This document discusses particle analysis and screening. It begins by defining key particle properties like size, shape, and density. Different measurement techniques are described that characterize particles based on these properties. Average particle sizes are defined for mixtures using various means. Screen analysis is then covered, including how to perform sieve analysis using standardized screen sizes and how to analyze the results. Material balances for screening operations are also presented, showing equations to calculate flow rates of undersize and oversize particles based on feed rates and mass fractions.

1. Chapter 3
Screen Analysis and separation
of Particles
Dr. Bilha Eshton

2. 3.1 Analysis of Solid particles
3.1.1 Characterization of solid particles
• Individual solid particles are characterized by their
size, shape and density.
• Particles of homogeneous solids have the same
density as the bulky material.
• Particles obtained by breaking up a composite solid
(e.g metal-bearing ore) have various densities usually
different from the density of the bulk material.
Dr. Bilha Eshton

3. Why measure particle properties?
1. Better control of product quality (cement, urea,
cosmetics etc.)
In an increasingly competitive global economy, better
control of product quality delivers real economic benefits
such as:
• ability to charge a higher premium for your product;
• reduce customer rejection rates.
Dr. Bilha Eshton

4. 2. Better understanding of products, ingredients
and processes
• improve product performance.
• troubleshoot manufacturing and supply issues
• optimize the efficiency of manufacturing processes
• increase output or improve yield
• stay ahead of the competition
3. Designing of equipment for different
operations
• For example equipment for crushing, grinding,
conveying, separation, storage etc.
Dr. Bilha Eshton

5. Which particle properties are important to
measure?
From a manufacturing and development perspective,
some of the most important physical properties to
measure are:
• particle size
• particle shape
• surface properties
• mechanical properties
• Microstructure
• Density
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6. 3.1.2 Particle shape
• The shape of individual particles is best expressed in terms of
sphericity (Φs) which is independent of particle size.
• For spherical particle of diameter Dp, Φs=1; for non-spherical
particle, the sphericity is defined by this relation:
Φ𝑠 ≡
6𝑉
𝑝
𝐷𝑝𝑠𝑝
… … … … … … … … … … … … (3.1)
• Where:
Dp = equivalent or nominal diameter of particle
sp = surface area of one particle
Vp = volume of one particle
Dr. Bilha Eshton

7. • The equivalent diameter is sometimes defined as
the diameter of a sphere of equal volume.
• For fine particles, Dp is usually taken to be the
nominal size based on screen analysis or
microscopic analysis.
• The surface area is found from adsorption
measurements or from the pressure drop in a
bed of particles.
• For many crushed materials, Sphericity is
between 0.6 and 0.8. For particles rounded by
abrasion, their sphericity may be as high as 0.95.
Dr. Bilha Eshton

8. For many crushed materials, Φs is between 0.6 and 0.8 as
shown in the Table below.
Dr. Bilha Eshton
Table 28.1 in Unit operations of
Chemical Eng. Vol 5

9. Some materials with their images
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10. 3.1.3 Particle Size
• The most important physical property of particulate
samples is particle size.
• Particle size measurement is routinely carried out across
a wide range of industries and is often a critical
parameter in the manufacturing of many products.
• Particle size has a direct influence on material
properties such as:
– Reactivity or dissolution rate e.g. catalysts, tablets
Dr. Bilha Eshton

11. – Stability in suspension e.g. sediments, paints
– Efficacy of delivery e.g. asthma inhalers
– Texture and feel e.g. food ingredients
– Appearance e.g. powder coatings and inks
– Flowability and handling e.g. granules
– Viscosity e.g. nasal sprays
– Packing density and porosity e.g. ceramics.
Dr. Bilha Eshton

12. • In general particle diameters may be specified for any
equi-dimensional particle. However, most particles
used in industries are not equi-dimensional i.e. that
are longer in one direction than in others.
• In order to simplify the measurement process, it is
often convenient to define the particle size using the
concept of equivalent spheres.
• In this case the particle size is defined by the diameter
of an equivalent sphere having the same property as
the actual particle such as volume or mass for
example.
Dr. Bilha Eshton

13. • The equivalent sphere concept works very well for
regular shaped particles.
• However, it may not always be appropriate for
irregular shaped particles, such as needles or plates,
where the size in at least one dimension can differ
significantly from that of the other dimensions.
• Such particles are often characterized by the second
longest major dimension. For example needle like
particles, Dp would refer to the thickness of the
particle, not their length.
Dr. Bilha Eshton

