1. Size reduction through grinding and sieving is important for easy handling and increased surface area. It requires significant energy, with only 1% used to create new surfaces. 2. The experiment involves grinding limestone using a ball mill, then sieving to determine size distributions initially and after grinding. Energy consumed is measured. 3. Bond's law relates energy to material reduction, with work index values provided for various materials. The experiment aims to calculate coefficients and work index for limestone based on size distributions and energy used.

1. FM 306: SIZE REDUCTION AND SIEVING
Introduction:
Reduction of particle size is an important operation in many chemical and other
industries. The important reasons for size reduction are:
Easy handling
Increase in surface area per unit volume
Separation of entrapped components
The operation is highly energy intensive; hence a variety of specialized equipment is
available for specific applications. The equipment may utilize one or more of the
following physical mechanisms for size reduction: (i) Compression, (ii) Impact, (iii)
Attrition, (iv) Cutting. Estimation of energy for the operation is important and is usually
done by empirical equations. Enormous quantities of energy are consumed in size
reduction operations. Size reduction is the most inefficient unit operations in terms of
energy, as 99% of the energy supplied goes to operating the equipment and producing
undesirable heat and noise, while less than 1% goes in creating new interfacial area.
Reduction to very fine sizes is much more costly in terms of energy as compared to
relatively coarse products.
Sieving refers to the separation of a mixture of particles of different sizes using sieves
each with a uniform sized opening. Standard sieves of specified opening sizes are used.
Sieves are stacked with the sieve with the largest opening on the top and the material is
separated into fractions by shaking. The material between two sieves is smaller than the
upper sieve opening but larger than the smaller sieve opening.
Objectives:
1. To grind the given limestone material to a smaller size using a ball mill and to
obtain the size distribution of the initial and final mixture by sieving.
2. To estimate the energy required for the grinding operation.
3. To analyze the results using available theories.
Procedure:
1. Weigh the given limestone sample and obtain the initial size distribution by
sieving.
2. Grind the sample in the ball mill for 30 minutes noting the energy consumed
during grinding.
3. Measure the size distribution by sieving.
4. Repeat steps 2 and 3.

2. Theory and Analysis:
The minimum energy required for crushing is the energy required for creating fresh
surface. In addition, energy is absorbed by the particulate material due to deformation,
friction, etc., which results in an increase of the material temperature. Defining the
crushing efficiency as
n
wawb
sc
W
AA
e
materialbyabsorbedEnergy
createdenergySurface )( −
==η (1)
Where is the surface energy per unit area and is the energy absorbed. We can
experimentally find
se nW
cη . The range of cη is between 0.06 – 1.00%. If mη is the
mechanical efficiency, the energy input is
mc
wawb
s
AA
eW
ηη
)( −
= (Since WW mn η= ) (2)
Finally, the grinding energy used per unit mass is
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=
saasbbpmc
s
DD
e
m
W
φφρηη
116
(3)
where m is mass of material being ground. In the above equationφ is the sphericity, sD is
the surface volume diameter and the subscripts a and b refer to the initial and final states,
respectively.
Experiments show that the first term in Eq. (3) is not independent of sD , and as a result
the above equation is difficult to use for analysis. Instead a number of empirical laws
have been proposed for calculation the energy requirements for crushing. The laws can be
unified in a differential form as follows:
n
s
s
D
Dd
k
m
W
d −=⎟
⎠
⎞
⎜
⎝
⎛
(4)
The different laws for the different values of the exponent are
n = 1 : ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
sb
sa
K
D
D
K
m
W
ln (Kick’s law) (5)

3. n = 2 : ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=
sasb
R
DD
K
m
W 11
(Rittinger’s Law) (6)
n = 3/2 :
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−=
ab
B
DD
K
m
W
8080
11
(Bond’s Law) (7)
Note that the definition of particle size in Bonds law is different: 80D = Particle size such
that 80% by weight of the sample is smaller than it.
Bonds law is often written in terms of the work index (Wi) as,
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−=
ab
i
DD
W
m
W
8080
11
10 (8)
Where the work index is defined as the energy required per unit mass in kWh/ton to
reduce an infinitely large particles to 80D = 100 µm. In the above equation, unit of 80D is
µm, of W is kWh and of m is ton. Values of the work index: obtained from experiments
for different materials are given in the table below.
Material Wi (kWh/ton)
Basalt 20.41
Coke 73.8
Limestone 11.6
Mica 134.5
Glass 3.08
Calcined clay 1.43
Dry Grinding work index is 1.34 times wet grinding index. Open circuit work index is
1.34 times closed circuit work index.
Questions:
1. Plot the initial distribution and distributions obtained after sieving.
2. Calculate the surface volume diameter in each case.
3. Obtain the diameter 80D for all three distributions.
4. Obtain the coefficients KK, KR and the work index, Wi for all the runs. Are there
any variations in coefficients / working indices in the runs?
5. Assuming reasonable values of cη and mη estimate es.
6. Do you have any suggestions to improve the experiments?