Kinetic theory of dilute weakly charged granular gases with hard-core and inverse power-law interactions under uniform shear flow

TL;DR

This paper develops a kinetic-theory framework to analyze the steady rheology of dilute, weakly charged granular gases with hard-core and inverse power-law interactions under uniform shear flow, achieving good agreement with simulations.

Contribution

It introduces a new kinetic-theory approach incorporating velocity-dependent restitution and potential effects, with analytical expressions fitting simulation data.

Findings

Excellent agreement between theory and DSMC simulations for shear stress and viscosity.

Velocity distribution remains nearly Maxwellian even under strong shear.

Derived transport coefficients accurately capture temperature dependence across shear rates.

Abstract

We develop a kinetic-theory framework to investigate the steady rheology of a dilute gas interacting via a repulsive potential under uniform shear flow. Starting from the Boltzmann equation with a restitution coefficient that depends on the impact velocity and potential strength, we derive evolution equations for the stress tensor based on Grad's moment expansion. The resulting expressions for the collisional rates and transport coefficients are fitted with simple analytical functions that capture their temperature dependence over a wide range of shear rates. Comparison with direct simulation Monte Carlo (DSMC) results shows excellent quantitative agreement for the shear stress, temperature anisotropy, and shear viscosity. We also analyze the velocity distribution functions, revealing that the system remains nearly Maxwellian even under strong shear.