Statistics about collisions of ellipsoids under shear flow

Abstract

Shear aggregation is an important phenomenon occurring during particle precipitation in a stirred chemical reactor. It concerns micro-particles that are often non-spherical or aggregated.Modelling of precipitation 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 of primary particles and of their cluster is considered and evaluated for the modelling of aggregation. An equivalent ellipsoid is defined from the inertia tensor. In this framework, the collision event becomes the collision between two equivalent ellipsoids and leads to a larger ellipsoid. The inertia tensor and the semi-axis lengths of the equivalent ellipsoid are explicitly calculated in the case of shear aggregation in a three-dimensional space.Two ways for performing these calculations are presented. The statistics of the equivalent ellipsoids associated with the set of collision events undergone by two given ellipsoids have been computed. Statistics includes the probability density for geometrical parameters and the average value. Collision rate constant, i.e. aggregation kernel, is also calculated.