Hydrodynamic profiles for an impurity in a open vibrated granular gas

TL;DR

This paper derives explicit hydrodynamic profiles for an impurity in a vibrated granular gas, showing the temperature ratio depends only on particle properties and influences impurity distribution, with predictions validated by simulations.

Contribution

It provides explicit expressions for impurity temperature and density profiles in a vibrated granular gas, highlighting the role of the temperature ratio in impurity positioning.

Findings

Temperature ratio depends only on particle properties.

Theoretical profiles agree with molecular dynamics simulations.

The impurity's density profile is influenced by the temperature ratio.

Abstract

The hydrodynamic state of an impurity immersed in a low density granular gas is analyzed. Explicit expressions for the temperature and density fields of the impurity in terms of the hydrodynamic fields of the gas are derived. It is shown that the ratio between the temperatures of the two components, measuring the departure from energy equipartition, only depends on the mechanical properties of the particles, being therefore constant in the bulk of the system. This ratio plays an important role in determining the density profile of the intruder and its position with respect to the gas, since it determines the sign of the pressure diffusion coefficient. The theoretical predictions are compared with molecular dynamics simulation results for the particular case of the steady state of an open vibrated granular system in absence of macroscopic fluxes, and a satisfactory agreement is found.