The Glass Transition in Driven Granular Fluids: A Mode-Coupling Approach

TL;DR

This paper applies a mode-coupling theory to driven granular fluids, revealing a glass transition at a critical density that depends on dissipation and space dimension, with non-universal critical dynamics.

Contribution

It derives a nonlinear equation for the scattering function in driven granular fluids and characterizes the glass transition and critical dynamics in these non-equilibrium systems.

Findings

Glass transition occurs at a critical packing fraction below random close packing.

Timescales diverge at the transition, influenced by compression rate.

Critical exponents depend on space dimension and dissipation level.

Abstract

We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear equation of motion for the coherent scattering function in two and three space dimensions. A glass transition is observed for all coefficients of restitution, epsilon, at a critical packing fraction, phi_c(epsilon), below random close packing. The divergence of timescales at the glass-transition implies a dependence on compression rate upon further increase of the density - similar to the cooling rate dependence of a thermal glass. The critical dynamics for coherent motion as well as tagged particle dynamics is analyzed and shown to be non-universal with exponents depending on space dimension and degree of dissipation.