Laws of Size Reduction

 1. Kicks Law

The Energy required to reduce the size of the particle is proportional to the ratio of the initial size of a typical dimensions to the final size of that dimensions .

E = K ln ( d1 / d2 )

E =  the Energy required per mass of the feed  .

K =  Kicks Constant .

d1 =  the Average initial size  .

d2 = the average size of the ground particles  .

d1/d2 =  the size reduction ratio and is used to evaluate the relative performance of different types of equipment , coarse grinding has below 8:1 where as in fine grinding ratio can exceed 100:1 .

2. Rittinger 's law 

The Energy Required for the size reduction of unit mass is proportional to the new surface area produced .

E = Kr ( 1/d2  - 1/d1 )

E =  the energy required per mass of the feed  .

Kr  =  Rittinger 's Constant .

d1 =  the average initial size 

d2 = the average size of the ground particles  .

1/d1 = S ,  S =  surface area , E =  Kr ( Sn  -  Si )

 

3. Bond 's Law

Energy used for size reduction is proportional to the new Cracks Length .

E/W = sqrt(100/d2) - sqrt(100/d1)

E =  energy required per mass of feed  .

W = the bond work index required to reduce a unit weight .

d1 = diameter of sieve aperture that allows 80% of the mass of the feed to pass .

d2  =  diameter of the sieve aperture that allows 80% of the mass of the ground material to pass .

NOTES :=

1. Kicks law gives reasonably good for coarse grinding in which there is a relatively small increase in the surface area per unit mass .

2. Rittingers Law gives better results with fine grinding where there is a much larger increase in the surface area .

3. Bonds law is intermediate between these two however equation rittingers law and bonds law were developed from studies of hard material and deviation from predicted results is likely with many materials .