Publication: Towards a Landau-Ginzburg-type theory for granular fluids
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2002-04
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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 Landau-Ginzburg (LG) models for critical and unstable fluids. 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 LG-equations 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.
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© 2002 Plenum Publishing Corporation. Annual International Conference on Discrete Simulation of Fluid Dynamics (9. 2000. Santa Fe, New Mexico). M.E. acknowledges stimulating discussion with E. Ben-Naim, R. Desai and R. Kapral. J.W. and R.B. acknowledge support of the foundation "Fundamenteel Onderzoek der Materie (FOM)", which is financially supported by the Dutch National Science Foundation (NWO). J.W. also acknowledges support of a Huygens scholarship. R.B. wants to thank the
Institute for Theoretical Physics of Universiteit Utrecht for its hospitality. R.B. is supported by Grant DGES-PB97-0076 (Spain)
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