Hydrodynamics of an inelastic gas with implications for sonochemistry

Abstract

The hydrodynamics for a gas of hard-spheres which sometimes experience inelastic collisions resulting in the loss of a fixed, velocity-independent, amount of energy $\Delta$ is investigated with the goal of understanding the coupling between hydrodynamics and endothermic chemistry. The homogeneous cooling state of a uniform system and the modified Navier-Stokes equations are discussed and explicit expressions given for the pressure, cooling rates and all transport coefficients for D-dimensions. The Navier-Stokes equations are solved numerically for the case of a two-dimensional gas subject to a circular piston so as to illustrate the effects of the enegy loss on the structure of shocks found in cavitating bubbles. It is found that the maximal temperature achieved is a sensitive function of $\Delta$ with a minimum occuring near the physically important value of $\Delta \sim 12,000K\sim 1eV$

35 pages, 9 figures

References in corpus (3)

• The Inelastic Maxwell Model
• Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
• Kinetic Theory and Hydrodynamics of Dense, Reacting Fluids far from Equilibrium