Spline solution of the continuous batch grinding equation

The batch grinding equation for the case of a continuous particle size distribution is difficult to solve analytically. In the cases where solutions have previously been obtained, simplified assumptions were made about the functional forms of the selection and breakage functions which has limited practical application. A numerical procedure that employs cubic B-splines and a Galerkin technique has been developed to solve the continuous batch grinding equation. This approach has the advantage that the selection and breakage functions can have complicated functional forms characteristic of practical situations. An initial particle size distribution with any functional form may also be handled. Results are presented using the present method which compare very well with experimental data.