Module 1.pdf

Mechanical Operations
(CH2004D)
DR. PRASANNA KUMAR S MURAL

Evaluation Scheme
Component Duration Weightage Date & Time
Mid Semester
Test
1:30 Hour 30
According to
Academic Calendar
End semester
exam
3 Hour 50
According to
Academic Calendar
Assignments/Test 45 min 10 Class Timings
Case study 10 Class Timings
Make up examinations: Only on the production of valid and genuine reasons
Grading: Policy: Absolute
2

Course outcomes
❖Understand basic principles of particles preparation and their
characterization
❖Determine the crushing efficiency of different size reduction
equipment’s using crushing laws
❖Acquire knowledge on different mixing and blending equipment’s
❖Select the appropriate equipment for particle separation
❖Design of filtration, sedimentation and cyclone separators
3

History of Chemical Engineering
❑Established in late 1800’s
❑George Davis, English consultant, presented Chemical Engineering at
Manchester Technical School, UK in 1887
❑ Lewis M Norton in 1888 introduced chemical engineering in
Massachusetts Institute of Technology, USA
❑Chemical Engineering in India was introduced by Prof. (Dr.) H L Roy at
Bengal Technical Institute, Calcutta (presently, Jadavpur University,
Kolkata)
❑In 1947, Prof. (Dr.) H L Roy founded first professional body called Indian
Institute of Chemical Engineers (IIChE) at Kolkata
4

Chemical Engineering
❑the branch of engineering concerned with the design and operation of
industrial chemical plants. A chemical or process plant is required to
carry out transformation of raw materials into desired products
efficiently, economically and safely.
❑Chemical Engineering is that branch of engineering which deals with
the production of bulk materials from basic raw materials in a most
economical way by chemical means.
❑A chemical Engineer is the one who develops, design, construct,
operates and controls any physical and/or chemical or biochemical
changing process
❑Chemical engineers works in four main segments of the chemical
process industries:- Research and development, design, production, and
sales
5

Chemical Engineering
Unit Operations
(by Dr. Arthur D Little in 1915)
Unit processes
(by P H Groggin in 1923)
Mechanical
Operations
Fluid Flow
Heat
Transfer
Mass
Transfer
Oxidation
Hydration
Hydrogenation
Halogenation
Nitration etc
Properties of Solid
Size Reduction
Size separation
Transportation of solids
Mixing
Feeding etc.,
Unit process involves
chemical conversions leading
to synthesis of new products
Unit operations involve
the physical change and
separation of the products
6

Mechanical Operations
❑Mechanical operations are those unit operations that involve
physically changing a material. It is all about dealing with the particles
❑Mechanical operation application in our daily life:-
❑The kitchen
7

Mechanical operation
application in Industrial Scale
Wheat Husking
Rice Husking Dough Kneading
8

Why do we need knowledge
of mechanical operations?
❖In general the feed material in the earths crust wont be available in
the desirable form
❖First mechanical operations will be used to convert the feed into the
required form and later continue with unit processes
❑Mechanical operations classification
◦ Particulate solids – Characterization & Handling of solids
(Transportation, storage etc..), size reduction, screening
◦ Particle dynamics – Sedimentation, filtration, classification
◦ Mixing – Mixing of solids & liquids
10

CHARACTERIZATION OF SOLID
PARTICLES
Individual solid particles are characterized by their size, shape, and
density
Homogeneous solids have the same density as the bulk material
Size and shape are easily specified for regular particles, such as spheres
and cubes
How to define size and shape of an irregular particle?
◦ The shape of an individual particle can be expressed in
terms of the sphericity (Φs)
11

Sphericity (Φs)
❑Defined as the surface-volume ratio for a sphere of diameter Dp
divided by the surface-volume ratio for the particle whose nominal size
is Dp
12
𝛷 =
Surface to volume ratio of sphere of diamenter Dp
Surface to volume ratio of particle whose nominal size is Dp
Surface area of sphere = π𝐷𝑝
2
Volume of sphere = (1/6) π 𝐷𝑝
3
Surface to volume ratio of sphere = 6/Dp
Surface to volume ratio of selected particle = Sp/Vp
Therefore Sphericity
Equivalent diameter is defined as the size of spherical particle having the same controlling
characteristics as the particle under consideration
It can be also defined as how close the irregular particle is to the sphere?

Find the sphericity of a cube of
dimension a x a x a
13

Find the sphericity of a cube of
dimension a x a x a
14

Importance of Particle Size and
Shape
There is an optimum particle size or at least a smallest and largest
acceptable size, for most items involving particles
❖The taste of chocolate is affected by of their respective ingredients.
❖Extremely fine amorphous silica is added to tomato ketchup to control
its flow.
❖Pharmaceutical tablets dissolve in our systems at rates determined in
part by particle size and exposed surface area.
❖ The settling time of concrete, dental filling, and broken-bone castes
procedure in accordance with particle size and surface area exposure.
16

The particle size can be measured using a wide range of measuring
techniques, such as
(i) Screening (for particles of size > 50 μm)
(ii) Sedimentation (for particles of size range of 1–100 μm)
(iii) Elutriation (for particles of size range of 5–100 μm)
(iv) Electron microscopy (for particles of size range of 0.0005–5 μm)
(v) Light scattering (for particles of size range of 0.1–10 μm)
(vi) Laser diffraction (for particles of size range of 0.1–600 μm)
(vii)Photon correlation spectroscopy (for sizes ranging a few nanometres
to a few μm).
17
Particle sizes Units
Coarse Inches or millimetres (in or mm)
Fine Screen size
Very fine Micrometers or nanometres (μm or nm)
Ultra fine Surface area per unit mass (m2/g)

• A sample of solid particles contains a wide range of particle sizes and
densities for which their analysis becomes extremely difficult.
• For this reason, the whole sample is separated into a number of fractions,
each of constant density and nearly constant size by some mechanical means
and then each fraction is analyzed separately, as discussed below.
• For a sample of uniform particles having diameter as Dp, total mass as m, and
density of each particle as ρp, the total volume of the particles is
• If the volume of one particle is Vp then the number of particles in the sample
is
Mixed particle sizes and size
analysis

• If the surface area of each particle is Sp then the total surface area of
particles is
• For a mixture of particles the analysis is done for each fraction of constant
density and constant size. The above equations are applied to each
fraction to estimate the number of particles and the total surface area
• The results for all the fractions are added to give what is called the specific
surface of the mixture, Ass, or total surface area of a unit mass of particles.
Where xi is mass fraction of given size
Average particle diameter (average of smallest and largest particle diameter in the
increment).

