THEORETICAL-ANALYSIS OF THE STEADY-STATE PARTICLE-SIZE DISTRIBUTION IN LIMITED BREAKAGE PROCESSES

The steady state particle size distribution is examined, resulting fro m a breakage process with a maximum stable size and a homogeneous cont inuous kernel. The dynamic breakage problem is transformed into one th at allows direct solutions for the steady state distribution. The latt er depends on the breakage kernel and on the ratio of critical to init ial size. As this ratio goes to zero the steady state distribution app roaches its limiting form obtained by the authors previously [7]. A ge neral 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 re veals several interesting features of the problem. For the general con tinuous kernel, the problem can be cast in a matrix form amenable to a conventional theoretical treatment. Finally, comparisons of the new r esults with existing solutions of the dynamic problem, for large times , confirm their validity.