Convective structures in a thin layer of an evaporating liquid under an airflow

Evolution of convective structures in a thin layer of an evaporating liquid (ethanol) located under a turbulent boundary layer of an airflow is studied experimentally and theoretically. Evolution of the structures is examined under conditions of an increased flow velocity. A transition is found from convective cells formed in the absence of the flow to convective rolls elongated in the streamwise direction. The theoretical analysis is performed within a two-dimensional model of the flow in the liquid layer. The boundary conditions on the liquid surface are obtained with the use of self-similar solutions for mean fields in the airflow. The onset and evolution of a periodic system of rolls are simulated numerically. Theoretical conclusions are compared with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 3–14, July–August, 2007.     

Effect of a latitudinal temperature gradient on convective motions arising in a rotating spherical layer

The hydrodynamics of planetary atmospheres and Interiors are frequently directly or indirectly connected with convective motions taking place in rotating liquid spherical layers in the field of a central force. Convective stability in a spherical layer at rest, in a central gravity field, was first discussed in [1, 2]. It was shown that the critical Rayleigh number Rao at which convective instability sets in and the wave number of the critical perturbations depend essentially on the thickness of the layer. As in the plane case, the problem of the convective stability of a spherical layer is found to be degenerate, and the form of the critical perturbations cannot be determined from the linear problem. In actuality, minimization of the Rayleigh number permits establishing only the wave numberl for the spherical harmonic Y _l ^m (θ, ?), realized at the limit of stability; the parameter m remains indeterminate and thus 2l+1 independent convective modes correspond to Rao. In [3] a study was made of the convective stability of a liquid in a slowly rotating thin spherical layer. It was shown that the presence of rotation eliminates the degeneracy; at the limit of stability there arise motions corresponding to the Y _l l (θ, ?) -harmonic with a degenerate maximum at the equator, and propagating in a wave manner toward the side opposite to the rotation. In the present work a study is made of the convective stability of a flow of liquid, arising in a rotating spherical layer due to a nonuniform distribution of the temperatures at one of the boundaries of the layer. In such a statement of the problem it is possible to model large-scale motions in the atmospheres of large planets having internal sources of heat and absorbing solar radiation near the cloud cover of the atmosphere. It is established that, depending on the relationships between the parameters imparting the rotation and the inhomogeneous distribution of the temperature, there is either stabilization or destabilization of the layer in comparison with a fixed layer of the same thickness and with the same, but uniformly distributed heat flux supplied to the layer. A study is made of the form of the corresponding critical perturbations.     

Linear stability analysis of convection in two-layer system with an evaporating vapor-liquid interface

Classical theories have successfully provided an explanation for convection in a liquid layer heated from below without evaporation. However, these theories are inadequate to account for the convective instabilities in an evaporating liquid layer, especially in the case when it is cooled from below. In the present paper, we study the onset of Marangoni convection in a liquid layer being overlain by a vapor layer. A new two-sided model is put forward instead of the one-sided model in previous studies. Marangoni-Bénard instabilities in evaporating liquid thin layers are investigated with a linear instability analysis. We define a new evaporation Biot number, which is different from that in previous studies and discuss the influences of reference evaporating velocity and evaporation Biot number on the vapor-liquid system. At the end, we explain why the instability occurs even when an evaporating liquid layer is cooled from below. 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 and KGCX-SW-409) The English text was polished by Keren Wang.     

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.     

Planar solidification of a warm flowing-liquid under different boundary conditions

Planar solidification of a warm flowing liquid with the convective heat transfer to the growing solid layer, has been analysed for the boundary conditions of constant temperature, constant heat flux and convective heat flux at the surface respectively. The mathematical formulation of the problem resulted in a coupled set of two differential equations in temperature and solid thickness as function of position, time and the problem parameters. Analytical expressions for the temperature distribution within the growing solid layer, the rate of solidification and the solidification time are obtained. The perturbation techniques employed here is simple and straight forward in contrast with the earlier techniques. Good agreement between the experimental results and the present solutions is obtained for the convective heat flux boundary condition. The results of this analysis are useful in the design and analysis of experiments dealing with freezing/melting in one dimension. The role of the parameter Stefan number which is small for phase change materials, is discussed in context with the storage of thermal energy.     