• The specific surface is an important property of solids and is dependent on
the condition of the surface as well as the particle size.
• For regular particles, the estimation of specific surface is easy, but the task is
difficult for irregular particles.
• In this connection, one parameter known as the specific surface ratio, NSSR, is
popularly used to overcome the difficulty, which is defined as the ratio of the
specific surface of the particle to the specific surface of a spherical particle of
the same diameter.
• The specific surface ratio is a function of average particle diameter. If Dp avg is
the average size of the particle then
where, Assp = Specific surface of the particle.
• The specific surface for a mixture of particles containing many different sizes of
particles of same density can now be expressed as
• For spherical particles NSSR = 1

Average particle sizes
Generally average size is used to describe the particle size of a mixture
Mean volume–surface mean diameter
• The volume–surface mean diameter (Dvs) is the most widely used among all
average sizes and is related to the specific surface area Ass. It is defined by
Replacing
• This is also known as Sauter Mean diameter
Mass mean diameter

Volume mean diameter
• Total volume of the sample divide by total number of particles.
Arithmetic mean diameter
• Based on total number of particles
Surface area mean diameter is used in the study of mass transfer, catalytic
reactions. Volume or Mass mean diameters are useful in the study of spray
drying, in the gravitational free settling velocity of a particle in a liquid, etc.

25
1. Finely divided clay is used as a catalyst in the petroleum industry. It has a density of 1.2
g/cc and sphericity of 0.5. The size analysis is as follows:-
Average
Diameter,
Dpi, avg (cm)
0.0252 0.0178 0.0126 0.0089 0.0038
Mass
Fraction, xi
(g/g)
0.088 0.178 0.293 0.194 0.247
Find the specific surface area and the Sauter mean diameter of the clay material.

29
The size analysis of a powdered material on a weight basis is represented by a straight
line from 0% weight at 100 micron particle size to 100 % weight at 101 micron particle
size. Calculate the Sauter mean diameter of the particles.

30
The size analysis of a powdered material on a weight basis is represented by a straight
line from 0% weight at 100 micron particle size to 100 % weight at 101 micron particle
size. Calculate the Sauter mean diameter of the particles.
Given data
x=0, Dpi = 1 µm
x=1, Dpi = 100 µm
0.0 0.2 0.4 0.6 0.8 1.0
0
20
40
60
80
100
Dpi
xi
Dpi
𝐷𝑝𝑖,𝑎𝑣𝑔 = 𝑚𝑥𝑖 + 𝑐
𝐷𝑝𝑖,𝑎𝑣𝑔 = 100𝑥𝑖 + 1

31
Xi Dpi (micron) Xi/Dpi
0 1 0
0.1 11 0.009091
0.2 21 0.009524
0.3 31 0.009677
0.4 41 0.009756
0.5 51 0.009804
0.6 61 0.009836
0.7 71 0.009859
0.8 81 0.009877
0.9 91 0.00989
1 101 0.009901
Sum=0.097215
Sauter mean diameter of the particles
𝐷𝑣𝑠 =
1
෎
𝑖=1
𝑖=𝑛
𝑥𝑖
𝐷𝑝𝑖,𝑎𝑣𝑔
Dvs = 1/0.097215 = 10.29 microns

SCREEN ANALYSIS
STANDARD SCREEN SERIES
• Standard screens are used to measure the size (and size distribution) of
particles in the size range between about 3 and 0.0015 in. (76 mm and 38 µm)
• MOC – Woven wire made of SS

Sieve Analysis
Sieve shaker
• The screen through which the particles have passed is called the limiting
screen and which has retained them is called the retaining screen.
• Material that remains on a given screening surface is the oversize (>) or plus
(+) material and that passing is the undersize (<) or minus (−) material
• Set of standard screens is arranged serially in 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
a definite time
• The particles retained on each screen are removed and weighed, and the
masses of the individual screen increments are converted to mass fractions

Method of Reporting
I. By calculating the mass
percentage of each size
fraction
II. By calculating the
cumulative percentage
of size fractions retained
on each sieve
III. By calculating the
cumulative percentage
of size fractions passing
through each sieve.

Differential plots are the plots of the mass fraction (or the percentage of mass fraction)
retained on each sieve versus average sieve size, while cumulative plots are the plots of
the mass fraction (or the percentage of mass fraction) passing through or retained on each
sieve versus particular sieve aperture.

Properties of particulate masses
• Masses of dry solid particles have many of the properties of a fluid
• They exert pressure on the sides and walls of a container; they flow through
openings or down a chute.
• Unlike most fluids, granular solids and solid masses permanently resist
distortion when subjected to a moderate distorting force.
• When the force is large enough, failure occurs and one layer of particles slides
over another, but between the layers on each side of the failure there is
appreciable friction.
Distinctive properties
• The pressure is not the same in all directions.

• Pressure applied in one direction creates some pressure in other directions,
but it is always smaller than the applied pressure. It is a minimum in the
direction at right angles to the applied pressure.
• A shear stress applied at the surface of a mass is transmitted throughout a
static mass of particles unless failure occurs.
• The density of the mass varies depending on the degree of packing of the
grains.
• The bulk density is a minimum when the mass is "loose"; it rises to a
maximum when the mass is packed by vibrating or tamping.
• Before a mass of tightly packed particles can flow, it must increase in volume
to permit interlocking grains to move past one another. Without such dilation
flow is not possible.
• Depending on their flow properties, particulate solids are divided into two
classes, cohesive (dry sand, grains) and noncohesive (wet clay).

