Rheological effects in the linear response and spontaneous fluctuations of a sheared granular gas

TL;DR

This paper investigates how small temperature perturbations in a sheared granular gas decay over time, revealing rheological effects and confirming the Onsager regression hypothesis through kinetic theory and simulations.

Contribution

It derives a closed equation for temperature decay in sheared granular gases incorporating rheological effects beyond the quasi-elastic limit.

Findings

The decay equation accurately predicts temperature relaxation.

Molecular dynamics simulations agree with theoretical predictions.

The Onsager postulate on fluctuation regression is validated.

Abstract

The decay of a small homogeneous perturbation of the temperature of a dilute granular gas in the steady uniform shear flow state is investigated. Using kinetic theory based on the inelastic Boltzmann equation, a closed equation for the decay of the perturbation is derived. The equation involves the generalized shear viscosity of the gas in the time-dependent shear flow state, and therefore it predicts relevant rheological effects beyond the quasi-elastic limit. A good agreement is found when comparing the theory with molecular dynamics simulation results. Moreover, the Onsager postulate on the regression of fluctuations is fulfilled.