Theory of thermostatted inhomogeneous granular fluids: a self-consistent density functional description

TL;DR

This paper develops a self-consistent density functional theory for inhomogeneous granular fluids driven by a heat bath, capturing non-equilibrium steady states and dissipation effects, validated against molecular dynamics simulations.

Contribution

It introduces a simplified configurational space description for inelastic granular fluids, extending dynamic density functional theory to include dissipation effects.

Findings

Good agreement with molecular dynamics simulations

The derived equation captures non-equilibrium steady states

Additional terms account for inelastic dissipation effects

Abstract

The authors present a study of the non equilibrium statistical properties of a one dimensional hard-rod fluid dissipating energy via inelastic collisions and subject to the action of a Gaussian heat bath, simulating an external driving mechanism. They show that the description of the fluid based on the one-particle phase-space reduced distribution function, in principle necessary because of the presence of velocity dependent collisional dissipation, can be contracted to a simpler description in configurational space. Indeed, by means of a multiple-time scale method the authors derive a self-consistent governing equation for the particle density distribution function. This equation is similar to the dynamic density functional equation employed in the study of colloids, but contains additional terms taking into account the inelastic nature of the fluid. Such terms cannot be derived from a Liapunov generating functional and contribute not only to the relaxational properties, but also to the non equilibrium steady state properties. A validation of the theory against molecular dynamics simulations is presented in a series of cases, and good agreement is found.