Onset of thermal convection in a horizontal layer of granular gas

TL;DR

This paper investigates the conditions under which thermal convection begins in a horizontal layer of granular gas, analyzing how inelastic collisions and various dimensionless parameters influence the onset and morphology of convection cells.

Contribution

It provides a theoretical analysis of the convection threshold in granular gases, incorporating inelasticity effects and deriving a necessary condition based on Schwarzschild's criterion.

Findings

Convection threshold depends on inelasticity, Froude, and Knudsen numbers.

A simple necessary condition for convection is formulated.

At low Froude numbers, convection instability transitions to phase separation.

Abstract

The Navier-Stokes granular hydrodynamics is employed for determining the threshold of thermal convection in an infinite horizontal layer of granular gas. The dependence of the convection threshold, in terms of the inelasticity of particle collisions, on the Froude and Knudsen numbers is found. A simple necessary condition for convection is formulated in terms of the Schwarzschild's criterion, well-known in thermal convection of (compressible) classical fluids. The morphology of convection cells at the onset is determined. At large Froude numbers, the Froude number drops out of the problem. As the Froude number goes to zero, the convection instability turns into a recently discovered phase separation instability.