Inertial dynamics of an interface with interfacial mass flux: Stability and flow fields’ structure, inertial stabilization mechanism, degeneracy of Landau’s solution, effect of energy fluctuations, and chemistry-induced instabilities

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.

Specific heat effects in two-dimensional shock refractions

“…The mixing-layer thickness variations would imply non-ideal flow modifications to the pictures described in the shock refraction problem, altering the local properties at the tangential discontinuities and introducing a characteristic length scale. Moreover, a detailed study of interfacial transport and mixing within the multi-species reacting shear layer that may be subject to multiple shocks interactions, transport of species and radiation, calls for multi-scale modelization coupling kinetic to meso-and macroscopic dynamics [59,60]. Nevertheless, the numerical analysis of complete turbulent, viscous and diffusive flows is out of the scope of this work, which serves to a prior understanding of the thermallyperfect considerations in shock refractions of high speed flows.…”

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

“…Particularly, group theory approach grasped the order in Rayleigh-Taylor mixing and explained the observations [11,19,[21][22][23][24][25][26][27]. For interfaces with interfacial mass flux, a rigorous theory of the interface stability was developed recently for ideal fluids [17,[28][29][30]. This theory discovered the inertial mechanism of interface stabilization, the instability of the conservative dynamics of accelerated interface, and the chemistry-induced instabilities [17,[28][29][30].…”

“…For interfaces with interfacial mass flux, a rigorous theory of the interface stability was developed recently for ideal fluids [17,[28][29][30]. This theory discovered the inertial mechanism of interface stabilization, the instability of the conservative dynamics of accelerated interface, and the chemistry-induced instabilities [17,[28][29][30]. It also resolved the prospect of Landau 1944 and found that classical Landau's solution for Landau-Darrieus instability is a perfect mathematical match [16,17].…”

“…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].…”

“…Interfaces with interfacial fluxes of heat and mass are essential in the processes of the atomization of liquid jets and the fluid vaporization [45][46][47], in the melting and evaporation of materials under high pressures and high strain rates, and in chemically reactive flows [7,9,28,48]. A good grip on the interface dynamics is needed for efficient purification of water and for enabling the transportation security of liquefied natural gas [20,49].…”