Hydrodynamics of an inelastic gas with implications for sonochemistry

TL;DR

This paper models the hydrodynamics of an inelastic gas with energy loss during collisions, exploring its effects on shock structures and temperature behavior relevant to sonochemistry.

Contribution

It introduces explicit expressions for transport coefficients and pressure in inelastic gases, and numerically analyzes shock structures influenced by energy loss.

Findings

Maximal temperature is highly sensitive to energy loss parameter .

Shock structures are significantly affected by inelastic collisions.

Temperature minimum occurs near   12,000K, relevant 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 $\Delta \sim 12,000K \sim 1eV$