This document discusses particle size analysis through sieve analysis. It explains that sieve analysis involves separating particulate materials into size fractions using screens with different sized meshes/openings and then determining the mass or volume of material in each fraction. This allows analyzing the particle size distribution. Screening methods like using grizzlies, stationary screens, mechanically vibrating screens, gyrating screens, and centrifugal screens are described for separating particles of different sizes. Key terms related to sieve analysis and screening are also defined.

1. Department of Chemical Engineering
University of Engineering & Technology
Peshawar, Pakistan

2.  Many natural and manufactured materials occur in a disperse form,
which means that they consist of differently shaped and sized particles.
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 behavior
 surface reaction
 taste
 miscibility
 filtration properties
 conductivity
 This list could be continued at great length. The examples clearly show
how important it is to have a 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.

3.  There are different methods for determining the particle distribution.
The choice of a particular method depends primarily on the
dispersion status, i.e. on the degree of fineness of the sample.

5.  The oldest and best-known method is particle size
determination by sieve analysis. The particle size
distribution is defined via the mass or volume. 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.
 Screening is a method of separating particles
according to size alone
screens are used on a large scale for the separation
of particles according to their sizes, and on a small
scale for the production of closely graded materials in
carrying out size analyses
The method is applicable for particles of a size as
small as about 50 μm

6. Undersize:
fines, pass through the screen openings
Oversize: tails:
Particles which do not pass through screen openings
 Industrial screens are made from woven wire, silk or
plastic cloth, metal bars, perforated or slotted metal
plates.
 Various metals are used, with steel and stainless steel
the most common.
 Standard screens range in mesh size from 4 in. to 400-
mesh

7. A single screen can separate feed into two
fractions
These are called un-sized fractions
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

8. Sieve passage
 The sieve passage is the fine material that passes through the sieve during a sieve analysis.
Sieve residue
 The sieve residue is the coarse material that remains on the sieve after a sieve analysis.
Sieving loss
 The sieving loss is the difference in weight between the original sample and the sum of the recovered fractions.
According to DIN 66 165 part 1 it should not exceed 1% of the original sample weight.
Relative open sieve area
 The relative open sieve area is the sum of all the open mesh areas of the sieve relative to the total area of the
sieve.
Available open sieve area
 The available open sieve area is the sum of the open mesh areas of the sieve that have not been blocked.
Cut sharpness
 The cut sharpness characterizes the quality of the sieving into individual fractions.
Equivalent diameter
 In sieving the equivalent diameter of a particle is the diameter of a sphere with the same mass or volume.
Undersize
 Mass fraction below a defined cut point.
Oversize
 Mass fraction above a defined cut point
Mesh
the number of openings in one inch of screen (The number of openings is the mesh size. So a 4-mesh
screenmeans there are four little square =s across one linear inch of screen

14. Cutting diameter Dpc: marks the point of
separation, usually Dpc is chosen to be the
mesh opening of the screen.
Actual screens do not give a perfect
separation about the cutting diameter. The
undersize can contain certain amount of
material coarser than Dpc, and the oversize
can contain certain amount of material that is
smaller than Dpc.

15.  Volume-surface mean diameter, defined by
If the number of particles in each fraction Ni is known, then
where xi = mass fraction in a given increment, = average diameter,
taken as arithmetic average of the smallest and largest particle
diameters in incremen

16.  If the number of particles in each fraction Ni is
known, then
 If NT = number of particles in the entire sample
then
 Arithmetic mean diameter is given by

17.  Mass mean diameter

19.  Volume mean diameter

22.  The volume of any particle is proportional to
its "diameter" cubed.
a = volume shape factor
Assuming that a is independent of size and is inverse of spherecity

25.  Stationary screens and grizzlies
 Mechanically Vibrating screens
 Gyrating screens
 Centrifugal Screens

26. A grizzly has a plane screening surface
composed of longitudinal bars up to 3 m long,
fixed in a rectangular framework
It is usually inclined at an angle to the horizontal
and the greater the angle then the greater is the
throughput although the screening efficiency is
reduced
Used for very coarse feed,
as from a primary crusher
The spacing between the
bars is 2 to 8 in. (50 –
200 mm)

