(658c) Development and Validation of Fundamental Closures for the Population Balance Using DEM

Flows of cohesive particles are subject to the formation and break-up of agglomerates. One approach to the continuum modeling of such flows is the population balance equation coupled with kinetic theory balances. The population balance includes sink and source terms representing agglomeration and breakage. These sink and source terms depend on the success factors of agglomeration and breakage, which quantify the fraction of collisions that result in agglomeration and breakage. Though known to be important, previous works have largely ignored the effect of particle properties and particle impact velocities on the success factors. The focus of this work is to develop a fundamental link between the success factors and the granular temperature found in kinetic theory by relating the distribution of normal particle impact velocities to the granular temperature. This distribution of impact velocities is then used to determine an effective coefficient of restitution for use in kinetic-theory closures. The resulting theoretical expressions derived for both the impact velocity distribution and the effective restitution coefficient are validated via discrete element method (DEM) simulations and shown to be critical for accurate predictions. DEM simulations are then utilized to determine the critical velocities of aggregation and breakage for the given particle-particle cohesion model. Finally, the full set of closed balances (population, mass, momentum, and granular energy) are validated in the spatially uniform homogeneous cooling and simple shear flow systems using DEM.