# Determination of particle size and particle size distribution using the sieving method

Aim: Determination of particle size and particle size distribution using sieving method.

Requirements:

(a) Chemicals: A sample of any granules or powder.

(b) Glassware and apparatus: Sieve set, mechanical sieve shaker, weighing balance etc.

Theory:

The powder contains particles of uniform size whereas granules are non-uniform in size. When sample of powder or granules is polydisperse, for application purpose they must be characterized for terms size, shape and particle size distribution. The particle size is expressed in terms of diameter.

The particle size distribution, (i.e. the number of particles of different sizes), is responsible for important physical and chemical properties such as: mechanical bulk behaviour, surface reaction, taste, miscibility, filtration properties and conductivity.

The examples clearly show how important it is to have knowledge of the particle distribution, particularly within the context of quality assurance in the production of bulk goods. If the particle distribution changes during the manufacturing process, then the quality of the finished product will also change.

Only a continuous monitoring of the particle size distribution can guarantee a constant product quality. Since all particles or granules in sample are never being uniformly spherical their size is expressed in terms of equivalent spherical diameters.

The equivalent spherical diameters include surface diameter, volume diameter, projected diameter, stokes diameter, volume-surface diameter and surfacesurface diameter. For sample with non-spherical particles or powder their size is measured horizontally by arbitrarily fixing line across the centre of the particle.

These measurements are expressed as Feret diameter, Martin diameter and the Projected area diameter. There is no universal method available for determination of particle size of a polydispersed powder. It is either derived from the arithmetic mean or harmonic mean or geometric mean.

Arithmetic mean of a powder is defined as the geometrical sum of the various particle sizes divided by the number of particles. It is mathematically written as

Arithmetic mean = Sum of particle / size Number of particles … (1.1)

Edmondson’s general equation for the average particle size is

dmean = (∑ ndp + f) 1/p / (∑ ndf) 1/p … (1.2)

Where, n is number of particles, d is diameter or the equivalent diameter and p is an index related to size of an individual particle.

The value of p can be 1, 2 or 3. If p = 1, it means length, p = 2 it means surface area and p = 3 means the volume.

The term f is a frequency factor which can be 0, 1, 2 and 3. More useful information is obtained when sample segregation methods are used, for example sieving method wherein number of particles of weights within a certain range is plotted as function of mean particle size.

Sieving method is simple method that gives reproducible results in short time but unfortunately is suitable for fine particle samples.

Procedure:

1. Arrange the set of sieves (IP or USP standard) in descending order. (Place sieve number 10 at top, below which place sieve numbers 20, 40, 60, 80, 100, respectively and 120 at the bottom).

2. Weigh, accurately, the given sample (100 g) and place in the top sieve. Cover sieve with lid to avoid loss during shaking.

3. Operate the sieve-shaking machine for 5 min.

4. Collect fractions of samples retained on each sieve and on receiver at the bottom of set.

5. Weigh samples using weighing balance.

6. Calculate per cent frequency of each size of particles.

7. Plot histogram (bar graph) of fractions (B) and% weight retained (C) as given in Table. Draw the% cumulative frequency curve (Q3) from the cumulative% weight retained against the nominal sieve mesh (x).

Calculations:

1. Calculation of cumulative% weight retained: % weight retained on sieve = Weight retained on sieve Total weight of powder × 100 … (1.3)

2. Calculation of% cumulative frequency: % Cumulative frequency =% weight retained on previous sieve +% weight retained on sieve under consideration … (1.4)

Precautions:

1. Shake powders or granules for short period.

2. Arrange sieves in perfect descending order of their size from top to receiver.

3. If the difference between the original sample weight and the sum of the individual fractions is greater than 1% then, according to Deutsches Institute Fur Normong (German Institute for Normalization) DIN 66 165, the sieving process must be repeated.

4. Avoid loss of sample during shaking and weighing.