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This work focuses on the interfacial dynamics with interfacial mass flux inthe presence of acceleration and surface tension. We employ the general matrixmethod to find the fundamental solutions for the linearized boundary valueproblem conserving mass, momentum and energy. We find that the dynamics can bestable or unstable depending on the values of the acceleration, the surfacetension and the density ratio. In the stable regime, the flow has thenon-perturbed fields in the bulk, is shear-free at the interface, and has theconstant interface velocity. The dynamics is unstable only when it isaccelerated, and when the acceleration value exceeds a threshold combiningcontributions of the inertial stabilization mechanism and the surface tension.The properties of this instability unambiguously differentiate it from otherfluid instabilities. Particularly, its velocity field has potential andvortical components in the bulk and is shear free at the interface. Itsdynamics describes the standing wave with the growing amplitude, and has thegrowing interface velocity. For strong accelerations, this fluid instability ofthe conservative dynamics has the fastest growth-rate and the largeststabilizing surface tension value when compared to the classical Landau andRayleigh-Taylor dynamics. We find the values of the initial perturbationwavelength at which the fluid instability can be stabilized and at which it hasthe fastest growth. We identify theory benchmarks for experiments andsimulations in high energy density plasmas and its outcomes for applicationproblems in nature and technology.

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