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.     

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.     

Thermocapillary instability of the equilibrium of a flat layer containing internal heat sources

In the absence of body forces, a factor which has a strong influence on the equilibrium stability of a nonuniformly heated liquid is the dependence of the coefficient of surface tension on the temperature and the thermocapillary effect generated by it. If the equilibrium temperature gradient is sufficiently great, then the presence of the thermocapillary forces on the free surface can lead to the occurrence of convective motion. The monotonie instability of the equilibrium of a flat layer was investigated in [1–3]. Analysis of nonmonotonic disturbances [4] showed that in the case of an undeformable free surface there is no oscillatory instability. In [5] it was found that oscillatory instability is possible if there is a nonlinear dependence of the coefficient of surface tension on the temperature. The present paper is devoted to numerical investigation of the equilibrium stability of a flat layer with respect to arbitrary disturbances. It is shown that for a deformable free boundary there appears an additional neutral curve, which corresponds to monotonie capillary instability. In addition, when the capillary convection mechanism is taken into account, there appears an oscillatory instability, which becomes the most dangerous in the region of small Prandtl and wave numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 27–31, March–April, 1991.I thank V. K. Andreev for a helpful discussion of the work.     

Thermocapillary convection in two-layer systems in the presence of a surface active agent at the interface

Convective instability in a layered system due to the thermocapillary effect was investigated in [1–5]. In these studies it was shown that the perturbations responsible for equilibrium crisis may build up either monotonically or in an oscillatory fashion. In [6] the stabilizing effect of a surface active agent (SAA) on thermocapillary instability was established for a layer with a free surface. For layers of infinite thickness the effect of SAA on thermocapillary convection was studied in [7–9]. The present investigation is concerned with thermocapillary convection in a system of two layers of finite thickness in the presence of an SAA. Convection due to the lift force is not considered. It is established that the principal result of the action of the SAA is not the stabilizing effect on the monotonic mode but the appearance of a new type of oscillatory instability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2 pp. 3–8, March–April, 1986.In conclusion the authors wish to thank E. M. Zhukhovitskii for discussind the results.     

Drift of a reacting droplet due to the chemoconcentration capillary effect

The motion of a droplet with a first-order chemical reaction taking place at its surface with the participation of a surfactant dissolved in the external medium is considered. Approximate expressions are obtained for the velocity and other characteristics of the autonomous motion of the droplet caused by the surface capillary forces due to the nonuniform distribution of the surfactant over the surface of the moving droplet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 51–61, May–June, 1990.     

Convection in a two-layer system due to the combined action of the Rayleigh and thermocapillary instability mechanisms

In a two-layer system loss of stability may be monotonic or oscillatory in character. Increasing oscillatory perturbations have been detected in the case of both Rayleigh [1, 2] and thermocapillary convection [3–5]; however, for many systems the minimum of the neutral curve corresponds to monotonic perturbations. In [5] an example was given of a system for which oscillatory instability is most dangerous when the thermogravitational and thermocapillary instability mechanisms are simultaneously operative. In this paper the occurrence of convection in a two-layer system due to the combined action of the Rayleigh (volume) and thermocapillary (surface) instability mechanisms is systematically investigated. It is shown that when the Rayleigh mechanism operates primarily in the upper layer of fluid, in the presence of a thermocapillary effect oscillatory instability may be the more dangerous. If thermogravitational convection is excited in the lower layer of fluid, the instability will be monotonic.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 166–170, January–February, 1987.     

Laminar boundary layer stability and delayed transition on a nonisothermal surface

The effect of a nonuniform surface temperature distribution on the boundary layer stability characteristics is further investigated. It is shown that the presence of fairly extensive areas of the surface within which the temperature of the body exceeds the free-stream temperature leads to the destabilization of the flow and the appearance of a local closed region of laminar flow instability.Paper presented at the Sixth All-Union Conference on Theoretical and Applied Mechanics (Tashkent, 1986). The results of references [8, 9], published after the conference, have been taken into account.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 52–57, March–April, 1989.     

