Size reduction theories

1. SIZE REDUCTION THEORIES

2. The energy requirement for particle size reduction is a function of input and output of particle size, hardness, strength and other properties of solids.

3. Various theories for energy requirement are:- Rittinger’s theory Kick’s theory Bond’s theory.

4. The energy required to reduce the size of particles is inversely proportional to the size raised to the some power. n …. (1). Where, E =amount of energy required to produce a change D =size of unit mass C, n =constants.  

5. Integrating equation (1), E= C ln(d i /d n ) …. (2) (d i /d n ) = reduction ratio. If n=1.0 equation (2) becomes Kick’s theory. If n=1.5 equation (2) becomes Bond’s theory. If n=2.0 equation (2) becomes Rittinger’s theory.

6. According to this theory energy E required for size reduction of unit mass is directly proportional to the new surface area produced. E=K R (S n – S i ) …. (3) Where S i = initial surface area S n = new specific surface area K R = Rittinger’s constant. E = amount of energy. Rittinger’s theory.

7. Applications:- Applicable to brittle materials undergoing fine milling. This theory ignore deformation before fracture.

8. This theory states that energy used in crack propagation is proportional to the new crack length produced. It also states that deforming set of particles is proportional to change in dimensions. E= 2K B ( ) …. (4) Where K B = Bond’s work index. Di = initial diameter Dn = new diameter.   Bond’s theory

9. Bond’s work index is the work required to reduce unit weight from a theoretical infinite size to 80% passing 100µm. This theory is useful for rough mill sizing . The work index is useful for comparing efficiency of milling operations.

10. This theory states that the energy used in deforming a set of particles of equivalent shape is proportional to ratio of change in size. E= K k …... (5) Where K k = Kick’s constant D i = diameter of particle in the initial stage D n = diameter of the new particles.   Kick’s Theory

11. For c ompression of large particles kick’s theory is useful.

12. Rittinger’s theory:- (n=2.0) Energy α new surface area formed. Bond’s theory:- (n=1.5) Energy used in crack propagation α Crack length produced. Kick’s theory:- (n=1.0) Energy α Ratio of change in size. Summary