文档介绍：PHYSICAL REVIEW E VOLUME 58, NUMBER 4 OCTOBER 1998
Hydrodynamics for granular flow at low density
J. Javier Brey
Fı´sica Teo´rica, Universidad de Sevilla, E-41080 Sevilla, Spain
James W. Dufty
Department of Physics, University of Florida, Gainesville, Florida 32611
Chang Sub Kim
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
Andre´s Santos
Departamento de Fı´sica, Universidad de Extremadura, E-06071 Badajoz, Spain
͑Received 13 March 1998; revised manuscript received 8 June 1998͒
The hydrodynamic equations for a gas of hard spheres with dissipative dynamics are derived from the
Boltzmann equation. The heat and momentum fluxes are calculated to Navier-Stokes order and the transport
coefficients are determined as explicit functions of the coefficient of restitution. The dispersion relations for the
corresponding linearized equations are obtained and the stability of this linear description is discussed. This
requires consideration of the linear t contributions to the energy balance equation from the energy sink
term. Finally, it is shown how these results can be imbedded in simpler ic model equations with the
potential for analysis of plex states.
͓S1063-651X͑98͒15709-4͔
PACS number͑s͒: , ,
I. INTRODUCTION tion parameter. The objective here is to provide a derivation
of the hydrodynamic equations from the Boltzmann equation
The rapid flow of granular media is frequently described using an extension of the Chapman-Enskog method to granu-
at the macroscopic level by the equations for fluid dynamics, lar media. The transport coefficients in the heat and momen-
modified to account for dissipation among the interacting tum fluxes at Navier-Stokes order are calculated as functions
particles ͓1͔. These equations are generally phenomenologi- of the coefficient of restitution using a first Sonine polyno-
cal with unknown transport coefficients and with unknown mial approximation, a