蒸发液层对流稳定性理论与实验研究进展

综述了蒸发液层稳定性理论分析和蒸发对流实验研究方面的最新进展. 首先回顾历史上经典的单层流Marangoni不稳定性分析.利用经典的单层流模型可以很好解释无蒸发液层的稳定性特性, 但是由于经典的单层流模型没有考虑蒸汽层与液层之间的动力学耦合关系,所以不能完全解释蒸发液层的Marangoni不稳定性特性.有的学者建立了考虑蒸汽层与液层的热耦合与动力学耦合关系的两层流模型, 并采用了界面温度连续这样的假设. 而在实验的观测中, 蒸发界面处的温度是不连续的, 特别是在蒸发量比较大的情况下, 汽/液界面处温度跳跃很明显. 由于界面温度连续假设在处于非平衡状态的系统中是不成立的, 所以这些模型虽然能给出一些新的有关系统稳定性的特性,但还是不能完全解释蒸发液层的Marangoni不稳定性的特性, 特别是为什么从底部冷却液层的时候, 在实验中仍然能够观察到Marangoni对流涡胞的出现的原因. 本文总结了前人的研究成果, 同时给出了蒸发系统的动力学建模过程和实验研究方法,并对各种模型的稳定性特性进行了总结. 最后, 指出了现有理论中存在的问题和有待进一步研究的问题.      

Convective and diffusive surfactant transfer in multiphase liquid systems

Laser interferometry was used to investigate diffusive and convective mass transfer in a multicomponent fluid mixture with a liquid–liquid or liquid–gas interface. For this purpose, an immobile gas bubble or insoluble fluid droplet, having the shape of a short cylinder with a free lateral surface, was inserted into a thin liquid layer. In the case of non-uniform distribution of the dissolved surfactant component, the Marangoni convection near the drop/bubble was initiated by the surface tension inhomogeneities, depending on the surfactant concentration. The applied experimental techniques allowed us to study the structure and evolution of the convective flows and concentration fields in a liquid layer, which due to its small thickness were nearly two-dimensional. Making use of both the vertical and horizontal orientation of the liquid layer, we investigated the mass transfer process at different levels of the interaction between gravity and capillary forces. During the experiments, we detected new solutocapillary phenomena, which were found to be caused by oscillatory regimes of solutal convection occurring around air bubbles and chlorobenzene drops in heterogeneous aqueous solutions of alcohol with a vertical surfactant concentration gradient. The role of the oscillatory instability in the processes of drop saturation by the surfactant from its water solution and an inverse process of surfactant extraction from the drop into the surrounding homogeneous fluid (water) was determined. A reasonable explanation for the driving mechanisms of the discovered effects has been proposed.     

Experimental Study of the Effect of Gas-Phase Thickness On Stability and Structure of the Flow in a Two—Layer Liquid—Gas System

The stability of a two-layer liquid—gas system with a variable ratio of layer thicknesses is experimentally studied. It is found that the critical value of the Marangoni number and the characteristic size of convective structures depend on the ratio of thicknesses of the gas and liquid phases. For ratios higher than ten, the gas layer can be considered as infinite.     

Thermocapillary convection in a plane liquid layer with concentration heat sources

Thermocapillary instability of a plane liquid binary-mixture layer with time-dependent surface tension is studied under weightlessness conditions. The liquid is heated (or cooled) due to heat release by an active admixture. The heat release rate is proportional to the active-component concentration. The admixture is transported by convection and diffusion. The active component “burns up” with time. The neutral curves for monotonous and oscillating disturbances are found for different values of the nondimensional parameters. Some nonlinear convection regimes are studied numerically by a finite-difference method. The dependence of the convective flow intensity on the Marangoni number is determined. The phase portraits of unsteady regimes are found.     

