Hydrodynamics of an endothermic gas with application to bubble cavitation
James F. Lutsko, "Hydrodynamics of an endothermic gas with application to bubble cavitation", J. of Chemical Physics, 125, 164319 (2006) http://jimlutsko.github.io/files/Lutsko_JCP_2006.pdf
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 occurring near the physically important value of Delta 12 000 K 1 eV.