1. Ert 318 : unit operations operations involving particulate solids
Dr. Hairul Nazirah Abdul Halim
School of Bioprocess Eng.

2. outline Introduction to particulate solids
Characterization of solid particles
Particle sizes
Screen analysis
Tyler standard screen analysis

3. Introduction
Large quantities of particles handled on the industrial scale
Silica gel
Thus, it is necessary to know:
- the distribution of particle sizes in the mixture
- the mean size of particles
It is frequently necessary to reduce the size of particles or form them into aggregates or sinters to ease the handling process
Amberlite

4. Characterization of solid particles
Individual solid particles are characterized by:
(a) Shape – regular – e.g. spherical or cubical
irregular – e.g. a piece of broken glass
(b) Size – influence the properties such as :
– the surface per unit volume
– the settling rate of particle in fluid
(c) Composition - determine properties such as
density and conductivity

5. Particle shape
The shape of an individual particle is expressed in terms of sphericity, which is independent of particle size
- For spherical particle of diameter, Dp ;
= 1
- For nonspherical particle;
Dp = nominal diameter of particle
Sp = surface area of one particle
ʋp = volume of one particle
(1)

6. - For particles rounded by abrasion; > 0.95
- For most of crush materials; < > 0.8
- For particles rounded by abrasion;
> 0.95
- For a cube and cylinder; = 1
Source ; Unit Operation of Chemical Engineering (McCabe,Smith & Harriot) ( Table 7.1 page 164)

7. Particle sizes Mixed particle sizes
In a sample of uniform particles of diameter Dp , the number
of particles in a sample, N is given by:
m = total mass of the sample
From Eq. (1) and (2), the total surface area of particle sample, A can be computed by:
(2)
(2)
(3)
These equation applicable to a mixture of particles having various sizes and densities, the mixture is sorted into fractions, each of constant density and approximately constant size.

8. Specific surface of mixture
The specific surface, Aw (the total surface area of a unit mass of particles) if and are constant is given by;
(4)

9. Average particle sizes
Volume-surface mean diameter ( )
The volume-surface mean diameter, is related to the Aw is given by:
By substituting Eq. (4) in Eq. (5);
(5)
(6)

10. Effective mean diameter, Dpm:
Arithmetic mean diameter ( ) Mass mean diameter ( )
where is the number of particles in the entire sample

11. Volume mean diameter ( )
Average volume of a particle = Divide the total volume of the sample with the number of particles in the mixture
The diameter of such a particle is the volume mean diameter ,
For samples consisting of uniform particles, these average diameters are all the same.
For mixtures containing particles of various sizes, however the several average diameters may differ widely from one another.

12. Number of particles in mixture
For a given particle shape, the volume of any particle is:
where is the volume shape factor.
It is different for various regular solids which are;
(1) for a sphere
(2) for a short cylinder (height = diameter)
(3) 1.0 for a cube
Assuming is independent of size:

13. screening
A method of separating a mixture or grains or particles into 2 or more size fractions.
The over sized materials are trapped above the screen, while undersized materials can pass through the screen.
Sieves can be used in stacks, to divide samples up into various size fractions and hence determine particle size distributions.
Sieves and screen are usually used for larger particle sized materials i.e., greater than approximately 50µm (0.050mm).

14. SIEVE TRAYS Pan (the finest particles retained here)
Sieve (different mesh size)
Sieve trays were put on a stack (shaker)

15. screen analysis
Used to measure the size of particles in the size range between in.(76 mm and 38 µm)
A set of standard screens is arranged serially in a stack, with the smallest mesh at the bottom and the largest at the top
The sample is placed on the top screen and the stack shaken mechanically for 20 min
The particles retained on each screen are removed and weighed, and the masses of the individual screen increments are converted to mass fractions or mass percentages of the total sample
Any particles that pass the finest screen are caught in a pan at the bottom of the stack

16. Tyler standard screen analysis
Tyler Standard Screen based on mesh opening sizes (200 mesh-screen).
The mesh number system is a measure of how many openings there are per linear inch in a screen.
Sizes vary by a factor of √2.
Refer Appendix 5 (McCabe) for the Tyler standard screen series.

17. Table 28.1 Screen analysis

18. Column 1 – mesh size
Column 2 – width of opening of the screens
Column 3 – the mass fraction of the total sample that is retained on the designated screen
xi is the number of the screen starting at the bottom of the stack; thus;
i = 1 for the pan, and screen i + 1 is the screen immediately above screen i
Column 4 – average particle diameter Dpi in each increment (particle diameter equal to the mesh opening of screen i)
Column 5 – cumulative fraction smaller than each value of Dpi
In screen analysis, cumulative fractions are sometimes written starting at the top of the stack and express as the fraction larger than a given size

19. THANK YOU