Here are the steps to solve this problem: (a) Surface area of cuboid = 2*(5*3 + 5*1 + 3*1) = 38 mm^2 Surface area of sphere = 4*π*r^2 Equating the two: 38 = 4*π*r1^2 r1 = √(38/4/π) = 3 mm Surface diameter = 2*r1 = 6 mm (b) Surface area of cuboid = 38 mm^2 Volume of cuboid = 5*3*1 = 15 mm^3 Surface area to volume ratio of cuboid = 38/15 = 2.53 mm^-1 Surface

1. ChE-205 Particle Technology
Saeed GUL, PhD
Professor and Postgraduate Advisor
Department of Chemical Engineering,
University of Engineering & Technology Peshawar, PAKISTAN
Screening

2. 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
Introduction

3. 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
Introduction

4.  Unsized fractions
A single screen can make a single
separation into two fractions i.e.
under size and oversize. Such type
of fractions is called unsized
fractions.
 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
Introduction
Single Deck Screen
Multi Deck Screen

5. 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.
Cutting diameter Dpc

6. Stationary screens and grizzlies
Mechanically Vibrating screens
Gyrating screens
Centrifugal Screens
Screening Equipments

7.  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
Screening Equipments
(Stationary screens and grizzlies)

8. 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
(Stationary screens and grizzlies)
Used for very coarse feed, as from a
primary crusher
The spacing between the bars is 2 to 8
in. (50 – 200 mm)
Screening Equipment

9. Screening Equipments
(Mechanically Operated Screens)
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

10.  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
Screening Equipments
(Vibrating screens)

11. Screening Equipments
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)

12. 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
Screening Equipments
(Gyrating screens)
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

13. 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.
Stratification

14. Screening Equipments
(Centrifugal Screens)
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.

15. 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
Material balances over a screen

16. F = D + B
FxF = DxD + BxB
Elimination of B from the equations gives
Elimination of D gives
Material balances over a screen

17. 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
Screen effectiveness

18. 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
Screen effectiveness

19.  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.
Capacity and effectiveness of screens

20. Factors Affecting the Effectiveness
Mesh Size and wire diameter
Capacity
Blinding
Moisture
Direction of approach of particle to screen surface
Cohesion
Adhesion

21. 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.
Example

22. 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
Solution of Example
From the table:
xF= 0.47
xD= 0.85
xB= 0.195

23. Consider a cuboid particle 5:00 3:00 1:00 mm. Calculate for
this particle the following diameters:
(a)the surface diameter (the diameter of a sphere having the
same surface area as the particle);
(b) the surface-volume diameter (the diameter of a sphere
having the same external surface to volume ratio as the
particle);

24. Calculate the equivalent volume sphere
diameter dv and the surface-volume equivalent
sphere diameter dsv of a cuboid particle of side
length 1, 2, 4 mm.