulative distribution is the sum of the differential distributions. The
cumulative distribution is obtained by accumulation of differential distribution, for instance, 80%
of the particles are smaller than 20um.
14. What is repeatability?
Repeatability is the relative error among multiple results from the same sample.
15. How is repeatability obtained?
In which, n is number of tests (normally n>=10);
xi is test results for each time;
x is average value of multiple tests;
σ is standard deviation;
Thus relative error of repeatability is:
16. What will affect repeatability?
1) Stability of the instrument or test method
2) Whether dispersion of the sample is fully obtained or not.
3) Whether the sampling is representative of the overall material?
4) Whether the operational procedures are standardized or not?
5) Working condition including voltage, temperature, clean environment, etc
1
)( 2
−
−
=
∑
n
x xi
σ
%100×=
x
σ
δ

17. What is the accuracy of an analyzer and how is it obtained?
It is the error between values for the test results generated by the instrument and the known value
of the standard sample. It is obtained by:
In which, x is the average value of multiple D50;
D is standard value of standard sample;
Δ is error of accuracy
18. Principle of laser particle size testing:
Laser particle size analyzers work according to the optical properties peculiar to lasers, such as
monochromaticity and collimation, to cause diffraction and scattering. The diffraction and
scattering phenomenon take place when the laser beam illuminates the dispersed particles in the
liquid. The diffracted or scattered light passes through the Furier lens to form a bull's-eye-shaped
ring of light on the focal plane. The radius of the light ring is related to the size of the particles and
the density of the diffracted light is related to the number of the relevant particles. The diffraction
and scattering signals from the particles are received through the circular array of the photoelectric
receiver on focal plane. Then the signals are transferred to the computer through an A/D transfer.
Lastly, the data is processed using Mie scattering theory or Fraunhofer diffraction theory. The
particle size distribution of the sample is thus obtained as per the illustration below.
19. Why use a laser as light source?
Lasers provide good collimation and monochromaticity for clear distribution of scattering the
spectrum.
%100×
−
=∆
x
xD

20. What is difference between Mie scattering and Fraunhofer diffraction?
Because of the computational advances in modern electronics, it is possible to calculate the
multitude of operations for Mie scattering. Mie theory represents the laws of scattering precisely.
Fraunhofer diffraction is an approximation of the Mie theory. It involves less computational power
but results in larger error especially on finer particles.
21. What causes aggregation?
Aggregation occurs when multiple particles adhere to each other to form a larger conglomerate.
Aggregation results from interaction between particles from either charges in the surrounding,
outside forces, or from van der Waals forces. Smaller particles are more prone to aggregation due
to stronger surface energy and opportunities to interact.
22. Frequently used methods for sample dispersion:
Particles can be dispersed through agitation, ultrasonic vibration, a dispersant or a combination
these techniques.
23. Requirements of the medium during particle size testing:
For particles tested in a liquid (medium), the requirements are: 1) high purity; 2) no physical or
chemical reaction with particles; 3) good affinity with particles, i.e. easy to disperse particles
24. What are frequently used mediums?
Water is the most frequently used medium. In addition, there are other available mediums, for
instance ethanol, gasoline, kerosene, a mixture of water and glycerin, ethanol and glycerin etc.
25. What is a dispersant?
A dispersant is a substance that is added to the medium in small amounts to weaken the tension
between the medium and particles to allow the particles to be dispersed better.
26. Usage & dosage of dispersant.
Before testing, mix dispersant in the medium until it is thoroughly dissolved. The ratio of
dispersant-to-water is approximately 0.2%-0.5%.
27. Is a dispersant necessary in the case of an organic solvent (such as ethanol) as the
medium?
No, generally organic solvents disperse particles efficiently enough by themselves.
28. How can the effect of a dispersant be evaluated?
1) Microscope: visually examine to see if aggregation exists.
2) Measurement: measure one sample with dispersant and one with out. Compare results.
29. Requirements for sampling of a dry powder:
1) Take multi-point samples from the main batch.
2) Reduce samples until it is uniform and then make multi-point sampling (4 points at least)

