Quasi-thermodynamics of powders and granular dynamics

Abstract

Granular dynamics simulations of inelastic spheres thermalised by mechanical vibrations are reported. The objective is to determine the conditions whereby inelastic spheres in a gravitational force field can behave quasi-thermodynamically. Granular temperatures and granular pressures are defined by analogy with molecular thermodynamics. Quasi-thermodynamic property profiles are then investigated as a function of the system state variables, surface density, gravitational field, and the vibrational frequency and amplitude. A quasi-thermodynamic phase-behaviour of crystallisation equilibria, and also mixing and segregation phenomena in binary systems, are observed. Conditions for granular steady-states to obey laws of corresponding states with small inhomogeneous thermodynamics systems are obtained. The results for a binary system are consistent with the thermodynamic interpretation of recently discovered experimental phase behaviour of binary powders fluidised by acoustic vibrations. The results may be regarded as a step towards a more formal description of various “self-assembly” phenomena of granular colloids, as ordering transitions of quasi-thermodynamic small systems.