Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity

Abstract

Kinetic theory for granular mixtures with a separate granular temperature for each solid phase is considered. The particle phases are assumed to follow a Maxwellian distribution with zero-order approximation of the Boltzmann equation. A solution strategy for solving the integrals of the collisional closure relations is presented. The present analysis enables the solution of these integrals without neglecting the solid particle hydrodynamic velocities in the distribution function. However, the solution strategy limits the validity of the closure relations to relatively small and moderate hydrodynamic velocity differences. Dependent on the magnitude of the hydrodynamic velocity difference, the present closure relations can differ significantly from the simplified models where such velocity difference is traditionally neglected.