Size Reduction
The term size reduction is applied to all the ways in which particles
of solids are cut or broken into smaller pieces.
Chunks of crude ore are crushed to workable size: synthetic
chemicals are ground into powder; sheets of plastic are cut into tiny
cubes or diamonds.
Commercial products must often meet stringent specifications
regarding the size and sometimes the shape of the particles they
contain.
Reducing the particle size also increases the reactivity of solids; it
permits separation of unwanted ingredients by mechanical methods;
it reduces the bulk of fibrous materials for easier handling and for
waste disposal.

• Solids may be broken in many different ways, but only four of them are
commonly used in size-reduction machines:
a. Compression (Coarse reduction of hard solids – gives relatively few fines)
b. Impact (gives coarse, medium and fine particles)
c. Attrition, or rubbing (very fine products from soft, nonabrasive materials)
d. Cutting (definite particle size & may be shape with few or no fines)
Principles of comminution
Criteria for comminution
• Comminution is a generic term for size reduction (Crushers, Grinders)
• Ideal crusher or grinder would (1) have a large capacity, (2) require a small
power input per unit of product, (3) yield a product of the single size or the
size distribution desired.

Characteristics of comminuted products
• The objective of crushing and grinding is to produce small particles from
larger
• Smaller particles are desired either because of their large surface area or
because of their shape, size, and number.
• One measure of the efficiency of the operation is based on the energy
required to create new surface
• Unlike an ideal crusher or grinder, an actual unit does not yield a uniform
product, whether the feed is uniformly sized or not.
• The product always consists of a mixture of particles, ranging from a definite
maximum size to very small particles.
• If the feed is homogeneous in particle shape and in chemical and physical
structure, the shapes of the individual units in the product may be quite
uniform

• The diameter ration of the largest and smallest particles in a comminuted
product is of the order of 104
• Because of this extreme variation in the sizes of the individual particles,
relationships adequate for uniform sizes must be modified when applied to
such mixtures.
• Unless they are smoothed by abrasion after crushing, comminuted particles
resemble polyhedrons with nearly plane faces and sharp edges and corners.
• The particles may be compact, with length, breadth, and thickness nearly
equal, or they may be plate like or needlelike.
• For compact grains, the largest dimension or apparent diameter is generally
taken as the particle size. For particles that are plate like or needle like, two
dimensions should be given to characterize their size

Energy and power requirements in comminution
• The cost of power is a major expense in crushing and grinding, so the factors
that control this cost are important.
• During size reduction, the particles of feed material are first distorted and
strained.
• The work necessary to strain them is stored temporarily in the solid as
mechanical energy of stress
• As additional force is applied to the stressed particles, they are distorted
beyond their ultimate strength and suddenly rupture into fragments (new
surface)
• Since a unit area of solid has a definite amount of surface energy, the creation
of new surface requires work, which is supplied by the release of energy of
stress when the particle breaks.
• By conservation of energy, all energy of stress in excess of the new surface
energy created must appear as heat

Crushing efficiency
• The ratio of the surface energy created by crushing to the energy absorbed by the
solid is the crushing efficiency (ηc)
• If es is the surface energy per unit area, Awb and Awa are the areas per unit mass of
product and feed then the energy absorbed by a unit mass of the material Wn is
• Experimental efficiency is usually measured by estimating es from theories of the
solid state, measuring Wn, Awb, Awa
• Usually the crushing efficiency is in the range of 0.06 to 0.15
• The energy absorbed by the solid (Wn) is less than total energy (W) fed to the
machine.
• Part of the total energy used to overcome the friction in the bearings and other
parts

• The ratio of the energy absorbed to the energy input is (ηm) the
mechanical efficiency
• If ሶ
𝑚 is the feed rate, the power required by the machine is

Comminution Laws
• It is not possible to find out the accurate amount of energy requirement for
size reduction of a given material, because
i. There is a wide variation in the size and shape of particles both in the
feed and product
ii. Some energy is wasted as heat and sound, which can’t be determined
exactly
• But, a number of empirical laws have been proposed to relate the size
reduction with the energy input to the machine. They are Rittinger’s Law
(1867), Kick’s Law (1885), and Bond’s Law (1952).
Rittinger’s Law : The work required for size reduction is proportional to the new
surface area created Where K = 1/ηc

• Replacing specific surface area gives
• The inverse of Rittinger’s (KR) is known as Rittinger’s number.
• Rittinger’s law is applicable for fine grinding where the increase in surface per
unit mass of material is predominant.
• This law is applicable for feed size of less than 0.05 mm.
Kick’s Law : The work required for crushing a given mass of material is constant
for a given reduction ratio irrespective of the initial size.
Where Kk is Kick’s constant
The reduction ratio is the ratio of initial particle size to final particle size.

• Kick’s law is based on stress analysis of plastic deformation within the elastic
limit.
• This law is more accurate than Rittinger’s law for coarse crushing where the
surface area produced per unit mass is considerably less.
• This law is applicable for feed size of greater than 50 mm.
Bond’s Law : The work required to form particles of size Dpp from a very large
particle size is proportional to the square root of the surface to volume ratio
(sp/vp) of the product.
This law is applicable for feed size between 0.05 and 50 mm

• The Bond’s constant (Kb) is dependent on the type of machine used and on
the material to be crushed.
• It is found more accurately using work index (Wi).
• It is defined as the gross energy requirement in kilowatt hour per short-ton of
feed (kWh/ton of feed) to reduce a very large particle to such a size that 80%
of the product will pass through a 100-µm or 0.1-mm screen.
• If P is in kW, ሶ
𝑚 in tons per hour, and Dpp is in μm then Kb = 10 Wi, and if Dpp
is in mm then Kb= 0.1Wi = 0.3162 Wi

270 kW of power is required to crush 150 tonnes/h of a material. If 80% of the feed passes
through a 50 mm screen and 80 % of the product passes through a 3-mm screen, calculate
the work index of the material. And what will be the power required for the same feed at
150 tonnes/h to be crushed to a product such that 80% is to pass through a 1.5 mm screen?

