Continuum theory for rapid cohesive-particle flows: general balance equations and discrete-element-method-based closure of cohesion-specific quantities

Abstract

The continuum description of rapid cohesive-particle flows comprises the population balance, which tracks various agglomerate sizes in space and time, and kinetic-theory-based balances for momentum and granular energy. Here, fundamental closures are provided in their most general form. In previous population balances, the probability (‘success factor’) that a given collision results in agglomeration or breakage has been set to a constant even though it is well established that the outcome of a collision depends on the impact (relative) velocity. Here, physically based closures that relate the success factors to the granular temperature, a (continuum) measure of the impact velocity, are derived. A key aspect of this derivation is the recognition that the normal component of the impact velocity dictates whether agglomeration occurs. With regard to the kinetic-theory balances, cohesion between particles makes the collisions more dissipative, thereby decreasing the granular temperature. The extra dissipation due to cohesion is accounted for using an effective coefficient of restitution, again determined using the derived distribution of normal impact velocities. This collective treatment of the population and kinetic-theory balances results in a general set of equations that contain several parameters (e.g. critical velocities of agglomeration) that are cohesion-specific (van der Waals, liquid bridging, etc.). The determination of these cohesion-specific quantities using simple discrete element method simulations, as well as validation of the resulting theory, is also presented.