Interface dynamics with heat and mass fluxes

Unstable interfaces ubiquitously occur in fluids, plasmas and materials, from the celestial event of supernova to the atomic level of plasma fusion. Knowledge of their fundamentals is in demand in science, mathematics, and engineering. Our work considers the classical problem of stability of a phase boundary having heat and mass fluxes across it and yields a rigorous theory resolving challenges not addressed before. By employing self-consistent boundary conditions for thermal heat flux, by identifying the perturbation waves' structure, and by thoroughly investigating the dependence of waves' coupling on system parameters, we discover new fluid instabilities in the advection, diffusion and low Mach regimes. We find that the interface stability is set primarily by the interplay of macroscopic inertial stabilization with destabilizing acceleration, and the microscopic thermodynamics and thermal heat flux creates vortical fields in the bulk.