Shock structure and temperature overshoot in macroscopic multi-temperature model of mixtures

Abstract

© 2014 AIP Publishing LLC. The paper discusses the shock structure in macroscopic multi-temperature model of gaseous mixtures, recently established within the framework of extended thermodynamics. The study is restricted to weak and moderate shocks in a binary mixture of ideal gases with negligible viscosity and heat conductivity. The model predicts the existence of temperature overshoot of heavier constituent, like more sophisticated approaches, but also puts in evidence its non-monotonic behavior not documented in other studies. This phenomenon is explained as a consequence of weak energy exchange between the constituents, either due to large mass difference, or large rarefaction of the mixture. In the range of small Mach number it is also shown that shock thickness (or equivalently, the inverse of Knudsen number) decreases with the increase of Mach number, as well as when the mixture tends to behave like a single-component gas (small mass difference and/or presence of one constituent in traces).