Hydrodynamics of an endothermic gas with application to bubble cavitation.
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 energy 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 approximately 12,000 K approximately 1 eV.
Lutsko
James F
JF
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, C.P. 231, Boulevard du Triomphe, 1050 Brussels, Belgium. jlutsko@ulb.ac.be