Convective instability of the thermovibrational flow of binary mixture in the presence of the Soret effect

Abstract

The convective instability of the thermovibration flow in a plane horizontal layer filled with an incompressible binary gaseous mixture is investigated. The study takes into account the effect of thermal diffusion or the Ludwig-Soret effect. Several instability mechanisms are discussed. To determine the instability threshold with respect to cell and long-wave perturbations, the Floquet theory was applied to the linearized equations of convection formulated in the Boussinesq approximation. We found that regime parametric instability can occur owing to the finite frequency vibrations. The evolution of plane, spiral and three-dimensional disturbances is studied. We demonstrated that, because of the properties of the system, the subharmonic response of plane disturbances to the external periodic action cannot be observed. The instability can be associated only with synchronous or quasiperiodic modes. Depending on the vibration parameters, modulations can stabilize or destabilize the base state. For spiral perturbations the stability boundary does not depend on the amplitude and frequency of vibrations. In the case of long-wave instability we apply the regular perturbation approach with the wavenumber as a small parameter in power expansions. The stability boundaries are found.