30. Requirements for suspension sampling:
1) Agitate thoroughly
2) Draw for the middle of the suspension.
31. What is the appropriate concentration of the suspension for laser particle size analysis?
Laser particle size analyzers operate properly only when the signal on the photoelectric receivers
are within a certain density range. These photoelectric signals are generated by the illumination of
scattered light. The received signal is subject to the number of particles in the suspension and
there size. The more particles that are in the suspension the weaker the signal is going to be.
Generally, the concentration value will be with 0.01% - 0.1% depending on the coarseness of the
particles.
32. Normal dispersants for common samples:
Sample name Dispersant Sample name Dispersant
CaCO3 Sodium pyrophosphate
PAAS
Graphite
Silicon carbide
White corundum
CMC, Tannic Acid
Sodium hexmetaphosphate
Talc Sodium pyrophosphate
Al powder Sodium pyrophosphate
Kaolin Sodium hexmetaphosphate
Sodium pyrophosphate
Quartz powder Sodium pyrophosphate
33. Methods for powder processing:
Particle size Particle sizeDry mode
Before
processing
After
processing
Wet mode
Before
processing
After
processing
Air mill <45µm 5µm
Impact mill <10mm 10µm
Vibration mill <10mm 10µm
Raymond mill Lump 150-30µm
Ball mill Lump 30-10µm
Agitating mill <45µm 60%-90%
particles 2µm
in diameter
34. Densities of some common samples:
Sample Density Sample Density Sample Density
CaCO3 2.7 Al powder 2.7 Aluminum oxide 3.98
Talc 2.7 Graphite 2.2 W powder 19.3
Kaolin 2.7 Barite 4.4 Diamond 2.39
Silicon dioxide 2.7 Zn powder

35. Conversation from sieve mesh number to micron size:
Mesh Num. µm Mesh Num. µm Mesh Num. µm
100 150 600 23 5000 2.5
150 100 800 18 10000 1.3
200 75 1000 13 12000 1
325 45 1250 10
400 38 2500 5
36. Mediums for common samples:
Sample name Medium name Sample name Medium name
CaCO3 Talc Water
30% Ethanol +water
Kaolin Graphite Water
Ethanol
Silicon dioxide Al powder Water
Water + Glycerin
Diamond Starch Octanol
Aluminum oxide
Water
Medicine Oil
Water
Silicon carbide Water
Water +Glycerin
Cement Kerosene
Ethanol +Glycerin
F A Q’s on Sedimentation Method
37. Principle for sedimentation method - Stokes law
Particle size distribution by sedimentation measures the particle speed of sedimentation in a liquid.
Larger particles settle faster than smaller ones in a liquid. The relationship between particle
diameter and speed of sedimentation is obtained in accordance to Stokes law:
From Stokes law, the particle speed of sedimentation is proportional to the square of the particle
diameter. It is clear that smaller particles lead to lower speeds of sedimentation. For example,
under the same conditions, if the ratio of two particles’ diameters is 10:1 then the ratio of
sedimentation speed of these two particles is 100:1.
2
18
)(
D
g
V
fs
η
ρρ −
=

Some sedimentation analyzers introduce centrifugal force in order to make the sedimentation
testing cycle faster while still maintain accuracy. The relation of speed and diameter under the
centrifugal state is as follows:
In which ω is angular velocity of the centrifuge and r is the distance from the particle to the axle’s
center. Due to high rpm of the centrifuge, ω2
r is significantly larger than gravitational acceleration
g. Therefore, for a given particle size, sedimentation speed Vc under a centrifugal state will be far
greater, hence, reducing the testing time.
38. Principle for sedimentation method - Bill law:
The particle diameter is obtained from Stokes law after knowing the particle speed of
sedimentation. In practice, direct measurement of the speed of sedimentation is difficult. In
sedimentation testing, various rates of light energy penetrate the suspension to indirectly measure
the particle speed of sedimentation. The quantitative relationship between the variation of light
energy and particle diameter at a certain time is given by the Bill law:
39. Applications of sedimentation instruments:
Sedimentation instruments are used for measuring inorganic powders such as metallic powders,
non-metallic powders and some synthetic powder, etc.
40. Powder not acceptable sedimentation measurement:
1) Organic powders
2) Magnetic powder
3) Powders out of test range
41. Influence on repeatability of test results:
1) Fully dispersed sample, ultrasonic time, suitability of dispersant and sedimentation medium.
2) Standardization of sampling method including sampling of bulk powder, reduction of dry
powder, sampling of suspension, etc.
3) Suitable surroundings including stability of voltage and temperature fluctuations.
42. Why is glycerin sometimes added to the sedimentation medium?
Glycerin effectively restricts the speed of sedimentation. This allows for coarse particles to be
measured more effectively over time.
2
2
18
)(
D
r
V
fs
c
η
ωρρ −
=
dDDDnkIIi ∫
∞
−=
0
2
0 )()lg()lg(

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