Patterns and Long Range Correlations in Idealized Granular Flows

TL;DR

This paper investigates the development of inhomogeneities and long-range correlations in idealized granular flows, combining molecular dynamics simulations with theoretical insights from spinodal decomposition to understand their evolution and boundary effects.

Contribution

It provides a detailed analysis of flow inhomogeneities and correlations in granular flows, integrating simulation results with Cahn--Hilliard theory for the first time.

Findings

Long-range spatial correlations observed in simulations.

Vortex size grows as square root of time.

Transitions to macroscopic shearing states occur.

Abstract

An initially homogeneous freely evolving fluid of inelastic hard spheres develops inhomogeneities in the flow field (vortices) and in the density field (clusters), driven by unstable fluctuations. Their spatial correlations, as measured in molecular dynamics simulations, exhibit long range correlations; the mean vortex diameter grows as the square root of time; there occur transitions to macroscopic shearing states, etc. The Cahn--Hilliard theory of spinodal decomposition offers a qualitative understanding and quantitative estimates of the observed phenomena. When intrinsic length scales are of the order of the system size, effects of physical boundaries and periodic boundaries (finite size effects in simulations) are important.