The shearing instability of a dilute granular mixture

TL;DR

This paper investigates the shearing instability in dilute granular mixtures using hydrodynamic equations and simulations, revealing a universal scaling behavior near the transition point.

Contribution

It provides a theoretical and simulation-based analysis of the shearing instability, including the critical size prediction and energy fluctuation scaling, extending understanding from one-component to mixture systems.

Findings

Divergent transversal velocity mode at instability

Good agreement between theory and Monte Carlo simulations

Energy fluctuations scale with the second moment of the distribution

Abstract

The shearing instability of a dilute granular mixture composed of smooth inelastic hard spheres or disks is investigated. By using the Navier-Stokes hydrodynamic equations, it is shown that the scaled transversal velocity mode exhibits a divergent behaviour, similarly to what happens in one-component systems. The theoretical prediction for the critical size is compared with direct Monte Carlo simulations of the Boltzmann equations describing the system, and a good agreement is found. The total energy fluctuations in the vicinity of the transition are shown to scale with the second moment of the distribution. The scaling distribution function is the same as found in other equilibrium and non-equilibrium phase transitions, suggesting the existence of some kind of universality.