Convective self-oscillations near an air-bubble surface in a horizontal rectangular channel

The concentration convection in an isothermal fluid near an air bubble clamped between the vertical walls of a horizontal channel with a rectangular cross-section is studied experimentally and numerically. The channel is filled with an aqueous solution of a surfactant with a nonuniform concentration. As a result of the competition between the gravitational convection in the cavity volume and the Marangoni convection near the bubble surface, an oscillation flow regime is established. This regime is observed experimentally over several hours. In the numerical experiment, the oscillations are obtained in the presence of an initial horizontal surfactant concentration gradient. Against the background of gravitational convection, short bursts of Marangoni convection with ten times greater intensity are observed. The convective flow patterns and the oscillation periods obtained experimentally and numerically are in fairly good agreement.     

Structure of the fluid interface in an external magnetic field in the presence of a magnetizable surfactant

The structure of the flat interface between two conventional fluids in an external magnetic field in the presence of a magnetizable surfactant is investigated with account for the dependence of the free energy of the system on the surfactant concentration gradients and the bearing phase density. The dependence of the surface tension tensor components on the magnetic field strength is determined.     

Oscillatory Marangoni convection around the air bubble in a vertical surfactant stratificationConvection de Marangoni oscillante autour d'une bulle d'air dans une stratification verticale surfactante

The solutocapillary Marangoni convection around a gas bubble in the inhomogeneous binary mixture of miscible fluids with a vertical surfactant concentration gradient was studied experimentally. A new phenomenon, the oscillatory instability of the surfactant mass transfer, near the bubble boundary, was detected and investigated. The interpretation of this effect as an interaction between the surfactant adsorption at the bubble free surface and solutocapillary and buoyancy convective mechanisms is proposed. The experimental data on oscillation period in relation to bubble dimensions, time, liquid layer thickness, physico-chemical fluid parameters and concentration gradients are presented and discussed. To cite this article: K. Kostarev et al., C. R. Mecanique 332 (2004).     

Effect of Convection on Formation of Adsorbed Surfactant Film under Dynamic Change of Solution Surface Area

The dynamics of the formation of a surface phase in aqueous solutions of surfactants in a tray with the Langmuir barrier system during one compression–expansion cycle of the interface boundary is investigated both experimentally and theoretically. Organic salts of fatty acids such as potassium laurate, caprylate, and acetate, which are members of the same homologous series, were used as surfactants. It is experimentally determined that the dependence of the surface pressure increment measured under the maximum compression of the surface on the volume concentration has a maximum, the position of which is different for all the studied surfactant solutions. It is shown that the position of the maximum corresponds to the concentration value at which a saturated monolayer of surfactant molecules is formed at the interface boundary. A theoretical model that considers the effect of the forced convection arisen in the bulk of the solution upon changing the surface area is proposed for the interpretation of the experimental results. The model allows one to render the main kinetic characteristics of the adsorption/desorption processes involving the compounds under study. A good agreement between the theoretical and experimental results is observed, but there is a discrepancy between them when diffusion is considered to be the only way surfactant molecules are transferred into the bulk phase. Based on the data, a new method for determination of the Langmuir–Shishkovsky constant is proposed.     

Effect of a Magnetizable Surfactant on the Motion of a Liquid Film on the Horizontal Surface

The motion of a thin liquid film of viscous incompressible fluid on the horizontal surface in the presence of a magnetizable surfactant on the free boundary in the external inhomogeneous magnetic field is investigated. Surfactant diffusion along the free surface and the dependence of the surface tension on the magnetic field strength are taken into account. The system of evolutionary equations is derived in the lubricant approximation and steady-state film flows and their stability in the case of constant film thickness and constant surfactant number density are investigated with regard to the Marangoni effect.     

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.     

Branching of an axially symmetric convective flow

The stability of an axisymmetric convective gas flow with respect to finite disturbances of the bottom temperature is studied numerically using a finite-difference method. The convective flow considered approximately describes the free convection developing in the atmosphere due to heating of the substrate surface. The temperature disturbance used increases the intensity of one of two possible flows and suppresses the other flow, with the opposite signs of the vortices. Using the methods of numerical experiment, the corresponding problem of branching of the solution is examined. It is shown that the transformation of one flow into the other far from the threshold of the onset of convection requires substantial disturbances of the temperature.     

Unraveling surfactant transport on a thin liquid film

When a drop of insoluble surfactant is deposited on the surface of a thin liquid film, a radial flow is induced by the resulting surface tension gradient. It is difficult in practice to measure or visualize the evolution of the surfactant concentration and the corresponding surface tension field. In this contribution, we propose a numerical technique which allows, in theory, the reconstruction of the surfactant concentration and surface tension fields from the knowledge of the free surface velocity. The method also requires the knowledge of the equation of state relating the surfactant concentration to the surface tension. The proposed method is based on a reformulation of the lubrication approximation which then takes as an input the free surface velocity field. As a by-product, the film thickness is also reconstructed. We also show in this contribution, that the surface diffusion coefficient can also be estimated, in principle. The methodologies are successfully tested on ideal, synthetic data-sets but also on under-resolved, noisy, data-sets more representative of true experimental conditions. This contribution may help shed some light on the phenomena involved in surfactant transport.     