Instability of a compound liquid jet

In the linear Rayleigh theory [1] the degree of stability of a jet is determined by the viscosity and inertia characteristics of the fluids and the interphase surface tension. The stability of a jet in an infinite medium increases with increase in the viscosity of both the jet and the medium [2, 3]. The presence of two interfaces is responsible for various features of the development of instability in a liquid layer on the surface of a cylinder, and in particular a layer on the inner surface of a cylinder is more unstable than one on the outer surface [4]. In [5, 6] the breakup of a hollow jet in an external medium was investigated. In this paper we examine, in the linear approximation, the stability of a compound jet of nonmiscible liquids with respect to small axisynmetric perturbations of the interfaces. The instability characteristics are given for jets with inviscid and very viscous outer shells. The conditions governing the suppression of rapidly growing instabilities of the inner part (core) of the jet by a viscous shell are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–8, July–August, 1985.     

Stability of stationary convective flow of a mixture in a vertical porous layer

In contrast to the corresponding viscous flow, the convective flow of a homogeneous liquid in a planar vertical layer whose boundaries are maintained at different temperatures is stable [1]. When a porous layer is saturated with a binary mixture, in the presence of potentially stable stratification one must expect an instability of thermal-concentration nature to be manifested. This instability mechanism is associated with the difference between the temperature and concentration relaxation times, which leads to a buoyancy force when an element of the fluid is displaced horizontally. In viscous binary mixtures, the thermal-concentration instability is the origin of the formation of layered flows, which have been studied in detail in recent years [2–4]. The convective instability of the equilibrium of a binary mixture in a porous medium was considered earlier by the present authors in [5]. In the present paper, the stability of stationary convective flow of a binary mixture in a planar vertical porous layer is studied. It is shown that in the presence of sufficient longitudinal stratification the flow becomes unstable against thermal-concentration perturbations; the stability boundary is determined as a function of the parameters of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–157, January–February, 1980.     

Thermocapillary instability of a plane layer with a vertical temperature gradient

The oscillating disturbances in a plane layer with a temperature gradient are analyzed. It is shown that for heating from below taking the deformability of the free surface into account leads to the appearance of short-wave oscillatory instability, which becomes the most dangerous mode. Moreover, the interaction of the capillary and thermocapillary instability mechanisms results in the appearance of oscillating disturbances of a new type, which lead to equilibrium crisis at high Marangoni numbers. It is established that when the free boundary is heated, the onset of convection is possible only with respect to oscillatory disturbances.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 19–23, May–June, 1992.     

Investigation of the azimuthal instability of the surface of a liquid phase in a melting channel

The instability of the molten metal layer on the walls of a melting channel is considered. A dispersion relation for small azimuthal perturbations of the free surface of the melt is obtained and investigated numerically. It is shown that the onset of azimuthal, monotonically increasing deformations of the surface is possible. The characteristics and conditions of onset of the deformations are determined.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 21–27, July–August, 1996.     

Instability of monochromatic waves on the surface of a liquid of arbitrary depth

A study is made of the stability, with respect to the spontaneous appearance of modulation, of steady periodic waves of small amplitude on the surface of an ideal liquid depth. The well-known instability of waves on the surface of a liquid of infinite depth disappears on making the transition to small depths.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 45–49, September–October, 1970.     

Motion of the surface separating two liquids of finite depth under the influence of variable force fields

We consider the motion of the surface separating two liquids in a nonstationary gravitational field or, equivalently, under the action of a variable acceleration (an overload) perpendicular to the surface. Conditions are derived for the instability of the surface separating two liquids of finite depth in periodic, constant, and impulsive force fields; the physical mechanism acting during the development of instability is studied, and some features of the onset of instability are investigated for the case in which the space is bounded.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 55–62, September–October, 1970.     

Onset of convection due to heating from above and heat release at an interface

A specific non-Rayleigh mechanism of convective instability in systems with an interface, developing in the presence of heating from above (anticonvection), was identified in [1, 2]. The onset of this type of instability requires a sharp difference in the physical parameters of the fluids. The effect of heat release and heat absorption on the onset of convection in systems for which this instability mechanism is possible is examined. In the presence of surface heat sources the directions of the temperature gradients in the two media may be different. The interaction of Rayleigh and non-Rayleigh types of instability is investigated. It is shown that for the water-mercury system on a certain interval of the parameters the oscillatory mode of instability is the most dangerous.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 16–20, May–June, 1990.     

