Population balance for aggregation coupled with morphology changes

In the past, the kinetics of aggregation has been extensively studied. Aggregation rates were measured and calculated thanks to a population balance. Aggregate morphologies were measured or got by computer simulations. However, the link between the aggregation kinetics and the morphology changes with time is not so clear. The modelling of aggregation may be even more complex as restructuring of aggregates occurs. The aim of this paper is to propose a new formulation taking into account at once kinetics of collision and morphology change rate. We built a bivariate population balance with matter volume and porous volume as internal parameters. The population balance equation contains the standard collision term and a convective term representing the porous volume change. The latter is split into two contributions, which is due to the aggregation process itself and the other one is due to the restructuring. The expressions of the first contribution are determined for Brownian and shear aggregations.