On interplay of surface tension and inertial stabilization mechanisms in the stable and unstable interface dynamics with the interfacial mass flux

Non-equilibrium dynamics of interfaces and mixing are omnipresent in fluids, plasmas and materials, in nature and technology, at astrophysical and at molecular scales. This work investigates dynamics of an interface separating fluids of different densities and having interfacial mass flux, and being influenced by the acceleration and the surface tension. We derive solutions for the interface dynamics conserving mass, momentum and energy, find the critical acceleration values separating stable and unstable regimes, and reveal the macroscopic inertial mechanism as primary mechanism of the interface stabilization. We show that while the surface tension influences only the interface, its presence leads to formation of vortical structures in the bulk. For large accelerations the conservative dynamics is unstable, leading to the growth of interface perturbations and the growth of the interface velocity. This new instability can be unambiguously discerned from other instabilities; for strong accelerations it has the fastest growth-rate and the largest stabilizing surface tension value when compared to Landau-Darrieus and Rayleigh-Taylor instabilities. We further find the values of initial perturbation wavelengths at which the conservative dynamics can be stabilized and at which it has the fastest growth. Our results agree with existing observations, identify extensive theory benchmarks for future experiments and simulations, and outline perspectives for application problems in nature and technology.