Segregation by thermal diffusion of an intruder in a moderately dense granular fluid

TL;DR

This paper develops a comprehensive theoretical model to analyze thermal diffusion and segregation phenomena in dense granular gases, revealing how gravity and dissipation influence the transition between Brazil-nut and reverse Brazil-nut effects.

Contribution

It extends previous dilute-limit theories to moderate densities using the inelastic Enskog equation, providing detailed phase diagrams for segregation transitions.

Findings

Segregation depends on gravity and thermal gradients.

Dissipation effects are more significant without gravity.

Results align with previous dilute-limit theories and experimental data.

Abstract

A solution of the inelastic Enskog equation that goes beyond the weak dissipation limit and applies for moderate densities is used to determine the thermal diffusion factor of an intruder immersed in a dense granular gas under gravity. This factor provides a segregation criterion that shows the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the system (masses, sizes, density and coefficients of restitution). The form of the phase-diagrams for the BNE/RBNE transition depends sensitively on the value of gravity relative to the thermal gradient, so that it is possible to switch between both states for given values of the parameters of the system. Two specific limits are considered with detail: (i) absence of gravity, and (ii) homogeneous temperature. In the latter case, after some approximations, our results are consistent with previous theoretical results derived from the Enskog equation. Our results also indicate that the influence of dissipation on thermal diffusion is more important in the absence of gravity than in the opposite limit. The present analysis extends previous theoretical results derived in the dilute limit case [V. Garz\'o, Europhys. Lett. {\bf 75}, 521 (2006)] and is consistent with the findings of some recent experimental results.