On the Relevance of Low-Mach-Number Asymptotics in Thermodynamics of Heterogeneous, Immiscible Mixtures

A conundrum in non-equilibrium thermodynamics of heterogeneous mixtures with microstructure concerns the selection of thermodynamic currents and forces in the entropy production rate from the multitude of available options. The objective of this article is to demonstrate that the low-Mach-number approximation can narrow down this ambiguity. More specifically, by postulating that the post-constitutive equations are well behaved with respect to this perturbation analysis we assert that thermal non-equilibrium should be chosen as an independent force even if this requires the explicit manipulation of the entropy inequality. According to our analysis, alternative choices result in post-constitutive equations; the incompressible limit of which gives rise to questionable predictions.