EVALUATION OF NUMERICAL METHODS FOR SIMULATING AN EVOLVING PARTICLE SIZE DISTRIBUTION IN GROWTH PROCESSES

The particle growth term renders hyperbolic the dynamic population balance equation. Problems associated with the numerical solution of hyperbolic partial differential equations with stationary grid methods are well known. Moreover in the common case of combined molecular particle growth and coagulation, the convolution integral of the coagulation terms makes the moving grid methods computationally intractable. To cope with practical problems, this work is focused on numerical solution methods, of the population balance equation, characterized by relatively small computational cost and fair accuracy - comparable to that of relevant experimental data. For this purpose, previous work on appropriate discretization of the coagulation terms is extended for the growth terms. Several numerical methods are systematically evaluated and further extended. Recommendations are made concerning the best method, by taking into account the nature of the problem, the prevailing physical conditions, and the main quantity of interest; i.e. certain specific moments, or the entire size distribution