Combined action of anticonvective and thermocapillary mechanisms of instability in multilayer systems

The nonlinear regimes of convection in the system of three immiscible viscous fluids heated from above are investigated. The interfaces are assumed to be flat. The boundary value problem is solved by the finite-difference method. Transitions between convective motions with different spatial structures are investigated. The common diagram of instability regimes is constructed. The new phenomena caused by direct and indirect interaction of anticonvective and thermocapillary mechanisms of instability are considered. Specifically, different oscillatory configurations where anticonvection arises mainly near the upper interface and thermocapillary convection appears mainly near the lower interface have been found.     

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.     

Flow coupling mechanisms in two-layer Rayleigh–Benard convection

 Rayleigh-Benard convection in two-layer systems is characterized by two distinct modes of flow coupling. These are: thermal coupling and mechanical coupling. Intellegible observations of the temperature field for both coupling mechanisms are provided. The flow coupling mechanisms are experimentally characterized as a function of the contrast in the buoyancy driving forces and in the viscosities of the two layers. Aside from the flow coupling between the layers, flow patterns in each layer, and their corresponding spatial transitions are found to be similar to those reported for single layer convection in rectangular boxes. Received: 7 January 1996/Accepted: 4 February 1997     

Rayleigh-Marangoni-Benard instability in two-layer fluid system

Rayleigh-Marangoni-Bénard instability in a system of two-layer fluids is studied numerically. The convective instabilities in the system of Silicon Oil (10cSt) and Fluorinert (FC70) liquids have been analyzed. The critical parameters at onset of convection are presented in a large range of two-layer depth ratios from 0.2 to 5.0. Numerical results show that the instability of the two-layer system depends strongly on its depth ratio. When the depth ratio increases, the instability mode changes from mechanical coupling to thermal coupling. Between these two typical coupling modes, a time-dependent oscillation is detected. Nevertheless, traveling wave states are found in the case of oscillatory instability. The oscillation mode results from the competition between Rayleigh instability and Marangoni effect. The project supported by the National Natural Science Foundation of China (10372105) and the Knowledge Innovation Program of Chinese Academy of Sciences (KJCX2-SW-L05)     

Onset of thermocapillary convection in a two-layer system with the release of heat at the interface

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 69–73, January–February, 1990.     

环形腔内双层薄液层热毛细对流的渐近解

为了解水平温度梯度作用下环形腔内双层薄液层热毛细对流的基本特性,采用渐近线方法获得了热毛细对流的近似解. 环形腔外壁被加热,内壁被冷却,上、下壁面绝热. 结果表明,当环形腔宽度与内半径比趋于零时,环形腔退化为矩形腔,所得到的主流区速度场和温度场的表达式演化为Nepomnyashchy 等得到的矩形腔内的结果;与数值模拟结果的比较发现,在主流区渐近解与数值解吻合较好.      

Connective instability of a two-layer system with thermally insulated boundaries

The investigation of the convective stability of mechanical equilibrium of two horizontal layers of immiscible fluids has revealed the characteristics of such systems [1–3]. In particular, it has been found that, as distinct from a homogeneous horizontal layer, under certain conditions two-layer systems experience convective instability when uniformly heated from above and, moreover, oscillatory instability when heated from below. In [1–3] the problem was solved for a system with isothermal outer boundaries. In this paper the stability of equilibrium of two-layer systems is investigated for thermally insulated outer boundaries. Special attention is given to the study of the long wave instability mode.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 22–28, March–April, 1986.The authors wish to thank O. V. Kustova for assisting with the computations.     

Convective instability in a two-layer system of reacting fluids with concentration-dependent diffusion

The development of convective instability in a two-layer system of miscible fluids placed in a narrow vertical gap has been studied theoretically and experimentally. The upper and lower layers are formed with aqueous solutions of acid and base, respectively. When the layers are brought into contact, the frontal neutralization reaction begins. We have found experimentally a new type of convective instability, which is characterized by the spatial localization and the periodicity of the structure observed for the first time in the miscible systems. We have tested a number of different acid–base systems and have found a similar patterning there. In our opinion, it may indicate that the discovered effect is of a general nature and should be taken into account in reaction–diffusion–convection problems as another tool with which the reaction can govern the movement of the reacting fluids. We have shown that, at least in one case (aqueous solutions of nitric acid and sodium hydroxide), a new type of instability called as the concentration-dependent diffusion convection is responsible for the onset of the fluid flow. It arises when the diffusion coefficients of species are different and depend on their concentrations. This type of instability can be attributed to a variety of double-diffusion convection. A mathematical model of the new phenomenon has been developed using the system of reaction–diffusion–convection equations written in the Hele–Shaw approximation. It is shown that the instability can be reproduced in the numerical experiment if only one takes into account the concentration dependence of the diffusion coefficients of the reagents. The dynamics of the base state, its linear stability and nonlinear development of the instability are presented. It is also shown that by varying the concentration of acid in the upper layer one can achieve the occurrence of chemo-convective solitary cell in the bulk of an almost immobile fluid. Good agreement between the experimental data and the results of numerical simulations is observed.     

Spurt and instability in a two-layer Johnson-Segalman liquid

The Johnson-Segalman model is an example of a model that exhibits a nonmonotone curve for the shear stress in terms of shear rate. There are many works based on such models for an explanation of the spurt phenomenon but they have concerned the one-dimensional problem. This paper concerns a model problem, taking a one-dimensionally stable spurted solution, viewed in two dimensions. A two-layer arrangement between walls in parallel shear, with a thin layer in the higher shear rate and the bulk of the fluid in the lower shear rate, is examined for linear stability in two dimensions. The spectrum is computed numerically for normal mode solutions. Instabilities with dominant growth rates for short waves are found. Thus, the one-dimensionally stable solutions of this model are actually two-dimensionally unstable.This research was sponsored by ONR Grant No. N00014-92-J-1664 and NSF Grant CTS-9307238.     

