Hydrodynamic instabilities in shear flows of cohesive granular particles

TL;DR

This paper extends a dynamic van der Waals model to study hydrodynamic instabilities in shear flows of cohesive granular particles, revealing how density structures form due to thermodynamic instability under shear.

Contribution

It introduces a modified model for cohesive granular flows and analyzes the conditions leading to hydrodynamic instabilities and structure formation.

Findings

Various steady-state density structures observed.

Instability triggered when pressure decreases with volume fraction.

Structures depend on volume fraction, shear rate, and inelasticity.

Abstract

We extend the dynamic van der Waals model introduced by A. Onuki [Phys. Rev. Lett. 94, 054501 (2005)] to the description of cohesive granular flows under a plane shear to study their hydrodynamic instabilities. Numerically solving the dynamic van der Waals model, we observe various heterogeneous structures of the density in steady states, where the viscous heating is balanced with the energy dissipation caused by inelastic collisions. Based on the linear stability analysis, we find that the spatial structures are determined by the mean volume fraction, the applied shear rate, and the inelasticity, where the instability is triggered if the system is thermodynamically unstable, i.e. the pressure, $p$, and the volume fraction, $\phi$, satisfy $\partial p/\partial\phi<0$.