Boris L. Smorodin

Convective instability of magnetized ferrofluids

Abstract Convective instability in a flat ferrofluid layer subject to a transverse uniform magnetic field is investigated theoretically. A temperature gradient imposed across the layer induces a concentration gradient of magnetic grains owing to the Soret effect. Both these gradients cause a spatial variation in magnetization that establishes a gradient of magnetic field intensity within the fluid layer. The field gradient induces in its turn a redistribution of magnetic grains due to magnetophoresis. The resulting self-consistent magnetic force tries to mix the fluid. Linear analysis performed for the case of realistic boundary conditions on confined horizontal planes predicts double-diffusive oscillatory instability in a certain region of parameters, whereas if the particle diffusion had been not operative, then only stationary instability would occur.

The onset of thermomagnetic convection in stratified ferrofluids

A non-uniform magnetic field causes an inhomogeneous distribution of magnetic grains in colloidal magnetics (so-called ferrofluids). The rate of concentration equilibrium settling is very low owing to the smallness of the particle diffusion coefficient. Therefore, if the equilibrium does not have enough time to settle, a ferrofluid behaves like a pure fluid, so that stationary convection occurs and no other. In the opposite case, that is when some non-uniform concentration profile has been formed, an oscillatory instability arises. The latter can be effectively excited under the action of a low-amplitude time-periodic magnetic field of an appropriate frequency.

On the parametric excitation of electrothermal instability in a dielectric liquid layer using an alternating electric field

Abstract The onset of electrothermal convective instability of a liquid dielectric subjected to an unsteady electric field is studied in the EHD approximation, when charge formation is produced only due to dielectrophoresis. Convective thresholds are found in two different cases: (i) instability of the liquid equilibrium in a horizontal layer, and (ii) instability of the liquid flow in a vertical layer. The stability boundaries are obtained when there is interaction of dielectrophoretic and gravitational forces. Stability plots of electrical Rayleigh number versus thermal Rayleigh number are given. We show that only synchronous response to variations of the external electric field of finite frequency exists when heating a horizontal layer from above. Quasiperiodic response to the external alternating action is possible in the case of a vertical layer. The influence of the Prandtl number on the stability thresholds is also examined. The asymptotic behavior of the critical parameters in the limiting case of low-frequency modulation is studied using the Wentzel–Kramers–Brillouin method.

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.

Electrothermoconvective instability of an ohmic liquid layer in an unsteady electric field

Abstract The electrothermoconvective instability of a plane horizontal layer of a poorly conducting, ohmic liquid subjected to a varying electric field is investigated in the EHD approximation, when the charge formation is produced by electroconduction. First, the spatio-temporal distributions of the electric field, charge and temperature are found for the quasiequilibrium base state. Then Floquet theory is applied for finding various instability thresholds in the linear approximation with and without the effect of buoyancy. The influence of a time-dependent electric field modulation on the behavior of the liquid layer is studied with and without an additional steady component. The limit of low-frequency electric field modulation is also studied. We show that, depending on the amplitude and frequency of modulation, the electric field can stabilize an unstable base state or destabilize the equilibrium of the liquid. Besides synchronous and subharmonic responses to variations of the external electric field, the instability can be associated with two-frequency quasiperiodic disturbances. The stability maps of (thermal) Rayleigh number versus electrical Rayleigh number found, illustrate the interplay between thermoconvection and electroconvection.

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.

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

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.

Long-scale nonlinear evolution of parametrically excited Marangoni convection

We consider a horizontal liquid layer with a deformable free upper surface heated from below so that on the bottom the heat flux is periodically changing and the averaged temperature of the layer equals zero. A set of nonlinear evolution equations is derived for the description of the spatiotemporal dynamics of the long-wave Marangoni instability. A bifurcation analysis near the threshold of the convection onset shows the existence of the subcritical as well as supercritical type of bifurcations. The region of supercritical bifurcation regime is found. The evolution equation for the surface deviation in the form of the well-known Cahn-Hilliard equation is obtained in the vicinity of the critical value of the Marangoni number.

Convection of a colloidal suspension in a Hele-Shaw cell

Abstract.The results of a theoretical study are presented dealing with convective heat and mass transfer in a colloidal suspension through a Hele-Shaw cell heated from below. The numerical analysis, based on a multi-component model, reveals that for a certain range of parameter values the dynamical regimes of travelling waves as well as oscillatory fingering formation are stable. The bifurcation phenomena and nonlinear evolution of spatiotemporal patterns that develop in the colloid suspension are modeled and discussed, paying special attention to the combined effects of gravity sedimentation, thermal diffusion with positive separation ratio and convection.Graphical abstract