Theoretical analysis of the steady state particle size distribution in limited breakage processes

Abstract

The steady state particle size distribution is examined, resulting from a breakage process with a maximum stable size and a homogeneous continuous kernel. The dynamic breakage problem is transformed into one that allows direct solutions for the steady state distribution. The latter depends on the breakage kernel and on the ratio of critical to initial size. As this ratio goes to zero the steady state distribution approaches its limiting form obtained by the authors previously [7]. A general theoretical analysis concerning the steady state distribution is presented herein. The asymptotic behaviour is determined with regard to various limits. Perturbation analysis for nearly uniform kernels reveals several interesting features of the problem. For the general continuous kernel, the problem can be cast in a matrix form amenable to a conventional theoretical treatment. Finally, comparisons of the new results with existing solutions of the dynamic problem, for large times, confirm their validity.