Kinetic theory of aggregation in granular flow

This article presents a mathematical formulation of the aggregation kinetics in granular flow. The traditional kinetic theory and its generalized application to granular flow does not allow for particle size to change with time thus cannot be used to describe particle flow with aggregation taking place. In this article, a collision success factor, quantifying the completely inelastic collision of particles, is introduced into the evaluation of collision rate. The kinetic transport equations are then transformed to include source terms that account for the effects of particle size and aggregation. The analytical solution of the collision success factor is obtained by integrating the relative velocity distribution function over its velocity domain from 0 to a critical value, which corresponds a balance between the repulsion and attraction forces in a collision. The factor has been found to depend on the mixture granular energy and the critical relative collision energy.