Momentum Transport in Granular Flows

TL;DR

This paper examines the limitations of binary collision assumptions in kinetic theories of granular flows, revealing that most realistic flows involve multi-particle interactions beyond binary collisions.

Contribution

It provides a microscopic derivation of momentum transport, compares it with kinetic theory, and quantifies the regimes where binary collision assumptions fail.

Findings

Binary collision assumption often invalid in realistic granular flows

Derived a microscopic momentum transport equation

Quantified regimes where binary collisions dominate

Abstract

We investigate the error induced by only considering binary collisions in the momentum transport of hard-sphere granular materials, as is done in kinetic theories. In this process, we first present a general microscopic derivation of the momentum transport equation and compare it to the kinetic theory derivation, which relies on the binary collision assumption. These two derivations yield different microscopic expressions for the stress tensor, which we compare using simulations. This provides a quantitative bound on the regime where binary collisions dominate momentum transport and reveals that most realistic granular flows occur in the region of phase space where the binary collision assumption does not apply.