Thermal convection in a viscoelastic liquid

The onset of convection in a layer of viscoelastic liquid heated from below is investigated. It is shown that the nature of the convective solution depends strongly on the particular constitutive relation used to characterize the viscoelasticity. For certain models and certain parameter ranges the convection is supercritical and stable, while for other models and parameter ranges it can be subcritical and unstable. It is suggested that observations of convective behavior can provide a test for constitutive relations proposed for a particular liquid. A Fourier representation of the solution to the nonlinear problem is developed which is shown to admit aperiodic, or chaotic, solutions in a specific truncation that generalizes the classical Lorenz system for the Newtonian Bénard problem.     

Stability of Plane Flow of a Liquid Dielectric in a Transverse Alternating Electric Field

The effect of an alternating arbitrary-frequency electric field on the stability of convective flow of a dielectric liquid occupying a vertical layer is investigated within the framework of the electrohydrodynamic approximation when charge formation is associated only with the nonuniform liquid polarization. The stability thresholds are determined in the linear approximation using Floquet theory. The competition between the dielectrophoretic and thermogravitational instability mechanisms is explored. It is shown that in the case of a harmonically modulated field either quasiperiodic perturbations or perturbations synchronous with the external action may be the most dangerous. One further critical perturbation mode corresponding to the subharmonic response to variation of the external field develops for triangular modulation. In the limiting case of low-frequency modulation the asymptotic behavior of the critical parameters is investigated using the Wentzel-Kramers-Brillouin method.     

Effect of free convection on thermodiffusion in a liquid mixture filling an inclined rectangular cavity

The convective motion which develops in an inclined cavity upon heating from above determines to a significant degree the form of the concentration field produced by thermodiffusion. The interaction of convective and thermodiffusion fluxes at small thermal Grashof numbers Gr causes the appearance of longitudinal jumps in concentration. Increase in temperature difference intensifies convection and encourages reduction in concentration gradients. The dominant role of convection for fixed Gr is determined by the angle of inclination of the liquid layer [1, 2]. A significant feature of liquid solutions is their low diffusion coefficient and thus high Schmidt number. This fact does not permit use of results obtained for gas mixtures, and greatly complicates numerical simulations. In contrast to [2], the present study will investigate thermodiffusion separation in a cavity with impermeable boundaries.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 73–76, September–October, 1986.In conclusion, the authors thank G. Z. Gershun for evaluation of the results and helpful remarks.     

Localized convective flows in a nonuniformly heated liquid layer

Within the class of exact solutions of the thermal-convection equations in the Oberbeck-Boussinesq approximation, which assumes a linear dependence of the temperature and the vertical velocity component on the height, a non-self-similar behavior of localized disturbances of a special type in a nonuniformly heated liquid layer is studied. It is shown that in an unstably stratified medium these disturbances can evolve to isothermal vortex structures of Burgers type. In the conditions of stable stratification or uniform heating of the layer, the disturbances considered tend to the state of rest in an oscillating or monotonic manner. New solutions describing self-similar convective vortices are found.     

Experimental investigation of convective flows in a plane horizontal fluid layer heated from below and rotating about the vertical axis

The convective coherent structures in a plane horizontal fluid layer, heated from below and capable of rotation about the vertical axis, are experimentally investigated. It is shown that with increase in the supercriticality the time it takes for the convective structures to be formed decreases sharply. Rotation and an increase in the layer thickness-to-diameter ratio lead to an increase in the steady-state attainment time.     

Stability of a liquid layer with bubbling

The article discusses a new type of instability of a horizontal layer of a motionless liquid, due to the motion of bubbles of gas or of particles of a suspension through the layer. It is shown that, when a certain critical mass flow rate of the gas or the suspension is attained, due to the essential inhomogeneity of the velocity of the gas bubbles, the layer becomes unstable and convective flow develops in a Bénard cell. With the motion of bubbles in the field of gravity, the criterion of instability is found to be independent of the size of the bubbles and the kinematic viscosity of the liquid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, July–August, 1974.     

