Rheological properties of a granular impurity in the Couette flow

TL;DR

This paper validates a theoretical model of granular impurity flow in a Couette setup against Monte Carlo simulations, showing good agreement even at high inelasticity and shear rates, and discusses extensions for broader conditions.

Contribution

It confirms the accuracy of a recent theoretical solution for nonlinear Couette flow of granular impurities under extreme conditions and proposes an extended model for wider shear rate ranges.

Findings

Good agreement between theory and Monte Carlo simulations at high inelasticity.

Extended theoretical solution applicable for shear rates below the threshold.

Preliminary simulation results offer insights for a comprehensive exact solution.

Abstract

We discuss in this work the validity of the theoretical solution of the nonlinear Couette flow for a granular impurity obtained in a recent work [preprint arXiv:0802.0526], in the range of large inelasticity and shear rate. We show there is a good agreement between the theoretical solution and Monte Carlo simulation data, even under these extreme conditions. We also discuss an extended theoretical solution that would work for large inelasticities in ranges of shear rate $a$ not covered by our previous work (i.e., below the threshold value $a_{th}$ for which uniform shear flow may be obtained) and compare also with simulation data. Preliminary results in the simulations give useful insight in order to obtain an exact and general solution of the nonlinear Couette flow (both for $a\ge a_{th}$ and $a<a_{th}$).