Size Reduction Equipment's
❖Classification on the basis of:-
i. The mode of operation,
ii. The method by which a force is applied and
iii. The size of feed and product

Mode of operation
➢Batch operation
➢Continuous operation

Method by which a force is
applied
➢Impact
➢Impact at one surface
➢Impact between particles
➢Compression between two solid surfaces
➢Crushing
➢Grinding
➢Rubbing the material between two surfaces
➢Shear action of the surrounding medium
➢Nonmechanical introduction of energy

Nonmechanical introduction
of energy
➢Thermal shock
➢Explosive shattering
➢Electrohydraulic crushing
➢Cryogenic crushing
➢Ultrasonic grinding

Size of feed and product
➢Coarse crushers (large feed size to (50-5) mm product size
➢Intermediate crushers [(50-5) mm to (5-1) mm product size]
➢Fine crushers/Grinders [(5-2) mm to ≈ 200 mesh]
➢Ultrafine grinders [6 mm to (1-50) µm]

Coarse crushers
➢Jaw crusher (Blake and Dodge)
➢Gyratory crusher
➢Cone crusher
➢Crushing rolls (smooth and toothed rolls)
➢Bradford breaker

Intermediate crushers
➢Roller mill
➢Cage mill
➢Granulator
➢Hammer mill
➢Impactor
➢Vertical Shaft impacter

Fine crushers/Grinders
➢Ball mill
➢Pebble mill
➢Rod mill
➢Tube mill
➢Attrition mill/Pulveriser

Selection Criteria of size
reduction Equipment
➢It should produce the materials of desired shape and size or thee size
distribution desired.
➢It should accept the maximum input size expected
➢It should have a large capacity
➢It should not choke or plug
➢It should pass unbreakable materials without causing damage to itself
➢It should operate economically with minimum supervision and
maintenance
➢The power input per unit weight of product should be small

Selection Criteria of size
reduction Equipment (contd..)
➢It should resist abrasive wear
➢It should be dependable and have prolonged service life
➢The replacement parts should be readily available at cheaper rate
➢The initial fixed cost and operating cost should be minimum
➢It should be easy and safe to operate
➢It should have easy access to internal parts for maintenance
➢It should be versatile one

Coarse/Primary crushers
Crushers are slow-speed machines for coarse reduction of large
quantities of solids
The main types are jaw crushers, gyratory crushers, smooth-roll
crushers, and toothed-roll crushers
The first three operate by compression and can break large lumps of
very hard materials, as in the primary and secondary reduction of rocks
and ores
Toothed-roll crushers tear the feed apart as well as crushing it; they
handle softer feeds like coal, bone, and soft shale

Jaw Crushers
• In a jaw crusher feed is admitted between two jaws, set
to form a V open at the top
• One jaw is nearly vertical and does not move (fixed
jaw); the other jaw with 200 to 300 inclination,
reciprocates in a horizontal plane (swinging jaw)
• The jaw faces are flat or slightly bulged; they may carry
shallow horizontal grooves
• It is driven by an eccentric so that it applies great
compressive force to lumps caught between the jaws
• Large lumps caught between the upper parts of the
jaws are broken, drop into the narrower space below,
and are re-crushed the next time the jaws close
• After sufficient reduction they drop out the bottom of
the machine
• The jaws open and close 250 to 400 times per minute
Operating Principle:-
• compression and there are no rubbing or grinding
actions,
• Generally produces cubical products with minimum fines

• The most common type of jaw crusher is
the Blake crusher
• In this machine an eccentric drives a
pitman connected to two toggle plates,
one of which is pinned to the frame and
the other to the swinging jaw
• The pivot point is at the top of the
movable jaw or above the top of the jaws
on the centerline of the jaw opening.

• The greatest amount of motion is at the bottom of the V, which
means that there is little tendency for a crusher of this kind to choke.
• Some machines with a 1.8 to 2.4 m feed opening can accept rocks 1.8
m in diameter and crush 1200 ton/h to a maximum product size of
250 mm
• Smaller secondary crushers reduce the particle size of pre-crushed
feed to 6 to 50 mm at much lower rates of throughput.
Industrial Applications:- Jaw crushers are widely applied to crush rocks of high or mild
hardness to soft ones, and ores as well as to slag, construction materials, marbles, etc. They
can be used in mining and metallurgical industries, construction, road, and railways

Gyratory crusher
• A gyratory crusher may be looked upon as a
jaw crusher with circular jaws, between
which material is being crushed at some
point at all times.
• A conical crushing head gyrates inside a
funnel-shaped casing, open at the top. As
shown in the side figure, the crushing head
is carried on a heavy shaft pivoted at the top
of the machine.
• An eccentric drives the bottom end of the
shaft. At any point on the periphery of the
casing, therefore, the bottom of the
crushing head moves toward, and then away
from, the stationary wall. Solids caught in
the V-shaped space between the head and
the casing are broken and re-broken until
they pass out the bottom.
• The crushing head is free to rotate on the
shaft and turns slowly because of friction
with the material being crushed.
Operating Principle:- Gyratory crushers, like jaw crushers, employ
compressive force for size reduction

• The speed of the crushing head is typically 125 to 425 gyrations per
minute.
• Because some part of the crushing head is working at all times, the
discharge from a gyratory is continuous instead of intermittent as in a
jaw crusher.
• The load on the motor is nearly uniform; less maintenance is required
than with a jaw crusher; and the power requirement per ton of
material crushed is smaller.
• The biggest gyratories handle up to 4500 ton/h.
• The capacity of a gyratory crusher varies with the jaw setting, the
impact strength of the feed, and the speed of gyration of the machine.
• The capacity is almost independent of the compressive strength of the
material being crushed.