14. Some common diameters used in microscope analysis
are statistical diameters such as:
• Martin’s diameter (length of the line which bisects
the particle),
• Feret’s diameter (distance between two tangents on
opposite sides of the particle) and
• shear diameter (particle width obtained using an
image shearing device).
• Some of these diameters are described in the next
slide
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15. Dr. Bilha Eshton

16. • If a sieve is used to measure the particle size, an
equivalent sphere diameter will be obtained. This is
the diameter of a sphere passing through the same
sieve aperture.
• If sedimentation technique is used to measure
particle size then, the particle diameter is expressed
as the diameter of a sphere having the same
sedimentation velocity under the same conditions.
• Other examples of the properties of particles
measured and the resulting equivalent sphere
diameters are given in the next slide.
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17. Dr. Bilha Eshton

18. UNITS FOR PARTICLE SIZE
Depending on convention, particle sizes are expressed in
different units depending on the size range involved.
• Coarse particles: inches or millimeters,
• very fine particles: micrometers or nanometers.
• Ultrafine particles: surface area per unit mass, i.e.
m2/g
Dr. Bilha Eshton

19. 3.1.4 Mixed particle sizes and size analysis
• In a sample of uniform particles of diameter Dp the total
volume of the particles is:
𝑉
𝑝 =
𝑚
𝜌𝑝
……………………………………………………..3.2
Where: m = total mass of the sample
ρp = density of particles
• The number of particles in a sample is then:
𝑁 =
𝑚
𝜌𝑝𝑉𝑝
……………………………………………………….3.3
• Total surface area of the particles is:
𝐴 = 𝑁𝑠𝑝 =
6𝑚
Φ𝑠𝜌𝑝𝐷𝑝
………………………………….3.4
Dr. Bilha Eshton

20. Particle Size Analysis
• To analyse the particle size for a mixtures of particles
having various sizes and densities, the mixture is sorted
into fractions, each of constant density and approximately
constant size.
• Each fraction can then be weighed, or the individual
particles in can be counted or measured by any method.
Equations 3.3 and 3.4 can then be applied to each fraction.
• Information from such particle size analysis is tabulated to
show the mass or number fraction in each size increment
as a function of the average particle size (size range).
Dr. Bilha Eshton

21. • An analysis tabulated based on size increment as a
function of average particle size is called a
differential analysis.
• An analysis which is obtained by adding,
consecutively, the individual increments, starting
with that containing smallest particles is called the
cumulative analysis.
• Both method are shown in a Figure (next slide)
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22. Differential Analysis
Cumulative Analysis
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23. Mass Quantities of sample of particles (Differential
Analysis)
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24. Cumulative mass fraction plot of data from previous
figure.
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25. 3.1.5 Specific Surface Area of Mixture
• If the particle density ρp and sphericity Φs are known, the
surface area of the particles in each fraction may be
calculated from eqn. 3.4 and the results for all fractions
added to give Aw, the specific surface area (i.e. the total
surface area per unit mass of particles).
• If ρp and Φs are constants, Aw is given by:
Dr. Bilha Eshton

26. • Hence, Aw ……………………………………3.5
Where subscript = individual increments
xi = mass fraction in a given increment
n = number of increments
ഥ
𝐷𝑝𝑖 = Average particle diameter, taken
as arithmetic average of smallest and
largest particle diameters in
increment.
Dr. Bilha Eshton

27. 3.1.6 Average Particle Size
The average particle size for a mixture of particles is defined by
the volume-surface mean diameter ഥ
𝐷𝑠 which is related to the
specific surface area Aw.
It is defined as:
ഥ
𝐷s ≡
6
Φ𝑠𝐴𝑤𝜌𝑝
…………………………………3.6
Substituting Aw (eq. 3.5) gives:
………………………………………3.7
Dr. Bilha Eshton

28. • If the number of particles in each fraction Ni is known
instead of the mass fraction, ഥ
𝐷𝑠 , is given by:
…………………………………..3.8
• And the arithmetic mean diameter ഥ
𝐷𝑁 is calculated by:
………………………………..3.9
Where:
NT = the number of particles in the entire sample.
Dr. Bilha Eshton

29. • The mass mean diameter ഥ
𝐷𝑤 is calculated from:
………………………………..3.10
• Dividing the total volume of the sample by the
number of particles in the mixture gives the average
volume of a particle. The diameter of such a particle
is a volume mean diameter calculated from:
………………………………..3.11
Dr. Bilha Eshton

30. • For samples consisting of uniform particles these
average diameters are all the same.
• For mixtures containing particles of various sizes,
average diameters may differ from one another.
Dr. Bilha Eshton