27. Stationary inclined woven-metal screens
operate in the same way like grizzlies
Separating particles 0.5 to 4 in. (12 to 100
mm)
Effective only with very coarse free-flowing
solids containing few fine particles

28. Mechanically operated screens are vibrated by means
of an electromagnetic device or mechanically
In the former case the screen itself is vibrated, and
in the latter, the whole assembly
Hummer electromagnetic
screen
Tyrock mechanical screen

29.  Because very rapid accelerations and retardations
are produced, the power consumption and the
wear on the bearings are high
 These screens are sometimes mounted in a
multi-deck fashion with the coarsest screen on
top, either horizontally or inclined at angles up to
45◦
 With the horizontal machine, the vibratory
motion fulfils the additional function of moving
the particles across the screen

30. There is therefore a tendency for blockage of the apertures by the
large material and for oversize particles to be forced through.
A very large mechanically operated screen
consists of a slowly rotating perforated cylinder with its axis at a
slight angle to the horizontal.
The material to be screened is fed in at the top and gradually
moves down the screen and passes over apertures of gradually
increasing size, with the result that all the material has to pass
over the finest screen.
Trommel

31. Rate of gyration is between
600 and 1800 r/min
Usually gyrated at the feed
end in a horizontal plane
The discharge end
reciprocates but does not
gyrate
This combination stratifies the feed, so that fine
particles travel downward to the screen surface,
where they are pushed through by the larger
particles on top

32.  This phenomenon occurs as vibration is
passed through a bed of material. This causes
coarse (larger) material to rise and finer
(smaller) material to descend within the bed.
The material in contact with screen cloth
either falls through a slot or blinds the slot or
contacts the cloth material and is thrown
from the cloth to fall to the next lower level.

33. Material is fed into the feed inlet and
redirected into the cylindrical sifting
chamber by means of a feed screw.
 Rotating, helical paddles within the
chamber continuously propel the material
against the screen, while the resultant,
centrifugal force on the particles
accelerates them through the apertures.
 These rotating paddles, which never
make contact with the screen, also serve
to breakup soft agglomerates.
Over-sized particles and trash are
ejected via the oversize discharge spout.

34.  Let F, D, and B be the mass flow rates of feed,
overflow, and underflow, respectively,
 and xF, xD, and xB be the mass fractions of
material A in the streams.
 The mass fractions of material B in the feed,
overflow, and underflow are 1- xF, 1- xD, and
1- xB.
F = D + B
FxF = DxD + BxB

35. F = D + B
FxF = DxD + BxB
Elimination of B from the equations gives
Elimination of D gives

36. 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. These quantities are DxD and
FxF respectively. Thus
where EA is the screen effectiveness based on
the oversize

37. Similarly, an effectiveness EB based on the
undersize materials is given by
A combined overall effectiveness can be
defined as the product of the two individual
ratios

38.  The capacity of a screen is measured by the
mass of material that can be fed per unit time
to a unit area of the screen.
 Capacity and effectiveness are opposing
factors.
 To obtain maximum effectiveness, the
capacity must be small,
 Large capacity is obtainable only at the
expense of a reduction in effectiveness.

39. A quartz mixture is screened through a 10-
mesh screen. The cumulative screen analysis
of feed, overflow and underfolw are given in
the table.
Calculate the mass ratios of the overflow and
underflow to feed and the overall
effectiveness of the screen.

40. Mesh Dp (mm) Feed Overflow Underflow
4 4.699 0 0 0
6 3.327 0.025 0.071 0
8 2.362 0.15 0.43 0
10 1.651 0.47 0.85 0.195
14 1.168 0.73 0.97 0.58
20 0.833 0.885 0.99 0.83
28 0.589 0.94 1.0 0.91
35 0.417 0.96 0.94
65 0.208 0.98 0.975
Pan 1.0 1.0
From the table:
xF= 0.47
xD= 0.85
xB= 0.195

42. Hummer electromagnetic
screen
Tyrock mechanical
screen