A contribution to the relationship of energy and particle size in the comminution of brittle particulate materials

Abstract

The contribution of this paper on the relationship of energy–particle size in the comminution of brittle particulate materials is based on two concepts: (a) the potential energy of a single particle and (b) the size distribution of particles in a particulate material. The potential energy Q x of a single particle of size x is defined as the energy required to create this particle. By definition Q x = q x M x , where q x is the specific energy per unit mass and M x the mass of the particle. The relationship, which relates the energy to the size of the material, is assumed to be an empirical one: (d q x /d x)=− C(1/ x m ), where C and m are constants. For particulate materials, the particle distribution is assumed to be the Gates, Gaudin, Schuhmann: P x = W 0( x/ y) α , where P x is the cumulative particle mass finer than x, W 0 is the total mass of the assembly, y is the maximum particle size (size modulus) and α is a constant (distribution modulus). The potential energy E y of a particle assembly is defined as the total energy of its particles. It is shown that for m>1 and α− m≠−1 then E y =( CW 0/( m−1))( α/( α− m+1)) y 1− m and for α− m=−1 then E y =( CW 0/( m−1))(ln y a / y a ). For m=1 and α≠0 then E y =− CW 0(ln y−1/ a). For α=0, which is practically impossible, then E y is not defined. The case for m<1 is not realistic because it gives negative values for the potential energy. The conditions for the application of the formulae above are presented in the text.