31. 3.1.7 Number of Particles in a Mixture
• Equation 3.3 is used to calculate the number of particles in
fraction and Nw, the total population in one mass unit of
sample is obtained by summation over all the fractions.
• For a given particle shape, the volume of any particle is
proportional to cube of its diameter.
• i.e. 𝑉
𝑝 = 𝑎𝐷𝑝
3……….……………………………………..3.12
Where a is the volume shape factor.
From equation 3.3 assume a is independent of size, then:
……………………….……….3.13
Dr. Bilha Eshton

32. 3.1.8 Screen (sieve) Analysis and Standard
screen series
• Standard screens are used to measure the size (and
size distribution) of particles in the range between 3
and 0.0015 in. (76 mm and 38μm).
• Testing sieves are made of woven wire screens, the
mesh and dimensions (openings) of which are
carefully standardized.
• The openings are square and each screen is identified
in meshes per inch. e.g. 10 mesh, Dpi = 1/10 = 0.1 in.
Dr. Bilha Eshton

33. Mesh No. is the numbers
of opening per linear
inch.
• Area of opening in any screen = 2 times the
area of opening in next smaller screen.
• Mesh dimension of any screen = 1.41 times
Mesh dimension of next smaller screen.
Dr. Bilha Eshton

34. • The actual openings are however smaller than those
corresponding to the mesh number, because of
thickness of wire.
• The common screen series is the Tyler standard screen
series. The area of the openings in any one screen in
this series is exactly twice to that of the openings in
the next smaller screen.
• The ratio of the actual mesh dimension of any screen
to that of the next smaller screen is √2 =1.41.
Dr. Bilha Eshton

35. • For close sizing, intermediate screen are available, each of
which has a mesh dimension = 1.189 times that of next smaller
standard screen.
• Analysis using standard screen: Screens are arranged serially in
a stack, with the smallest mesh at the bottom and the largest at
the top. Materials are loaded at top and then shacked for a
period of time (e.g. 20 minutes).
• The particles retained of each screen are removed, weighed
and masses of individual screen increments are converted into
mass fraction of total sample.
• Any particle that passed the finest screen are caught in the pan
at the bottom of stack. Results of screen analysis are then
tabulated.
Dr. Bilha Eshton

36. Table 1. Tyler standard screen series (Appendix 20)
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37. Dr. Bilha Eshton

38. Dr. Bilha Eshton
Table 2. Other standard screen series

39. A typical screen analysis is shown in Table 3 (next slide)
• First column: mesh size,
• second column: width of opening of screen,
• third column: mass fraction of total sample that is retained
on that screen xi (where i is the number starting from the
bottom of the stack),
• fourth column: averaged particle size Dpi (since the particle
on any screen are passed immediately by the screen ahead
of it, the averaged of these two screen are needed to specify
the averaged size in that increment).
• Fifth column: cumulative fraction smaller than Dpi.
Dr. Bilha Eshton

40. Table 3: Screen Analysis
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41. Example 1
The screen analysis shown in Table 3 applies to a
sample of crushed quartz. The density of particles is
2650 kg/m3 and the shape factor are a=2 and Φs =
0.571. For material between 4-mesh and 200-mesh in
particle size, calculate:
(a) Aw in square millimeters per gram and Nw in
particles per gram.
(b)ഥ
Dv, ഥ
Ds , ഥ
Dw and Ni for the 150/200- mesh increment.
(c) What fraction of the total number of particles is in
the 150/200- mesh increment?
Dr. Bilha Eshton

42. 3.2 SCREENING
• Screening is a method of separating particles
according to size alone by a semipermeable
membrane (or screening surface).
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43. • In screening, the solids are dropped on, or through a
screening surface.
• The under size or fines particles pass through the
screen openings; the oversize or tails do not.
• Material passed through a series of screens of
different sizes is separated into sized fractions, i.e.
fractions in which both the maximum and minimum
particle sizes are known.
• The final portions consist of particles of more uniform
size than those of the original mixture.
Dr. Bilha Eshton

44. The screening surface may consist of:
(i) woven-wire (ii) perforated plastic cloth
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(iii) grizzly bars and wedge wire sections