Effets des forces de Coriolis sur le seuil convectif stationnaire d'une couche liquide confinée en cellule de Hele–Shaw annulaire en rotationEffects of the Coriolis forces on the stationary convectif threshold of a liquid layer confined in an annular Hele–Shaw Cell in rotation

The convective instability of a horizontal liquid layer confined in an annular Hele–Shaw cell subject to a constant rotation and submitted to a centrifugal gradient of temperature is investigated. Using a linear stability analysis, we study the effects of both Coriolis forces and curvature aspect on the stationary convective threshold when the Prandtl number is of the order of unity or larger than unity. We show that the Coriolis forces have a stabilizing effect, and the wave number is independent of these forces. However, a multicellular regime in the radial direction is observed for small Ekman numbers. The results related to the influence of the curvature are also shown. To cite this article: S. Ramezani et al., C. R. Mecanique 330 (2002) 633–640.     

Stability of two-layer fluid flow

The problem of two-layer convective flow of viscous incompressible fluids in a horizontal channel with solid walls in the presence of evaporation is considered in the Oberbeck–Boussinesq approximation assuming that the interface is an undeformable thermocapillary surface and taking into account the Dufour effect in the upper layer which is a mixture of gas and liquid vapor. The effects of longitudinal temperature gradients at the boundaries of the channel and the thicknesses of the layer on the flow pattern and the evaporation rate are studied under conditions of specified gas flow and the absence of vapor flow on the upper boundary of the channel. It is shown that the long-wavelength asymptotics for the decrement is determined from the flow characteristics, the longwavelength perturbations occurring in the system decay monotonically, and the thermal instability mechanism is not potentially the most dangerous.     

磁场对双扩散液层热毛细对流的影响

通过数值模拟的方法对磁场作用下的双扩散液层热毛细对流进行了研究, 模型中同时考虑了热毛细效应和溶质毛细效应的存在. 研究结果显示, 外部磁场能够有效削弱液层内热毛细对流的强度, 改变热毛细对流的对流结构; 随着磁场强度的增大, 液层内热毛细对流的对流强度逐渐减小, 热质传递过程中扩散效应逐渐得到增强; 最终, 溶质浓度沿水平方向呈梯度分布. 因此, 当磁场强度足够大时能够实现晶体生长中所需的纯扩散条件.     

Quadratic convective flow of radiated nano-Jeffrey liquid subject to multiple convective conditions and Cattaneo-Christov double diffusion

A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiation, magnetohydrodynamic (MHD), and convective conditions are accounted. The conversion of governing equations into ordinary differential equations is prepared via stretching transformations. The consequent equations are solved using the Runge-Kutta-Fehlberg (RKF) method. Impacts of physical constraints on the liquid velocity, the temperature, and the nanoparticle volume fraction are analyzed through graphical illustrations. It is established that the velocity of the liquid and its associated boundary layer width increase with the mixed convection parameter and the Deborah number.     

Penetrative convection in sublayer of water including density inversion

Numerical solutions of stability and convective flow in an infinite horizontal water layer, including density inversion, have been obtained using a finite element code. The evolution of the temperature field and flow pattern near the onset of convection are studied in detail. It is known that natural convection develops primarily in the lower unstably stratified layer. Of interest is the penetration of the convection rolls into the upper stably stratified layer and concurrent liquid entrainment as a function of the increasing Rayleigh number at different aspect ratios. Individual convection rolls may grow and expand before splitting up into two roll cells. It is shown that changing the aspect ratio influences critical Rayleigh number, flow symmetry, flow pattern, and transitions between flow patterns. Numerical results on heating from above or from below, agree well with available results in the literature. A correlation to predict critical Rayleigh numbers is given for the case of heating from above.