Kinetic Theory of Granular Gases

Abstract

Kinetic Theory of Granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics — a theory which has mainly evolved over the last decade. The book is aimed at readers from the advanced undergraduate level upwards and leads on to the present state of research. Throughout, special emphasis is put on a microscopically consistent description of pairwise particle collisions which leads to an impact-velocity-dependent coefficient of restitution. The description of the many-particle system, based on the Boltzmann equation, starts with the derivation of the velocity distribution function, followed by the investigation of self-diffusion and Brownian motion. Using hydrodynamical methods, transport processes and self-organized structure formation are studied. An appendix gives a brief introduction to event-driven molecular dynamics. A second appendix describes a novel mathematical technique for derivation of kinetic properties, which allows for the application of computer algebra. The text is self-contained, requiring no mathematical or physical knowledge beyond that of standard physics undergraduate level. The material is adequate for a one-semester course and contains chapter summaries as well as exercises with detailed solutions. The molecular dynamics and computer-algebra programs can be downloaded from a companion web page.

Droplet and cluster formation in freely falling granular streams

“…[23][24][25]. The system starts as an ensemble of up to 70,000 monodisperse spheres of diameter d inside a cylindrical reservoir (hopper).…”

The second and third Sonine coefficients of a freely cooling granular gas revisited

“…(11) and neglecting a k with k ≥ 4 and nonlinear terms (like a 2 2 , a 2 a 3 , and a 2 3 ). Furthermore, if a 3 is also neglected, the corresponding approximation will be denoted by L a 2 {X}.…”

“…The expressions for the coefficients A i , B i , and C i as functions of α and d were derived by van Noije and Ernst [5] and by Brilliantov and Pöschel [2,17]. They are given in Appendix A.…”

“…mal restitution 0 < α ≤ 1 [1,2]. Kinetic theory arguments similar to those followed in the elastic case allow one to derive the Boltzmann and Enskog equations [3] for the velocity distribution function f (r, v,t).…”

Choosing Hydrodynamic Fields

“…Another approach using additional fields is the moment method of Grad [19,20]. Here, motivated by current applications of hydrodynamics to granular fluids [3,12,14,18], related but different issues are addressed. Section 2. outlines the basic ingredients for a derivation of hydrodynamic equations near a state of uniformity, from the underlying equations of nonequilibrium statistical mechanics [5,6].…”