On vibrational convective instability of a horizontal binary mixture layer with Soret effect

Abstract

The stability of the mechanical equilibrium of a plane horizontal binary mixture layer with Soret effect in the presence of a static gravity field and high frequency vibration is studied theoretically. The horizontal boundaries of the layer are assumed to be rigid, isothermal and impermeable. A linear theory of stability is developed. The instability boundary and characteristics of the critical disturbances are determined.

Convective Instability of the Flow of a Binary Mixture under Conditions of Vibration and Thermal Diffusion

“…In microgravity (Gr = 0), the binary mixture is unstable to cellular vibrational perturbations (dashed curves). In this particular case, monotonic perturbations are less dangerous, as was demonstrated in [7]. An increase in the Grashof number initiates origination of a thermal gravitational flow: interaction of vibrational and hydrodynamic modes of instability increases the thresholds of vibrational convection; simultaneously, the boundary of the monotonic mode decreases.…”

“…The theory of convection of binary mixtures employs the Boussinesq approximation with allowance for dissipative processes of diffusion and thermal diffusion [6]. Instability of the binary mixture filling a plane horizontal channel bounded by rigid impermeable walls and possessing thermal diffusion in the field of longitudinal vibrations was considered in [7,8].In the present work, we study the vibrational convective instability of an upward-downward flow of an incompressible binary mixture with thermal diffusion in a vertical layer in the presence of longitudinal high-frequency harmonic vibrations.Formulation of the Problem. We consider a binary mixture of nonreacting components, which fills the space between vertical solid plane-parallel planes x = ±h (vertical layer).…”

“…The theory of convection of binary mixtures employs the Boussinesq approximation with allowance for dissipative processes of diffusion and thermal diffusion [6]. Instability of the binary mixture filling a plane horizontal channel bounded by rigid impermeable walls and possessing thermal diffusion in the field of longitudinal vibrations was considered in [7,8].…”

“…The condition of impermeability for the flux of matter at the boundaries of the layer of the binary fluid leads to long-wave instability (k = 0). We write the solution of the amplitude problem (7) in the form of series in terms of the small parameter k:…”

“…2) In the absence of gravity (Gr = 0 and Ra v = 0), the threshold of the long-wave mode of a thermal vibrational flow [7] is determined by the condition…”