Kinetic theory of multicomponent dense mixtures of slightly inelastic spherical particles

A kinetic-type theoretical approach is developed for the transport processes involved in flows of dense mixtures of solid particles with distribution in particle size. The particles are treated as being smooth, nearly elastic, and spherical. Starting from the reduced Liouville equation, a generalized Boltzmann equation that includes the effects of inelastic collisions is stated, assuming the condition of particle chaos. The nonequilibrium velocity distribution function is derived for particles of each size using a generalized Grad moment method. The theory is applied to study the rheology of multicomponent mixtures of granular materials undergoing steady shearing flows.