Smooth Roll Crusher
• Two heavy smooth-faced metal rolls turning
on parallel horizontal axes are the working
elements of the smooth-roll crusher
illustrated in side Figure
• Particles of feed caught between the rolls
are broken in compression and drop out
below.
• The rolls turn toward each other at the same
speed. They have relatively narrow faces and
are large in diameter so that they can "nip"
moderately large lumps.
• Typical rolls are 600 mm (24 in.) in diameter
with a 300-mm (12-in.) face to 2000 mm (78
in.) in diameter with a 914-mm (36-in.) face

• Roll speeds range from 50 to 300 r/min
• Smooth-roll crushers are secondary crushers, with feeds 12 to 75 mm
(1/2 to 3 in.) in size and products 12 mm (1/2 in.) to about 1 mm
• The limiting size Dp,max of particles that can be nipped by the rolls
depends on the coefficient of friction between the particle and the roll
surface, but in most cases it can be estimated from the simple relation
• The particle size of the product depends on the spacing between the
rolls, as does the capacity of a given machine
• Smooth-roll crushers give few fines and virtually no oversize
• They operate most effectively when set to give a reduction ratio of 3 or 4
to 1; that is, the maximum particle diameter of the product is one-third
or one-fourth that of the feed
where R = roll radius
d = half the width of the gap between the rolls

• The forces exerted by the roll are varied from 8700 to 70,000
N/cm of roll width.
• To allow unbreakable material to pass through without damaging
the machine, at least one roll must be spring mounted.

Toothed-roll Crushers
• In many roll crushers the roll faces carry
corrugations, breaker bars, or teeth
• Such crushers may contain two rolls, as in
smooth-roll crushers, or only one roll
working against a stationary curved breaker
plate
• A single-roll toothed crusher is shown in
right side figure
• Machines known as disintegrators contain
two corrugated rolls turning at different
speeds, which tear the feed apart, or a small
high-speed roll with transverse breaker bars
on its face turning toward a large slow-speed
smooth roll
• Some crushing rolls for coarse feeds carry
heavy pyramidal teeth

• Other designs utilize a large number of thin-toothed disks that saw
through slabs or sheets of material
• Toothed-roll crushers are much more versatile than smooth-roll
crushers, within the limitation that they cannot handle very hard solids
• They operate by compression, impact, and shear, not by compression
alone, as do smooth-roll machines
• They are not limited by the problem of nip inherent with smooth rolls
and can therefore reduce much larger particles
• Some heavy-duty toothed double-roll crushers are used for the
primary reduction of coal and similar materials
• The particle size of the feed to these machines may be as great as 500
mm (20 in.); their capacity ranges up to 500 tons/h

Grinders
The term grinder describes a variety of size-reduction machines for
intermediate duty.
The product from a crusher is often fed to a grinder, in which it is
reduced to powder.
The chief types of commercial grinders described in this section are
hammer mills and impactors, rolling-compression machines,
attrition mills, and tumbling mills.

Hammer mill
• These mills contain a high-speed rotor
turning inside a cylindrical casing. The
shaft is usually horizontal.
• Feed dropped into the top of the casing is
broken and falls out through a bottom
opening.
• In a hammer mill the particles are broken
by sets of swing hammers pinned to a
rotor disk.
• It shatters into pieces, which fly against a
stationary anvil plate inside the casing and
break into still smaller fragments.
• These in turn are rubbed into powder by
the hammers and pushed through a grate
or screen that covers the discharge
opening.

• Several rotor disks, 150 to 450 mm (6 to 18 in.) in diameter and each carrying
four to eight swing hammers, are often mounted on the same shaft.
• The hammers may be straight bars of metal with plain or enlarged ends or
with ends sharpened to a cutting edge.
• Intermediate hammer mills yield a product 25 mm (1 in.) to 20-mesh in
particle size.
• Hammer speeds may reach upto 110 m/s (360 ft/s); they reduce 0.1 to 15
ton/h to sizes finer than 200-mesh.
• Hammer mills grind almost anything-tough fibrous solids like bark or leather,
steel turnings, soft wet pastes, sticky clay, hard rock.
• The capacity and power requirement of a hammer mill vary greatly with the
nature of the feed and cannot be estimated with confidence from theoretical
considerations.
• Commercial mills typically reduce 60 to 240 kg of solid per kilowatt hour of
energy consumed.

Impactor
• An impactor illustrated in the Figures,
resembles a heavy-duty hammer mill except
that it contains no grate or screen. Particles
are broken by impact alone, without the
rubbing action characteristic of a hammer
mill.
• Impactors are often primary-reduction
machines for rock and ore, processing up to
600 ton/h.
• They give particles that are more nearly
equidimensional (more "cubical") than the
slab-shaped particles from a jaw crusher or
gyratory crusher. The rotor in an impactor,
as in many hammer mills, may be run in
either direction to prolong the life of the
hammers.

Rolling-compression Machines
• In this kind of mill the solid particles are
caught and crushed between a rolling
member and the face of a ring or casing.
• The most common types are rolling-ring
pulverizers, bowl mills, and roller mills.
• In the roller mill shown, vertical cylindrical
rollers press outward with great force
against a stationary anvil ring or bull ring.
• They are driven at moderate speeds in a circular path. Plows lift the solid lumps
from the floor of the mill and direct them between the ring and the rolls, where the
reduction takes place.
• Product is swept out of the mill by a stream of air to a classifier separator, from
which oversize particles are returned to the mill for further reduction.

• In a bowl mill and some roller mills, the bowl or ring is driven; the
rollers rotate on stationary axes, which may be vertical or horizontal.
• Mills of this kind find most application in the reduction of limestone,
cement clinker, and coal. They pulverize up to 50 ton/h. When
classification is used, the product may be as fine as 99 percent through
a 200-mesh screen.
Attrition Mills
• In an attrition mill particles of soft solids are rubbed between the
grooved flat faces of rotating circular disks. The axis of the disks is
usually horizontal, sometimes vertical.
• In a single-runner mill one disk is stationary and one rotates; in a
double-runner machine both disks are driven at high speed in opposite
directions.

• Feed enters through an opening in the hub of
one of the disks; it passes outward through the
narrow gap between. the disks and discharges
from the periphery into a stationary casing.
• The width of the gap, within limits, is adjustable.
At least one grinding plate is spring mounted so
that the disks can separate if unbreakable
material gets into the mill.
• Mills with different patterns of grooves,
corrugations, or teeth on the disks perform a
variety of operations, including grinding,
cracking, granulating, and shredding, and even
some operations not related to size reduction at
all, such as blending and feather curling.

