Thermocapillary instability of a liquid layer in the presence of a soluble surfactant

The effect of capillarity on the stability of a plane layer of viscous heat-conducting liquid in the presence of a soluble surfactant is investigated. It is found that an increase in surfactant solubility has a stabilizing effect on equilibrium. Monotonic instability is the most dangerous mode in the case of long-wave perturbations, whereas in the short-wave region loss of stability is induced by oscillatory perturbations.Krasnoyarsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–8, January–February, 1996.     

Rayleigh-Taylor instability of a thin liquid layer in the presence of three-dimensional perturbations

We consider the evolution of small three-dimensional perturbations of an accelerated thin liquid layer. The analytical solutions obtained correspond to various types of initial perturbations: in the form of a layer, in the initial velocities, and in the thickness of the layer. Depending on the dimensionless parameters which characterize the initial data, the perturbations can increase exponentially with time, remain bounded, and change the phase. Institute of Experimental Physics, Sarov 607200. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 3–9, January–February, 1999.     

Occurrence of thermocapillary convection in a two-layer system in the presence of a soluble surfactant

The present study considers the effect of the solubility of a surfactant on monotonic oscillatory thermocapillary instability of equilibrium in a two-layer system. It is established that with increase in the parameter which characterizes the solubility of the surfactant a reduction takes place in the threshold of the monotonic instability; finally the monotonic perturbations become most dangerous.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–175, March–April, 1988.     

Supercritical thermocapillary convection regimes in a liquid layer “on the ceiling”

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 58–66, March–April, 1994.     

The appearance of thermocapillary convection in the nonmoving layer of a liquid of variable viscosity

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 30, No. 6, pp. 114–119, November–December, 1989.     

Steady thermocapillary motion in a horizontal layer of liquid metal locally heated from above

The article considers stationary thermocapillary convection in a thin horizontal layer of fluid with Prandtl number Pr < 1 when it is being locally heated from above in conditions in which the curvature of the free surface is small. It is shown that the motion has a cellular structure. The size of the convective cell is determined from the solution to the spectral problem to which the integration of the free convection system of equations reduces. If the Maragoni (Péclet) number is sufficiently high, the length of the convective cell turns out to be large in comparison with the thickness of the layer. The convection picture is considered and an expression obtained for the velocity of the developing flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 146–152, November–December, 1984.     

Stability of thermocapillary advective flow in a slowly rotating liquid layer under microgravity conditions

The stability of thermocapillary flow developed in a slowly rotating fluid layer under microgravity conditions is investigated. Both boundaries of the layer are free and assumed to be plane. The tangential thermocapillary Marangoni force exerts on the boundaries, where heat transfer takes place in accordance with the Newton law, the temperature of the medium in the neighborhood of the boundaries being a linear function of the coordinates. The axis of rotation is perpendicular to the liquid layer, rotation is weak so that the centrifugal force can be neglected. Being the solution of the Navier-Stokes equations, the thermocapillary flow in question can be described analytically. The neutral curves which describe the wavenumber dependence of the critical Marangoni number for various Taylor numbers and various directions of the horizontal temperature gradient on the layer boundaries are obtained within the framework of the linear stability theory. The behavior of finite-amplitude perturbations beyond the stability threshold is studied numerically.     

Oscillatory instability of advective flow in a horizontal cylinder in the presence of a rotating magnetic field

The oscillatory instability of advective conducting fluid flow in a horizontal circular cylinder in the presence of a rotating magnetic field is investigated. For Prandtl numbers Pr = 0 and 0.01 calculations showed that in both cases the monotonic instability observed in the absence of a field and in weak fields transforms into oscillatory instability at sufficiently large magnetic Taylor numbers. At Pr ?? 0, oscillatory instability appears at substantially higher magnetic Taylor numbers.     

Orientation instability of the layer of a nematic liquid crystal

The origin of periodic structures in a layer of a lyotropic nematic liquid crystal observed in the director (vector, describing the anisotropic properties of the medium) reorientation experiment is studied. Such perturbations with the wavevector perpendicular to the initial orientation can develop in a liquid crystal layer in the unstable equilibrium state when the director is parallel to the walls under the condition that its orthogonality to the boundary corresponds to the minimum anchoring energy. It is shown that the linear dependence of the domain period on the layer thickness observed experimentally can be theoretically described when the Frank orientation elasticity energy is considered in the most general form taking the divergence terms into account and the anchoring energy of orientation is small as compared with the bulk energy. A relation between the coefficient of the divergence terms (saddlesplay elastic constant) and two other coefficients in the Frank energy is obtained.     

