Characteristic length and time scales for granular dynamics at low density


Francisco Vega Reyes (Universidad de Extremadura)


We study in this theoretical work a system of many identical particles that collide inelastically (i.e., there is kinetic energy loss after collisions). The system is supposed to be at any times at low density, enough to make non-binary collision events statistically irrelevant. We analyze the relevant time and length scales in the problem. We are interested in detecting and characterizing 'microscopic'-'macroscopic' scale separation, in order to look for hydrodynamic (or 'normal') states in the system. In particular, we present a set of hydrodynamic steady state solutions for a simple geometric configuration that corresponds to the traditional problem of a Couette or Fourier flow [1,2]. Additionally, we also study the transition to a normal solution for transient states in a homogeneous granular gas as it evolves to a homogeneous steady state. Our results, supported by computer simulations (Monte Carlo direct simulation method and molecular dynamics) confirm the existence of a set of normal solutions in the granular gas for a wide range of situations.

[1] F. Vega Reyes, A. Santos, and V. Garzo, Phys. Rev. Lett. 104, 028001 (2010).
[2] F. Vega Reyes, A. Santos, and V. Garzo, J. Fluid Mech. 719, 431 (2013).

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