Statistical mechanics of dense granular fluids - contacts as quasi-particles

TL;DR

This paper introduces a statistical mechanics framework treating contacts as quasi-particles to describe slow, dense granular fluids, predicting coordination number behavior and jamming transition under shear.

Contribution

It extends Edwards statistical mechanics to dynamic granular systems by modeling contacts as quasi-particles, enabling analysis of coordination and jamming.

Findings

Contact potential $ u$ relates to shear rate and coordination number.

Predicted shear rate at jamming $ ightarrow u=0$ and coordination number scaling.

Supports with existing literature on granular jamming and coordination.

Abstract

A new first-principles statistical mechanics formulation is proposed to describe slow and dilated granular fluids, where prolonged intergranular contacts vitiate collision theory. The contacts, where all the important physics takes place, are regarded as quasi-particles that can appear and disappear. A contact potential, $\nu$, is defined as a measure of the fluctuations and the mean coordination number per particle and its fluctuations are calculated as a function of it. This formulation extends the Edwards statistical mechanics to slow dynamic systems and converges to it when the motion stops. The theory is applied to a model system of a simply sheared granular material in the limit of small confining stress. The dependence of the contact potential on the shear rate is derived, making it possible to calibrate $\nu$ experimentally and predict the coordination number distribution as a function of the shear rate. Setting next $\nu=0$ as the jamming point, where the critical mean coordination number is $z_c$, a finite value is found for the shear rate there, $\dot{\gamma}_c$. A simple mean field theory then yields the scaling of the mean coordination number and its fluctuations near $\dot{\gamma}_c$. Existing results in the literature appear to support the predictions.