Multi(4)-variate population balance modeling for shear aggregation in 3D space

Shear aggregation of micrometric particles is an important phenomenon occurring in agitated chemical reactors. The resulting clusters of particles are porous and more or less elongated. It has previously been proved that the equivalent ellipsoid computed from the inertia tensor describes well the colliding clusters [F.Gruy and P. Nortier « Statistics about collisions of ellipsoids under shear flow » Colloids and Surfaces A: Physicochemical and Engineering Aspects, 558(2018)250-262]. The aim of the current paper is to consider chosen kinetic and morphological aspects of the complete aggregation dynamics. Monte Carlo simulations are used as a means of investigation. Four representations of the collision event have been compared: the classical collision of oriented clusters of sphere (A), the collision of oriented equivalent ellipsoids (B), the orientation-averaged collision of equivalent ellipsoids (C), the use of approximate expressions for C (D). For each case, the probability density functions of various morphological parameters of the cluster population are calculated as a function of the time. The comparison of the generated data shows that the approximate expressions for the aggregation kernel and the ellipsoid parameters allow for fast and representative simulations of the shear aggregation of suspensions.