Inertia tensor as morphological descriptor for aggregation dynamics
Résumé
Multidimensional population balance modelling is a powerful tool to study the dynamics of the precipitation and particularly the aggregation of particles. This approach involves the selection of internal parameters describing the particle. Among them, morphological or geometrical descriptors are required. In this paper, the inertia or gyration tensor is considered and evaluated for the modelling of aggregation. An equivalent ellipsoid to the aggregate is defined from the tensor. Firstly, a general expression for the inertia tensor of the aggregate resulting from the collision of two aggregates is presented. In this framework, the collision event becomes the collision between two equivalent ellipsoids and leads to a larger ellipsoid. Secondly, the inertia tensor and the characteristics of the equivalent ellipsoid are explicitly calculated in the case of shear aggregation in a two-dimensional space. An approximate calculation is also presented and checked. Finally, the shear aggregation of a set of disks in a two-dimensional space is simulated using simultaneously this modelling of the collision event and Monte-Carlo simulations for all the collisions. This is compared with classical Monte Carlo simulations where the colliding particles are clusters of disks. Physical properties of the cluster population as, for instance, the distribution of elongation or anisotropy factor at different times are presented.