Dynamic properties of a confined quasi-two-dimensional granular fluid driven by a stochastic bath with friction

TL;DR

This study analyzes how external stochastic driving and gas interactions affect the transport properties and stability of a confined quasi-two-dimensional granular fluid, providing analytical results validated by simulations.

Contribution

It extends the kinetic theory of granular fluids to include stochastic bath effects and validates the predictions with DSMC simulations.

Findings

External driving significantly modifies transport coefficients.

Theoretical predictions for temperature and kurtosis match simulation results.

Homogeneous steady state remains stable under studied conditions.

Abstract

This paper investigates the dynamic properties of a confined quasi-two-dimensional granular fluid at moderate densities, modeled within the framework of the Enskog kinetic equation. The system is described using the so-called $\Delta$-model, which incorporates energy injection through modified collision rules, and is further extended to account for the influence of an interstitial gas via a viscous drag force and a stochastic Langevin-like term. By applying the Chapman-Enskog method, the Navier-Stokes transport coefficients and the cooling rate are derived analytically considering the leading terms in a Sonine polynomial expansion. The study focuses on steady-state conditions and examines how the combined effects of inelastic collisions and external driving influence transport properties such as the viscosity and the thermal conductivity. Theoretical predictions for the steady temperature and the kurtosis are validated against direct simulation Monte Carlo (DSMC) results, showing excellent agreement. The findings reveal that the external driving significantly alters the transport coefficients compared to dry (no gas phase) granular systems, challenging previous assumptions that neglected these effects. Additionally, a linear stability analysis demonstrates that the homogeneous steady state is stable across the explored parameter space.