Shock induced Richtmyer-Meshkov instability in the presence of a wall boundary layer

An experimental investigation on gaseous mixing zones originated from the Richtmyer-Meshkov instability has been undertaken in a square cross section shock tube. Mass concentration fields, of one of the two mixing constituents, have been determined within the mixing zone when the shock wave passes from the heavy gas to the light one, from one gas to an other of close density, and from the light gas to the heavy one. Results have been obtained before and after the coming back of the reflected shock wave. The diagnostic method is based on the infrared absorption of one of the two constituents of the mixing zone. It is shown that the mixing zone is strongly deformed by the wall boundary layer. The consequence is the presence of strong gradients of concentration in the direction perpendicular to the shock wave propagation. Finally, it is pointed out that the mixing goes more homogeneous when the Atwood number tends to zero.     

Stability of thermocapillary motion in a cylindrical layer

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 50–52, July–August, 1989.     

Growth rates of the Marangoni instability in a layer of elastic liquid

The problem of thermocapillary (Marangoni) convection in a layer of viscoelastic liquid is considered. The stability boundary for this problem has been previously calculated in various cases by a number of authors. Here attention is fixed on the magnitude of the growth rate in the parameter regime corresponding to instability. Two noteworthy features are pointed out. First, there are anomalously large values of the growth rate at or near the limiting special case of a Maxwell fluid. Second, the complex values of the growth rate (corresponding to overstability, or the onset of instability via oscillatory motion) coalesce into real (positive) values at moderately supercritical values of the Marangoni number, suggesting that overstability might be elusive to observation.     

Orientational instability of a lyotropic nematic liquid crystal layer

The problem of periodic domain initiation in a thin lyotropic nematic liquid crystal layer is studied. This layer has a planar director initial orientation, but the anchoring energy is minimized by the homeotropic one. The periodic structures whose wave vector is perpendicular to the director exist during the director reorientation process from the planar orientation to the homeotropic one when the reorientation wave front appears. It is shown that the divergent terms of the Prank orientation elasticity energy plays an important role in this effect. The saddle-splay Prank constant and the anisotropic anchoring energy coefficient are estimated.     

Numerical modeling of thermocapillary convection in a liquid layer with a nonlinear dependence of the surface tension on temperature

The principal characteristics of thermocapillary convection in a rectangular channel with one of the boundaries heated to a temperature higher and the other to a temperature lower than T₀ are investigated numerically on the basis of the Navier-Stokes equations. Certain convection characteristics corresponding to normal and anomalous thermocapillary effects are qualitatively compared. The conditions under which self-similar solutions of the type obtained in [10] can be used to describe the flow in a bounded region are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 138–143, January–February, 1991.     

Nonlinear instability of a liquid jet in the presence of a uniform electric field

The nonlinear electrohydrodynamic stability of an irrotational jet in the presence of capillary force and weak viscous stress on the surface has been studied. Two nonlinear modified Schrödinger equations are obtained. Neglecting the viscous stress, the classic Schrödinger equations are obtained. The stability conditions of steady state solutions are investigated, using the modulation concept. It is found that the viscous stress produces a resonance (say a viscous resonance) away from the critical point. For the progressive waves, we obtained modified transition curves inserting the viscous stress. The classic nonlinear cutoff wave number is obtained and this means that the viscous stress has a fluctuating effect on the perturbed jet, away from the critical points.     

Thermocapillary instability of a liquid layer with allowance for the soret effect

The effect of thermodiffusion on the onset of thermocapillary instability in the presence of a surfactant is investigated with reference to a plane liquid layer. It is shown that taking the Soret effect into account leads to destabilization in the case of heating of both the rigid surface and the free boundary. Krasnoyarsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 2000.     

Convective instability in a rapidly rotating fluid layer in the presence of a non-uniform magnetic field

Magnetoconvective instabilities in a rapidly rotating, electrically conducting fluid layer heated from below in the presence of a non-uniform, horizontal magnetic field are investigated. It was first shown by Chandrasekhar that an overall minimum of the Rayleigh number may be reached at the onset of magnetoconvection when a uniform basic magnetic field is imposed. In this paper, we show that the properties of instability can be quite different when a non-uniform basic magnetic field is applied. It is shown that there is an optimum value of the Elsasser number provided that the basic magnetic field is a monotonically decreasing or increasing function of the vertical coordinate. However, there exist no optimum values of the Elsasser number that can give rise to an overall minimum of the Rayleigh number at the onset of magnetoconvection if the imposed basic magnetic field has an inflexion point. The project supported by the National Natural Science Foundation of China (40174026 and 40074041)