Thermal diffusion segregation in granular binary mixtures described by the Enskog equation

Abstract

The diffusion induced by a thermal gradient in a granular binary mixture is analyzed here in the context of the (inelastic) Enskog equation. Although the Enskog equation neglects velocity correlations among particles that are about to collide, it retains the spatial correlations arising from volume exclusion effects and thus is expected to be applicable for moderate densities. In the steady state with gradients only along a given direction, a segregation criterion is obtained from the thermal diffusion factor A by measuring the amount of segregation parallel to the thermal gradient. As expected, the sign of the factor A provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the mixture (the masses and sizes of particles, concentration, solid volume fraction and coefficients of restitution). The form of the phase diagrams for the BNE/RBNE transition is illustrated in detail for several systems, with special emphasis on the significant role played by the inelasticity of collisions. In particular, an effect already found in dilute gases (segregation in a binary mixture of identical masses and sizes but different coefficients of restitution) is extended to dense systems. A comparison with recent computer simulation results reveals good qualitative agreement at the level of the thermal diffusion factor. The present analysis generalizes to arbitrary concentration previous theoretical results derived in the tracer limit case. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.