• Single-runner mills contain disks of buhrstone or rock emery for reducing
solids like clay and talc, or metal disks for solids like wood, starch,
insecticide powders, and carnauba wax.
• Metal disks are usually of white iron, although for corrosive materials
disks of stainless steel are sometimes necessary. Double-runner mills, in
general, grind to finer products than single-runner mills but process
softer feeds.
• Air is often drawn through the mill to remove the product and prevent
choking.
• The disks may be cooled with water or refrigerated brine to take away
the heat generated by the reduction operation.
• Cooling is essential with heat-sensitive solids like rubber, which would
otherwise be destroyed.

• The disks of a single-runner mill are 250 to 1400 mm (10 to 54 in.) in
diameter, turning at 350 to 700 r/min. Disks in double-runner mills turn
faster, at 1200 to 7000 r/min.
• The feed is pre-crushed to a maximum particle size of about 12 mm (½
in.) and must enter at a uniform controlled rate.
• Attrition mills grind from ½ to 8 ton/h to products that will pass a 200-
mesh screen.
• The energy required depends strongly on the nature of the feed and the
degree of reduction accomplished and is much higher than in the mills
and crushers described so far.
• Typical values are between 8 and 80 kWh per ton of product.

Tumbling Mills
• A cylindrical shell turning about a horizontal axis
and filled to about half its volume with a solid
grinding medium forms a tumbling mill.
• The shell is usually steel, lined with high-carbon
steel plate, porcelain, silica rock, or rubber.
• The grinding medium is metal rods in a rod mill,
lengths of chain or balls of metal, rubber, or
wood in a ball mill, flint pebbles or porcelain or
zircon spheres in a pebble mill.
• For intermediate and fine reduction of abrasive
materials tumbling mills are unequaled.
• Batch and continuous modes of operation

• In batch grinding, a measured quantity of the
solid to be ground is loaded into the mill through
opening
• The opening is then closed and the mill run for
several hours; it is then stopped and the product
is discharged.
• In a continuous mill the solid flows steadily
through the revolving shell, entering at one end
through a hollow trunnion and leaving at the
other end through the trunnion
• In all tumbling mills, the grinding elements are
carried up the side of the shell nearly to the top,
from where they fall on the particles underneath.
• The energy expended in lifting the grinding units
is utilized in reducing the size of the particles.

• In a rod mill, much of the reduction is done by
rolling compression and by attrition as the rods
slide downward and roll over one another.
• The grinding rods are usually steel, 25 to 125
mm in diameter, with several sizes present at
all times in any given mill.
• The rods extend the full length of the mill.
• Rod mills are intermediate grinders, reducing a
20-mm feed to 10-mesh, often preparing the
product from a crusher for final reduction in a
ball mill.
• They yield a product with little oversize and a
minimum of fines.

• In a ball mill or pebble mill most of the reduction is done by impact as the balls or pebbles drop
from near the top of the shell.
• In a large ball mill the shell might be 3 m in diameter and 4.25 m long. The balls are 25 to 125
mm in diameter; the pebbles in a pebble mill are 50 to 175 mm in size.
• A tube mill is a continuous mill with a long cylindrical shell, in which material is ground for 2 to 5
times as long as in the shorter ball mill.
• Tube mills are excellent for grinding to very fine powders in a single pass where the amount of
energy consumed is not of primary importance.
• Putting slotted transverse partitions in a tube mill converts it into a compartment mill.

• One compartment may contain large balls,
another small balls, and a third pebbles.
• This segregation of the grinding media into
elements of different size and weight aids
considerably in avoiding wasted work, for the
large, heavy balls break only the large particles,
without interference by the fines.
• The small, light balls fall only on small particles,
not on large lumps they cannot break.
• Segregation of the grinding units in a single chamber is a characteristic of the
conical ball mill illustrated in Fig.
• Feed enters from the left through a 60° cone into the primary grinding zone,
where the diameter of the shell is a maximum.

• Product leaves through the 30° cone to the right.
• A mill of this kind contains balls of different sizes, all of which wear and
become smaller as the mill is operated.
• New large balls are added periodically. As the shell of such a mill rotates, the
large balls move toward the point of maximum diameter, and the small balls
migrate toward the discharge.
• The initial breaking of the feed particles, therefore, is done by the largest balls
dropping the greatest distance; small particles are ground by small balls
dropping a much smaller distance.
• The amount of energy expended is suited to the difficulty of the breaking
operation, increasing the efficiency of the mill.

Action in tumbling mills
• The load of balls in a ball or tube mill is normally such that when the mill is
stopped, the balls occupy about one-half the volume of the mill.
• The void fraction in the mass of balls, when at rest, is typically 0.4.
• The grinding may be done with dry solids, but more commonly the feed is a
suspension of the particles in water.
• This increases both the capacity and the efficiency of the mill.
• Discharge openings at appropriate positions control the liquid level in the
mill, which should be such that the suspension just fills the void space in the
mass of balls.
• When the mill is rotated, the balls are picked up by the mill wall and carried
nearly to the top, where they break contact with the wall and fall to the
bottom to be picked up again.

• Centrifugal force keeps the balls in contact with the wall and with each other
during the upward movement.
• While in contact with the wall, the balls do some grinding by slipping and
rolling over each other, but most of the grinding occurs at the zone of impact,
where the free-falling balls strike the bottom of the mill.
• The faster the mill is rotated, the farther the balls are carried up inside the
mill and the greater the power consumption.
• The added power is profitably used because the higher the balls are when
they are released, the greater the impact at the bottom and the larger the
productive capacity of the mill
• If the speed is too high, however, the balls are carried over and the mill is
said to be centrifuging.
• The speed at which centrifuging occurs is called the critical speed.