Temperature fields in a liquid due to the thermocapillary motion of bubbles and drops

 Experiments were performed on the motion of isolated air bubbles and drops of Fluorinert FC-75 moving in a Dow-Corning silicone oil under the action of an applied temperature gradient in a reduced gravity environment aboard the Space Shuttle in orbit. The disturbance of the imposed temperature field due to the motion of the objects was studied optically using a shearing interferometer with a Wollaston prism and the results of a typical bubble run were compared with theoretical predictions. Also, the liquid velocity field surrounding the bubbles and drops has been qualitatively investigated in a few runs by the observation of tracer particles dispersed in the continuous phase fluid. The measurement techniques are described, and the results for the temperature and flow fields are presented and discussed. Received: 27 June 2000/Accepted: 17 November 2000     

Oscillatory thermocapillary instability of a liquid layer in the presence of a surfactant

The effect of capillarity and a surfactant on the stability of a liquid layer in the presence of a vertical temperature gradient is investigated. It is found that the surfactant leads to the appearance of both monotonic and oscillatory instability, the presence of a surface concentration destabilizing the equilibrium in the case of heating from below. When the free surface is heated, the surfactant stabilizes the capillary instability.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 6–10, January–February, 1993.     

The stability of the motion of a liquid,due to thermocapillary forces

A study is made of the stability of the plane-parallel flow of a viscous liquid in a layer with a free boundary, under weightless conditions. The motion of the liquid is due to the dependence of the surface tension on the temperature. An exact solution for an unperturbed boundary is obtained by the same method used in [1], but with a more general boundary condition for the temperature. A study of the stability was carried out by the method of small vibrations, taking account of the perturbation of the free boundary. The article discusses the asymptotic behavior of long waves at small Reynolds numbers, and the conditions for instability are found.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 94–98, November–December, 1971.     

Interaction of the thermovibrational and thermocapillary convection mechanisms

Thermal convection in microgravity induced by the combined action of thermocapillary forces and vibrations is considered. In the high-frequency approximation the thermovibrational forces are written for the case in which isothermal mixing of the fluid is unimportant. The authors' own work and new results of investigating the effect of vibration on thermocapillary instability, of numerically modeling the heat and mass transfer in open cavities and of experiments on the vibrational suppression of surface deformation are reviewed. The prospects for the practical application of the results obtained are discussed.     

Convective instability of a fluid in two-layer saturated strata

The problem of convective instability of a fluid in a system consisting of two horizontal porous strata with different permeabilities and a permeable common boundary is considered. The problem is investigated in parametric form as a function of the stratum thickness ratio and stratum permeabilities. As distinct from a uniform stratum, in this case the neutral curve can have one or two minima depending on the relationship between the parameters. The case of two minima is characterized by the condition of loss of stability of the fluid in the system as a whole and in the thinner stratum with greater permeability. These minima correspond to significantly different wave numbers. Makhachkala. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 165–169, January–February, 1999.     

Rayleigh instability of a charged viscous drop

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 11–17, September–October, 1991.     

Convection due to the selective absorption of radiation in a porous medium

A model for convection due to the selective absorption of radiation in a fluid saturated porous medium is investigated. The model is based on a similar one introduced for a viscous fluid by Krishnamurti [x]. Employing this adapted model we show the growth rate for the linearised system is real. A linear instability analysis is performed. Global stability thresholds are also found using nonlinear energy theory. An excellent agreement is found between the linear instability and nonlinear stability Rayleigh numbers, so that the region of potential subcritical instabilities is very small, demonstrating that the linear theory accurately emulates the physics of the onset of convection. Received February 10, 2003 / Accepted February 10, 2003/ Published online May 9, 2003 / B. Straughan     

Convection due to the selective absorption of radiation in a porous medium

A model for convection due to the selective absorption of radiation in a fluid saturated porous medium is investigated. The model is based on a similar one introduced for a viscous fluid by Krishnamurti [x]. Employing this adapted model we show the growth rate for the linearised system is real. A linear instability analysis is performed. Global stability thresholds are also found using nonlinear energy theory. An excellent agreement is found between the linear instability and nonlinear stability Rayleigh numbers, so that the region of potential subcritical instabilities is very small, demonstrating that the linear theory accurately emulates the physics of the onset of convectionReceived: 10 February 2003, Accepted: 11 March 2003, Published online: 12 September 2003     

Convection due to the selective absorption of radiation in a porous medium

Continuum Mech. Thermodyn. (2003) 15: 451-462 Digital Object Identifier (DOI) 10.1007/s00161-003-0125-5 Published online September 12, 2003-© Springer-Verlag 2003 Due to a technical error, the present contribution has been published twice in this journal. This article has already appeared in Volume 15 Number 3 (June 2003) and should be cited accordingly. Springer-Verlag wishes to apologize to its customers and readers for this mistake.Published online: 27 Oktober 2003     

Development of the Rayleigh–Taylor instability due to interaction of a diffusion mixing layer of two gases with compression waves

A mathematical model of mechanics of a two-velocity and two-temperature mixture of gases is developed. Based on this model, the evolution of the mixing layer of two gases of different densities, which are accelerated by a compression wave, is considered by methods of numerical simulation. A solution of an initial-boundary problem is obtained in a one-dimensional approximation. This solution describes the formation of a diffusion layer between the two gases. The problem of interaction of this layer with the compression wave, the heavy medium being accelerated by the light medium, is solved numerically. Problems of instability development in a sine-perturbed mixing layer accelerated by a compression wave are solved numerically in a two-dimensional unsteady formulation. The calculated width of the mixing region is in reasonable agreement with experimental data.