Dalton's and Amagat's laws fail in gas mixtures with shock propagation

Abstract

As a shock wave propagates through a gas mixture, pressure, temperature, and density increase across the shock front. Rankine-Hugoniot (R-H) relations quantify these changes, correlating post-shock quantities with upstream conditions (pre-shock) and incident shock Mach number [1-5]. These equations describe a calorically perfect gas, but deliver a good approximation for real gases, provided the upstream conditions are well-characterized with a thermodynamic mixing model. Two classic thermodynamic models of gas mixtures are Dalton's law of partial pressures and Amagat's law of partial volumes [6]. Here we show that neither thermodynamic model can accurately predict the post-shock quantities of interest (temperature and pressure), on time scales much longer than those associated with the shock front passage, due to their implicit assumptions about behavior on the molecular level, including mixing reversibility. We found that in non-reacting binary mixtures of sulfur hexafluoride (SF6) and helium (He), kinetic molecular theory (KMT) can be used to quantify the discrepancies found between theoretical and experimental values for post-shock pressure and temperature. Our results demonstrate the complexity of analyzing shock wave interaction with two highly disparate gases, while also providing starting points for future theoretical and experimental work and validation of numerical simulations.