• Little or no grinding is done when a mill is
centrifuging, and operating speeds must be less
than the critical.
• The speed at which the outermost balls lose contact
with the wall of the mill depends on the balance
between gravitational and centrifugal forces
• Consider the ball at point A on the periphery of the
mill. Let the radii of the mill and of the ball be R and
r, respectively.
• The center of the ball is, then R - r meters (or feet) from the axis of the mill.
• Let the radius AO form the angle α with the vertical.
• Two forces act on the ball. The first is the force of gravity mg, The second is the
centrifugal force (R - r) ω2 where ω = 2Πn and n is the rotational speed

• The centripetal component of the force of gravity is
mg cosα and this force opposes the centrifugal
force.
• As long as the centrifugal force exceeds the
centripetal force, the particle will not break contact
with the wall.
• As the angle α decreases, however, the centripetal
force increases, and unless the speed exceeds the
critical, a point is reached where the opposing
forces are equal and the particle is ready to fall
away. The angle at which this occurs is found by
equating the two forces, giving
At the critical speed, α=0,
cosα=1, and n becomes the
critical speed nc
• Usually runs at 65-80% of critical speed

Capacity and power requirement of tumbling mills
• The maximum amount of energy that can be delivered to the solid being
reduced can be computed from the mass of the grinding medium, the speed
of rotation, and the maximum distance of fall.
• In an actual mill the useful energy is much smaller than this, and the total
mechanical energy supplied to the mill is much greater.
• Energy is required to rotate the shell in its bearing supports.
• Majority of the energy delivered to the grinding medium is wasted in
overgrinding particles that are already fine enough and in lifting balls or
pebbles that drop without doing much if any grinding.
• Good design, of course, minimizes the amount of wasted energy.

• Complete theoretical analysis of the many interrelated variables is
virtually impossible, and the performance of tumbling mills is best
predicted from computer simulations based on pilot-plant tests.
• Rod mills yield 5 to 200 ton/h of 10-mesh product; ball mills produce 1 to
50 ton/h of powder of which perhaps 70 to 90 percent would pass a 200-
mesh screen.
• The total energy requirement for a typical rod mill grinding hard material
is about 4kWh/metric ton (5 hp-h/ton); for a ball mill it is about
16kWh/metric ton (20 hp-h/ton).
• Tube mills and compartment mills draw somewhat more power than this.
• As the product becomes finer, the capacity of a given mill diminishes and
the energy requirement increases

Ultrafine Grinders
Many commercial powders must contain particles averaging 1 to 20
μm in size, with substantially all particles passing a standard 325-
mesh screen that has openings 44 μm wide.
Mills that reduce solids to such fine particles are called ultra fine
grinders.
Ultrafine grinding of dry powder is done by grinders, such as high-
speed hammer mills, provided with internal or external
classification, and by fluid-energy or jet mills.
Ultrafine wet grinding is done in agitated mills.

Fluid Energy Mills
• In these mills the particles are suspended in a high
velocity gas stream.
• Some reduction occurs when the particles strike or
rub against the walls of the chamber, but most of the
reduction is believed to be by interparticle attrition.
• Internal classification keeps the larger particles in the
mill until they are reduced to the desired size.
• The suspending gas is usually compressed air or
superheated steam, admitted at a pressure of 7 atm
through energizing nozzles.
• The grinding chamber is an oval loop of pipe 25 to
200 mm in diameter and 1.2 to 2.4 m high.

• Feed enters near the bottom of the loop through a venturi injector.
• Classification of the ground particles takes place at the upper bend of the
loop.
• As the gas stream flows around this bend at high speed, the coarser
particles are thrown outward against the outer wall while the fines
congregate at the inner wall.
• A discharge opening in the inner wall at this point leads to a cyclone
separator and a bag collector for the product.
• Fluid-energy mills can accept feed particles as large as 12 mm but are more
effective when the feed particles are no larger than 100-mesh.
• They reduce up to 1 ton/h of non-sticky solid to particles averaging 1/2 to
10 μm in diameter, using 1 to 4 kg of steam or 6 to 9 kg of air per kilogram
of product. Loop mills can process up to 6000 kg/h.

Mechanical Separations
Separations are extremely important in chemical manufacturing
◦ Physical separation
◦ Chemical separation
Mechanical separations are applicable to heterogeneous mixtures,
not to homogeneous solutions
The techniques are based on physical differences between the
particles such as size, shape, or density
They are applicable to separating solids from gases, liquid drops
from gases, solids from solids, and solids from liquids

METHOD liquid-
liquid
solid-solid gas-liquid gas-solid liquid-solid
1. Decantation yes
2. Coalescence yes yes
3. Centrifugation yes yes yes
4. Screening yes
5. Elutriation, Classification yes
6. Magnetic attraction yes
7. Cyclone flow yes yes yes
8. Settling, Differential settling yes yes yes yes
9. Flotation yes yes
10. Inertial precipitation: De-
misting, Scrubbing
yes yes
11. Foam-breaking yes
12. Electrostatic precipitation yes yes
13. Filtration yes yes
14. Flocculation yes
15. Hydroclone flow yes
16. Wicking and Expression yes

• Two general methods are the use of a sieve or membrane, such as a
screen or a filter, which retains one component and allows the other to
pass; and the utilization of differences in the rate of sedimentation of
particles or drops as they move through a liquid or gas.
Screening
• Screening is a method of separating particles according to size alone
• In industrial screening the solids are dropped on, or thrown against, a
screening surface
• The undersize, or fines, pass through the screen openings; oversize, or
tails, do not.
• A single screen can make a single separation into two fractions. These are
called unsized 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.
• Screening is occasionally done wet but much more commonly dry.
• Industrial screens are made from woven wire, silk or plastic cloth,
metal bars, perforated or slotted metal ·plates, or wires that are wedge
shaped in cross section.
• Various metals are used, with steel and stainless steel the most
common.
• Standard screens range in mesh size from 4 in. to 400-mesh, and
woven metal screens with openings as small as 1 μm are commercially
available.

• Screens finer than about 150-mesh are not commonly used,
however, because with very fine particles other methods of
separation are usually more economical.

