Towards a LandauGinzburgtype Theory for Granular Fluids
Abstract
In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent LandauGinzburg (LG) models for critical and unstable fluids (e.g. spinodal decomposition). The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LGequations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field. Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.
 Publication:

arXiv eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:condmat/0103086
 Bibcode:
 2001cond.mat..3086W
 Keywords:

 Statistical Mechanics
 EPrint:
 19 pages, LaTeX, 8 figures