This document discusses particle size distribution and how it is measured. It defines different particle size metrics like volume mean diameter and provides examples of their significance. It describes common methods to measure particle size distribution including sieve analysis, dynamic image analysis, and laser diffraction. Sieve analysis separates particles by size and weighs the fractions, dynamic image analysis uses image processing to determine particle outlines, and laser diffraction analyzes angular light scattering patterns to calculate particle sizes.

1. The generalized form of the equations
(ASTM E 799) is:
where,
ഥD = averaging process
Di = the diameter of ith particle
What is Particle Size Distribution ?
Ferret diameter
Volume−based particle size equals the diameter of the sphere
that has the same volume as a given particle. 𝑫 𝒗 = 𝟐
𝟑 𝟑𝑽
𝟒𝝅
Area-based particle size equals the diameter of the sphere that has the
same surface area as a given particle.
𝑫 𝒔 =
𝟐 𝟒𝑨
𝝅
Hydrodynamic or aerodynamic particle size equals the diameter of the
sphere that has the same drag coefficient as a given particle.
D50 is the diameter of the particle that 50% of a sample's mass is smaller
than and 50% of a sample's mass is larger than.
frequency and undersize particle size distribution
Arithmetic or number mean or ഥ𝐃10/D[1,0] : It is the average
diameter of particle size of the particles.
Volume/surface mean or ഥ𝐃32/D[3,2] : In fluid dynamics, Sauter
mean diameter (SMD, d32 or D[3, 2]) is an average of particle size.
It is defined as the diameter of a sphere that has the
same volume/surface area ratio as a particle of interest.
Mean diameter over volume or ഥ𝐃43/D[1,0]: It is center of mass for
frequency distribution and is also called the DeBroukere mean.
different equivalent
diameters
d50 d90
d10
Particle-size distribution (PSD) of a powder, or granular material, or
particles dispersed in fluid, is a list of values or a mathematical function that
defines the relative amount, typically by mass, of particles present according
to size.

2. What is it’s significance ?
Particle size distribution has effect on the following :
• Used for calculating solid friction factor.
• Terminal settling velocity(𝜔 𝑓𝑜).
• Flowability increases with particle size.
• Increase in particle size decreases bulk density
• Loose poured and tapped bulk density depend
on D[3,2](surface-volume mean particle
diameter).
• HR increases when D[3,2] decreases and fines
level increases.
• As D[3,2] decreases, the powder becomes more
cohesive and occupies more volume in the
loosely poured state than free flowing particles.
• Decrease in particle size will increase viscosity.
• Increase in particle size will decrease viscosity.
• A wide particle distribution will lead to lower
viscosity.
• As long as there is a constant particle size, if
more particles are introduced, flow behaviour will
shift from Newtonian to shear thin to shear thick.
How do we measure it ?
sieving analysis
Measuring Principle :
Sieve analysis is used to divide the particulate
material into size fractions and then to determine the
weight of these fractions. In this way a relatively
broad particle size spectrum can be analyzed quickly
and reliably. [Range:40 µm to 125 mm]
Standard : ASTM C136 / C136M - 14
Make/Model : Retsch - AS 400 control, AS 200 tap
Dynamic image analysis system
Measuring Principle :
Dynamic Image Analysis analyzes the
shadow projections of particles. It
transform grayscale images through a
multistep algorithm into binary images to
determine the exact outlines. [Range:0.8
µm to 8 mm]
Standard : ISO 13322-1, ISO 13322-2
Make/Model : Retsch – CAMSIZER P4(20 µm
to 30 mm), CAMSIZER X2(0.8 µm to 8 mm)

3. How do we measure it ? Contd…
typical image analysis steps
Measuring Principle :
• In a laser diffraction measurement a laser beam passes through a
dispersed particulate sample and the angular variation in intensity of the
scattered light is measured.
• Large particles scatter light at small angles relative to the laser beam and
small particles scatter light at large angles.
• The angular scattering intensity data is then analyzed to calculate the
size of the particles that created the scattering pattern using the Mie
theory of light scattering.
• The particle size is reported as a volume equivalent sphere diameter.
Standard : ISO 13320:2009
Laser diffraction size analyzer
Make/Model : Malvern – Mastersizer 3000 (10nm to
3.5mm), HORIBA LA-960 (0.01 μm to 5000 μm)
dry analysis of powder
Basic Optical System of a Laser Diffraction Particle Size Analyzer