Material Balances over Screen
• Let F, D, and B be the mass flow rates of the feed, overflow, and
underflow, respectively, and XF, XD, and XB be the mass fraction of
material A in these three streams.
• The material A in the feed must also leave in these two streams
• Elimination of B from above equations
• Elimination of D from above equations

Screen Effectiveness
• The effectiveness of a screen (often called the screen efficiency) is a
measure of the success of a screen in closely separating materials A
and B.
• If the screen functioned perfectly, all of material A would be in the
overflow and all of material B would be in the underflow.
• 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
• The mass fractions of material B in the feed, overflow, and underflow
are 1-XF, 1-XD, and 1-XB
• Since the total material fed to the screen must leave it either as
underflow or as overflow

• A combined overall effectiveness can be defined as the product of
the two individual ratios
• Substituting D/F and B/F
Screening Equipment
• In most screens the particles drop through the openings by gravity; in
a few designs they are pushed through the screen by a brush or
centrifugal force

• Coarse particles drop easily through large
openings in a stationary surface, but with
fine particles the screen surface must be
agitated in some way, such as by shaking,
gyrating, or vibrating it mechanically or
electrically

Stationary Screens And Grizzlies
• A grizzly is a grid of parallel metal bars set in an
inclined stationary frame
• The slope and the path of the material are
usually parallel to the length of the bars
• Very coarse feed, as from a primary crusher,
falls on the upper end of the grid. Large chunks
roll and slide to the tails discharge; small lumps
fall through to a separate collector.
• In cross section the top of each bar is wider than the bottom, so that the bars can
be made fairly deep for strength without being choked by lumps passing partway
through
• The spacing between the bars is 50 to 200 mm, used in separating particles from
12 to 100 mm. Effective only with very coarse free flowing solids and few fine
particles

Gyrating screens
• Two screens, one above the other, are held in a
casing inclined at an angle between 16° and 30°
with the horizontal
• The feed mixture is dropped on the upper
screen near its highest point
• Casing and screens are gyrated in a vertical
plane about a horizontal axis by an eccentric
that is set halfway between the feed point and
the discharge.
• The rate of gyration is between 600 and 1800 r/min. The screens are
rectangular and fairly long, typically 0.5 to 1.2 m to 1.5 to 4.3 m
• Oversize particles fall from the lower ends of the screens into collecting ducts;
fines pass through the bottom screen into a discharge chute.

• Finer screens are usually gyrated at the feed end in a horizontal plane
• The discharge end reciprocates but does not gyrate. This combination of
motions stratifies the feed, so that fine particles travel downward to the
screen surface, where they are pushed through by the larger particles on top
• Often the screening surface is double, and between the two screens are
rubber balls held in separate compartments
• As the screen operates, the balls strike the screen surface and free the
openings of any material that tends to plug them
• Dry, hard, rounded or cubical grains ordinarily pass without trouble through
screens, even fine screens; but elongated, sticky, flaky, or soft particles do
not. Under the screening action such particles may become wedged into the
openings and prevent other particles from passing through
• A screen plugged with solid particles is said to be blinded

Vibrating Screens
• Screens that are rapidly vibrated with small amplitude are less likely to
blind than are gyrating screens
• The vibrations may be generated mechanically or electrically. Mechanical
vibrations are usually transmitted from high-speed eccentrics to the
casing of the unit and from there to steeply inclined screens
• Electrical vibrations from heavy-duty solenoids are transmitted to the
casing or directly to the screens
• Ordinarily no more than three decks are used in vibrating screens.
• Between 1800 and 3600 vibrations per minute are usual.
• A 48 by 120 in. (1.2 to 3 m) screen draws about 4 hp (3 kW).

Comparison of ideal and actual screens
• The objective of a screen is to accept a feed containing a mixture of
particles of various sizes and separate it into two fractions, an underflow
that is passed through the screen and an overflow that is rejected by the
screen.
• Either one, or both, of these streams may be a product
• An ideal screen would sharply separate the feed mixture in such a way
that the smallest particle in the overflow would be just larger than the
largest particle in the underflow.
• Such an ideal separation defines a cut diameter Dpc, that marks the point
of separation between the fractions.
• Usually Dpc, is chosen to be equal to the mesh opening of the screen.

• Actual screens do not give a perfect separation about the cut
diameter
• The closest separations are obtained with spherical particles on
standard testing screens but even here there is an overlap between
the smallest particles in the overflow and the largest ones in the
underflow
• The overlap is especially pronounced when the particles are
needlelike or fibrous or where the particles tend to aggregate into
clusters that act as large particles
• Some long, thin particles may strike the screen surface end wise and
pass through easily, while other particles of the same size and shape
may strike the screen sidewise and be retained

Capacity and effectiveness of screens
• 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, and large
capacity is obtainable only at the expense of a reduction in effectiveness.
• In practice, a reasonable balance between capacity and effectiveness is
desired.
• Although accurate relationships are not available for estimating these
operating characteristics of screens, certain fundamentals apply, which can be
used as guides in understanding the basic factors in screen operation.
• The capacity of a screen is controlled simply by varying the rate of feed to the
unit. The effectiveness obtained for a given capacity depends on the nature of
the screening operation

• The overall chance of passage of a given undersize particle is a function of the
number of times the particle strikes the screen surface and the probability of
passage during a single contact
• If the screen is overloaded, the number of contacts is small and the chance of
passage on contact is reduced by the interference of the other particles.
• The improvement of effectiveness attained at the expense of reduced capacity
is a result of more contacts per particle and better chances for passage on
each contact.
• Ideally, a particle would have the greatest chance of passing through the
screen if it struck the surface perpendicularly, if it were so oriented that its
minimum dimensions were parallel with the screen surface, if it were
unimpeded by any other particles, and if it did not stick to, or wedge into, the
screen surface

Effect of mesh size on capacity of screens
• 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
✓ on the number of contacts between the particle and the screen surface
• When these factors are all constant, the average number of particles passing
through a single screen opening in unit time is nearly constant, independent
of the size of the screen opening.
• If the size of the largest particle that can just pass through a screen is taken
equal to the width of a screen opening, both dimensions may be represented
by Dpc
• For a series of screens of different mesh sizes, the number of openings per
unit screen area is proportional to 1/Dpc
2

• The mass of one particle is proportional to Dpc
3
• The capacity of the screen, in mass per unit time, is, then, proportional to
(1/Dpc
2) Dpc
3 = Dpc
• Then the capacity of a screen, in mass per unit time, divided by the mesh
size should be constant for any specified conditions of operation.
Problem – What rotational speed in RPM would you recommend for a ball mill
that is 1000 mm in diameter charged with 70 mm balls

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