Absolute instability of an interface between two magnetic fluids in the presence of a tangential velocity discontinuity and an external magnetic field

The nature of the instability of the surface of a tangential velocity discontinuity between two incompressible, inviscid, capillary, nonconducting, linearly magnetizable fluids in an external magnetic field is considered. An absolute instability criterion is obtained in analytic form. When the gravity force is negligible, this criterion does not depend on the value of the surface tension. When the surface tension is negligible, the absolute instability criterion is obtained for the region of the flow parameters in which the causality condition for the system in question is satisfied. If the magnetic field is tangential to the interface, all the criteria obtained are also applicable to the case of nonmagnetic, perfectly conducting fluids, i.e., to the case of ideal magnetohydrodynamics.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 21–26, September–October, 1995.     

Development of two-dimensional perturbations on the surface of a tangential discontinuity

A study is made of the asymptotic behavior at long times of initially localized small two-dimensional perturbations of the interface of two fluids in the presence of a tangential discontinuity of the velocity; surface tension is taken into account. The development of one-dimensional perturbations was considered earlier in [1]. The asymptotic behavior of the perturbed region is found, i.e., in the xyt space there is found a cone with apex at the origin such that perturbations tend to infinity with increasing t along rays within the cone, while perturbations tend to zero along the remaining rays. Conditions are found under which the instability of the tangential discontinuity is not absolute, i.e., when these conditions are satisfied, flows with tangential discontinuity of the velocity can take place. These conditions, like the shape of the cone, do not depend on the magnitude of the surface tension.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 12–16, May–June, 1979.     

Effect of an insoluble surfactant film on the stability of the concentration-driven Marangoni flow

The stability and the structure of the concentration and capillary driven Marangoni flow from a localized source is experimentally investigated in the presence of an adsorbed layer of an insoluble surfactant. It is found that the presence of the surfactant on the interface leads to the instability of the main axisymmetric flow with the result that a secondary azimuthally-periodic flow with a multivortex structure is developed. The structure of the convective motion on the interface is studied as a function of the Marangoni flow intensity and the surface density of the surfactant. The azimuthal wavenumber is shown to increase with the Marangoni number and to decrease with increase in the surface density of the surfactant. It is established that there exists a threshold value of the surface density of the surfactant at which the surface flow does not occur.     

Onset of oscillatory thermocapillary convection in systems with a deformable interface

Oscillatory interfacial instability is investigated with allowance for the deformation of the interface. The possibility of two types of oscillations being excited is established. One of these is similar to the well-known type in systems with a plane interface, while the other is determined by the oscillations of the deformable surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 11–16, July–August, 1991.     

Stability of a plane-parallel convective flow of a liquid in a horizontal layer

We consider the stationary plane-parallel convective flow, studied in [1], which appears in a two-dimensional horizontal layer of a liquid in the presence of a longitudinal temperature gradient. In the present paper we examine the stability of this flow relative to small perturbations. To solve the spectral amplitude problem and to determine the stability boundaries we apply a version of the Galerkin method, which was used earlier for studying the stability of convective flows in vertical and inclined layers in the presence of a transverse temperature difference or of internal heat sources (see [2]). A horizontal plane-parallel flow is found to be unstable relative to two critical modes of perturbations. For small Prandtl numbers the instability has a hydrodynamic character and is associated with the development of vortices on the boundary of counterflows. For moderate and for large Prandtl numbers the instability has a Rayleigh character and is due to a thermal stratification arising in the stationary flow.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 95–100, January–February, 1974.     

Generation of Nonlinear Waves on a Viscoelastic Coating in a Turbulent Boundary Layer

Self–induced excitation of periodic nonlinear waves on a viscoelastic coating interacting with a turbulent boundary layer of an incompressible flow is studied. The response of the flow to multiwave excitation of the coating surface is determined in the approximation of small slopes. A system of equations is obtained for complex amplitudes of multiple harmonics of a slow (divergent) wave resulting from the development of hydroelastic instability on a coating with large losses. It is shown that three–wave resonant relations between the harmonics lead to the development of explosive instability, which is stabilized due to the deformation of the mean (Sover the wave period) shear flow in the boundary layer. Conditions of soft and hard excitation of divergent waves are determined. Based on the calculations performed, qualitative features of excitation of divergent waves in known experiments are explained.