On the steady-state size distribution of dispersions in breakage processes

Abstract

Breakage processes are considered in the absence of agglomeration or coagulation. A new method is proposed, based on a population balance type of formulation, applicable to systems (such as dispersions) that may be characterized by a maximum stable particle size. In this method, considerable simplification is achieved by means of a transformation that effectively eliminates the breakage frequency, thus allowing the convenient computation of steady state through solution of an integral equation. To compute the steady state, apart from the maximum size and the breakage kernel, only an estimate of the initial distribution is required. Two functional forms of binary breakage kernels which can represent a large variety of possible breakage mechanisms are proposed (by an appropriate selection of parameter values). For the sake of completeness, analytical solutions are also presented for several, relatively simple kernels. Finally, a study is made to assess the influence of initial conditions on the steady-state size distribution, which is helpful in tackling the inverse problem of determining the breakage kernel using limited experimental data.