45. 3.2.1 Material balance over a screen
• Simple material balance can be written over a
screen which is useful in calculating the ratios
of feed, oversize and undersize from the
screen.
• Consider a feed which contains material A and
B to be separated.
• Let F, D and B be the mass flow rates of feed,
overflow and underflow, respectively.
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46. • and let xF, xD and xB be the mass fractions of
the material A in these three streams.
• The mass fractions of material B in the feed,
overflow and underflow are: 1-xF, 1-xD and 1-xB
respectively.
• Since the total material fed to the screen must
leave it either as underflow (B)or as overflow
(D), then:
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47. 𝐹 = 𝐷 + 𝐵……………………………………3.14
• The material A in the feed must also leave in
these two streams, then
𝐹𝑥𝐹=𝐷𝑥𝐷+𝐵𝑥𝐵…………………………….3.15
• Eliminating B from equations 3.14 and 3.15 gives
𝐷
𝐹
=
𝑥𝐹−𝑥𝐵
𝑥𝐷−𝑥𝐵
…………………………………………3.16
Dr. Bilha Eshton

48. Eliminating D from equation 3.15 gives:
𝑩
𝑭
=
𝒙𝑫−𝒙𝑭
𝒙𝑫−𝒙𝑩
…………………………………….3.17
Dr. Bilha Eshton

49. 3.2.2 Effectiveness of screens
• The effectiveness of a screen (or screen efficiency) is a
measure of the success of a screen in separating
materials A and B.
• If the screen functioned properly, all material A would
be in the overflow and all material B would be in the
underflow.
Dr. Bilha Eshton

50. • A common measure of screen effectiveness is the ratio
of oversize material A that is actually in the overflow
to the amount of A entering with the feed.
• Screen effectiveness with respect to material A is
therefore:
𝐸𝐴=
𝐷𝑥𝐷
𝐹𝑥𝐹
………………………………………...3.18
• Where EA is the screen effectiveness based on the
oversize.
Dr. Bilha Eshton

51. • Similarly an effectiveness based on the undersized
material is given by:
𝐸𝐵=
𝐵(1−𝑥𝐵)
𝐹(1−𝑥𝐹)
…………………………………………..3.19
A combined overall effectiveness can be defined as the
product of the two individuals and if the product is
denoted by E, we get:
……........…………………………….3.20
Dr. Bilha Eshton

52. • Substituting D/F and B/F from equation 3.16 and
3.17 into equation 3.20 gives
……….………….3.21
Example 2
A quartz mixture having the screen analysis shown in Table 3
(next slide) is screened through a standard 10-mesh screen.
The cumulative screen analysis of overflow and underflow are
given in the Table. Calculate the mass ratios of the overflow
and underflow to feed and the overall effectiveness of the
screen.
Dr. Bilha Eshton

53. Dr. Bilha Eshton

54. 3.2.3 Capacity of screens
• The capacity of screens is measured by the mass of material
that can be fed per unit time to a unit area of the screen.
• The probability of passage of a particle through a screen
depends on the fraction of the total surface represented by
openings, on the ratio of the diameter of the particle to the
width of an opening in the screen, and on the number of
contacts between the particle and the screen surface.
• For a series of screens of different mesh sizes, the number of
openings per unit screen area is proportional to 1/Dpc
2 where
Dpc = width of screen opening.
Dr. Bilha Eshton

55. 3.3 Screening equipment
• Varieties of screen are available for different
purposes.
• In most screen particles drop through openings by
gravity.
• Some of screening equipment include: Stationary
screens and grizzlies; Gyrating screens; Vibrating
screens; Centrifugal sitter.
Dr. Bilha Eshton

56. 3.3.1 Grizzly Screens
• consist of a set of parallel bars held apart by spacers
at some predetermined opening.
• Bars are frequently made of manganese steel to
reduce wear.
• A grizzly is widely used before a primary crusher in
rock- or ore-crushing plants to remove the fines
before the ore or rock enters the crusher.
• It can be a stationary set of bars or a vibrating screen.
• Types: (i) stationary grizzly (ii) flat grizzlies (iii)
vibrating grizzlies.
Dr. Bilha Eshton

57. Grizzly Screens
Vibrating Grizzlies
Stationary Grizzlies
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58. 3.3.2 Vibrating Screens
• They are used as standard practice when large
capacity and high efficiency are desired.
• The capacity, especially in the finer sizes, is so much
greater than that of any of the other screens that they
have practically replaced all other types when
efficiency of the screen is an important factor.
• Advantages include accuracy of sizing, increased
capacity per unit area, low maintenance cost per ton
of material handled, and a saving in installation space
and weight.
Dr. Bilha Eshton

59. • They are divided into two main classes:
(i) mechanically vibrated screens (ii) electrically vibrated screens
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60. 3.3.3 Gyrating Screens
• the machine gyrates in a circular motion at a near level
plane at low angles. The drive is an eccentric gear box
or eccentric weights
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61. On your own, read:
3.3.4 Revolving screens
3.3.5 Centrifugal sifters
END OF CHAPTER
Dr. Bilha Eshton