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

Abstract

This work focuses on the interfacial dynamics with interfacial mass flux in the presence of acceleration and surface tension. We employ the general matrix method to find the fundamental solutions for the linearized boundary value problem conserving mass, momentum and energy. We find that the dynamics can be stable or unstable depending on the values of the acceleration, the surface tension and the density ratio. In the stable regime, the flow has the non-perturbed fields in the bulk, is shear-free at the interface, and has the constant interface velocity. The dynamics is unstable only when it is accelerated, and when the acceleration value exceeds a threshold combining contributions of the inertial stabilization mechanism and the surface tension. The properties of this instability unambiguously differentiate it from other fluid instabilities. Particularly, its velocity field has potential and vortical components in the bulk and is shear free at the interface. Its dynamics describes the standing wave with the growing amplitude, and has the growing interface velocity. For strong accelerations, this fluid instability of the conservative dynamics has the fastest growth-rate and the largest stabilizing surface tension value when compared to the classical Landau's and Rayleigh-Taylor dynamics. We find the values of the initial perturbation wavelength at which the fluid instability can be stabilized and at which it has the fastest growth. We identify theory benchmarks for experiments and simulations in high energy density plasmas and its outcomes for application problems in nature and technology.

Interface dynamics and flow fields’ structure under thermal heat flux, thermal conductivity, destabilizing acceleration and inertial stabilization

“…(3) In each regime, solutions 3(4) depend only on density ratio R and are the same as those of the conservative dynamics with zero thermal heat flux in ideal fluids [17,[28][29][30][31]. Particularly: solution 3 has zero perturbed velocity and pressure fields; solution 4 must have zero integration constant to obey the boundary conditions far from interface [17,[28][29][30][31]73]. We omit their consideration here.…”

“…Theory [17,[28][29][30] studied the dynamics of the interface with interfacial mass flux for ideal incompressible fluids free from thermal heat flux. It also analyzed the effect of surface tension understood as tension at the phase boundary [31,73]. Realistic processes are often accompanied by fluxes of thermal heat across the interface and by non-ideal thermodynamics in the bulk, including thermal conductivity caused by inelastic interactions of particles at atomic scales [14,15,17].…”