An improved discretized population balance equation (PBE) is proposed in this study. This improved discretized PBE has new probability distribution functions for aggregates produced in non-uniform discrete coagulation modeling. The authors extended an improved particle coagulation model previously developed to an adjustable geometric size interval (q), where q is a volume ratio of class k + 1 particles to class k particles (nu k+ 1 /nu k = q). This model was compared with exact numerical solutions of continuous (uniform discretized) PBEs and applied to simulate the particle aggregation and breakup with fractal dimensions lower than 3. Further, comparisons were made using the fractal aggregate collision mechanisms of orthokinetic coagulation with the inclusion of flow induced breakup. In the course of the investigation the new algorithm was found to be a substantial improvement in terms of numerical accuracy, stability, and computational efficiency over the continuous model. This new algorithm makes it possible to solve fractal particle aggregation and breakup problems with high accuracy, perfect mass conservation, and exceptional computational efficiency, thus the new model can be used to develop predictive simulation techniques for the coupled coagulation using computational fluid dynamics (CFD) and chemical reaction modeling. (c) 2005 Elsevier Ltd. All rights reserved.