Bela Myznikova

On the convective instability of a horizontal binary mixture layer with Soret effect under transversal high frequency vibration

Abstract The stability of the mechanical equilibrium of a plane horizontal binary mixture layer with Soret effect in the presence of high frequency transversal vibration is studied. The asymptotic analysis for long-wave disturbances and the numerical solution of the spectral amplitude problem for cellular disturbance has shown that independently of properties of the binary mixture the effect of transversal vibration is always stabilizing. The critical values of Rayleigh number and the characteristics of critical disturbances are determined.

Thermocapillary instability of a liquid layer under heat flux modulation

The parametric excitation of the Marangoni instability in a horizontal liquid layer is analyzed in the case of a heat flux periodically varying at the deformable interface. Two response modes of the convective system to an external periodic stimulation, synchronous and subharmonic ones, have been found. The cellular and long-wave instability thresholds are compared. The neutral stability curves are presented for a variety of external conditions. It is shown that contrary to the classical parametric resonance, the synchronous disturbances may become most dangerous for the stability of the base state, and the long-wave mode may cause the instability prior to the cellular mode within a definite range of parameters.

Evolution of convective patterns in a binary-mixture layer subjected to a periodical change of the gravity field

A theoretical study has been made of the convective stability and developed heat transfer regimes in a horizontal, binary-mixture layer with negative Soret coupling. The system is under temperature gradient and finite-frequency vibration. Both analytical and numerical examinations are presented. The limiting case of long-wave disturbances is studied using the perturbation method. To find instability thresholds in the linear approximation the Floquet theory is applied. The stability borders and characteristics of critical disturbances are determined depending on the vibration frequency for typical gaseous, liquid, and colloidal mixtures. The phase mapping and the Fourier spectra are used to describe the nonlinear evolution of the convective system. It is shown that supercritical flows within the first and second resonance domains develop via soft-mode transitions at critical parameter values which are consistent with the predictions of the linear stability theory. The nonlinear convection patterns demonstr...

On the Soret-Driven Thermosolutal Convection in a Vibrational Field of Arbitrary Frequency

The instability of a plane horizontal layer of an incompressible binary mixture with Soret effect is investigated in the presence of transversal vibrations of arbitrary frequency. The boundaries of the layer are assumed to be rigid, impermeable and isothermal. A linear instability analysis for normal modes is carried out using the Floquet theory. The boundaries of instability and the characteristics of the critical disturbances are determined. In addition to the gravity field modulation, the instability can be associated with quasi-periodic disturbances. It is shown that, depending on the amplitude and frequency of modulation, the vibrations can stabilize an unstable base state or destabilize the equilibrium of the liquid. The limit case of low-frequency modulation of the gravity field is studied.

A model for the heating of slender samples in monoellipsoidal mirror furnaces

The heating and melting of cylindrical slender samples in monoellipsoidal mirror furnaces are studied. A one-dimensional model that includes the radiative exchange between the sample and the mirror is formulated. The temperature dependence of the physical properties of the sample is taken into account in the model. Convection in the melt is not considered. The results obtained with the model are compared with experimental data for silicon and graphite samples.

Parametrical convection of a binary mixture in the modulated gravity field

The convective instability of the incompressible liquid binary mixture, which appears in a plane horizontal layer is investigated in the presence of gravity field modulation (transversal vibrations of arbitrary frequency). The examination is carried out taking into account the effect of the thermal diffusion. To determine the instability thresholds, the Floquet theory is used, which is applied to the linearized equations of convection written under the Boussinesq approximation. At the finite modulation frequency the parametric instability domains can appear. Vibrations can produce or modify the resultant flow behavior under both microgravity and terrestrial conditions.