Hydrodynamic Correlation Functions of a Driven Granular Fluid in Steady State

TL;DR

This study investigates the dynamic correlation functions of a driven granular fluid, revealing how relaxation times, sound waves, and transport coefficients behave at different densities and inelasticities, with results aligning with hydrodynamic and kinetic theories.

Contribution

It provides a detailed analysis of time-dependent correlation functions in a driven granular fluid, incorporating inelastic collisions and comparing results to hydrodynamic and kinetic models.

Findings

Relaxation time increases with volume fraction.

Sound waves are observed at small wave numbers.

Transport coefficients agree with kinetic theory predictions.

Abstract

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function, F_incoh(q,t), is seen to follow time-density superposition with a relaxation time that increases significantly as volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,omega) we compare our results to the predictions of generalized fluctuating hydrodynamics which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,omega) and the longitudinal current correlation function C_l(q,omega). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.