• flocculation;
  • particulate processes;
  • particle-size distribution;
  • integro-differential equation;
  • Method of Lines


A numerical procedure has been developed to solve the population balance equation (PBE) for the flocculation of colloidal suspensions. It has the flexibility to cope with different flocculation kinetics and spread in particle volume. The two key steps in this procedure are the adoption of the logarithm of particle volume as the independent variable and the implementation of uniform discretization in the logarithmic domain. Together they allow the PBE to be represented accurately over the entire particle range overcoming the failure of the popular geometric discretization scheme to represent the PBE satisfactorily for large particles. The Method of Lines is used to convert the PBE from an integro-differential equation into a set of first-order ordinary differential equations, which is then integrated using commercial scientific computing software. The procedure has been tested for different kinetics and initial particle distributions. Preservation of particulate volume of between 1 and 8% is consistently observed. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3043–3053, 2012