SPLINE-GALERKIN SOLUTION OF DYNAMIC EQUATIONS FOR PARTICLE COMMINUTION AND COLLECTION

The population balance equation is solved for particles undergoing a combination of growth, comminution, and collection. The approximation method is to use a weighted Galerkin technique with cubic B-splines and an implicit scheme for solving the system of ordinary differential equations. The cubic splines are defined on a graded mesh. The performance of the method is investigated by solving a model problem with simple but nonsmooth kernels. The weight function is chosen so that singularities in the equation can be easily treated. A self-similar solution for comminuted particles is shown to be a useful representation for the solution of the population balance equation provided that this equation is solved over a sufficiently long time interval. Stationary solutions of the equation are obtained for a model that describes both particle comminution and collection. (C) 1995 Academic Press. Inc.