Theory of granular gases: some recent results and some open problems

Abstract

One of the goals of the present paper is to present a brief, and admittedly somewhat biased, review of some recent theoretical advances in the field of granular gases. Another goal is to highlight some challenges facing this field. A third goal is to present some new results concerning the Chapman–Enskog expansion. These include an extension to weakly frictional granular gases, and a study of a stationary granular gas subject to a heat flux (an earlier study describing a stationary sheared granular gas is presented as well). In addition, a computer-aided method for inverting the linearized Boltzmann operator, which should be useful for kinetic theorists, is presented in an appendix. A further goal is to briefly discuss possible extensions beyond Boltzmann kinetics, as well as beyond hydrodynamics, i.e., the moderately dense regime on one hand, and the Knudsen regime on the other hand. An attempt is made throughout this paper to put granular gases in a general context, by distinguishing between those features that are common to granular and molecular gases and those that are not. Also, stress is put on the physics (and methods) rather than phenomena. While this is not a review article, parts of it are intended for the uninitiated in the field.