Numerical simulation of convective flows in a soil during the evaporation of water containing a dissolved admixture

The concentration profile is investigated for a solution that saturates a low-permeability soil. The simulation results showed the presence of three flow regimes. The salt accumulated near the phase transition boundary increases the solution density and may lead to the development of natural concentration-induced convection which interacts with the rising flow (forced convection). The stability threshold of the forced flow and the effect on it of natural convection that arises are determined. It is shown that at intense flow to the evaporation surface the admixture concentration increases at this boundary rapidly and reaches the saturation concentration. In this case, the admixture precipitates. In the slow evaporation regime the admixture diffuses from the high-concentration region, which prevents the development of convective flow.     

离子选择性表面电对流的多块LB模拟

离子选择性表面(如纳米通道、离子交换膜等)复杂的动力学现象为微纳流控技术的发展提供了新思路. 向带有离子选择性表面的电解质溶液施加电压, 通过液体的电流密度会经历复杂的非线性变化过程; 当电压超过某一临界值时会引发对流现象, 这种流动被称为第二类电渗或离子选择性表面的电对流, 关于此类问题的数值求解引发了大量的研究. 本文提出一种基于多块网格加密的格子玻尔兹曼方法(lattice Boltzmann method, LBM)的数值模型, 用于模拟第二类电渗流动. 结合该算法, 给出了求解流动、电势和离子浓度的网格信息交换方程, 较好地解决了此类问题中大浓度梯度边界对计算分辨率的要求. 利用该数值模型模拟获得的电流?电压特性曲线先随着电压升高而迅速增大, 随后达到饱和状态, 与理论解吻合良好. 此外, 模拟结果还表明, 当流动发生后, 相对低电压下的流动倾向于形成大涡且流动呈指数趋势增强; 而较大电压则会先激发多个小涡, 并逐渐合并为大涡流动, 且大涡流动有更高的离子输运效率. 此外, 除了模拟离子选择性表面的电对流现象, 本文提出的数值格式还可拓展到其他电流体动力学问题的模拟.      

Unsteady mixed convection boundary-layer flow with suction and temperature slip effects near the stagnation point on a vertical permeable surface embedded in a porous medium

The unsteady mixed convection boundary-layer flow near the two-dimensional stagnation point on a vertical permeable surface embedded in a fluid-saturated porous medium with suction and a temperature slip effect is studied numerically. Similarity equations are obtained through the application of a similarity transformation technique. The shooting method is used to solve these similarity equations for different values of the mixed convection, wall mass suction, the unsteadiness and the slip parameters. Results show that multiple solutions exist for certain ranges of these parameters. Some limiting forms are then discussed, namely strong suction, the free convection limit, the situation when there is a large temperature slip and when the time dependence dominates.     

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.     

Boundary effect on free convection flow in a porous medium at given heat transfer from a vertical surface

The system of momentum and energy conservation equations governing free convection flow near a vertical surface in a semi-infinite porous medium subject to the boundary conditions of the third kind is considered in the boundary layer approximation. Asymptotic expansions in the powers of the Darcy parameter Da are constructed. The dependence of flow parameters on the parameters Da and xGr is studied. Analytical solutions applicable throughout the entire flow region are constructed.     

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.     

Combined thermosolutal buoyancy and surface-tension flows in a cavity

In this article, the thermosolutal buoyancy and surface-tension convection flows are numerically studied with a fourth-order Runge-Kutta time-splitting finite element method. The physical model for a square cavity containing a top free surface and two different temperature and concentration side walls is described by the Navier-Stokes, energy and species concentration equations. On the track of flow pattern, the existence of surface tension will alter the evolution of the flow field and influence the local heat and mass transfer rates near the top free surface. In addition, the surface tension dominated flow field under a zero-gravity condition is studied for r = 0 and 1 to investigate the interaction between thermal surface tension and solutal surface tension. The results show that temperature and concentration make opposing contributions to the flow and display local variance in temperature and concentration distributions near surface boundary. Received on 29 July 1998     

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.     

剪应力对培养内皮细胞表面ATP浓度的调节

剪应力信号转导是目前细胞生物力学的研究热点之一。Ca^2＋作为一种第二信使在剪应力信号转导中扮演了重要角色，钙信号转导是通过胞内自由Ca^2＋浓度变化来实现的。胞内Ca^2＋浓度的大小不仅依赖于细胞承受剪应力的大小，同时依赖于细胞外ATP的浓度。本文采用剪应力诱发内皮细胞分泌ATP的时变模型，通过对平行平板流动腔中的ATP浓度场进行数值模拟，分析了剪应力对培养内皮细胞表面ATP浓度的影响。结果表明，剪应力诱发的ATP分泌明显影响细胞表面附近ATP的浓度；剪应力、对流和扩散效应、ATP的水解作用共同决定了细胞外表面附近ATP的浓度。这一结果提示，剪应力大小并非剪应力信号转导过程中的唯一决定因素；剪应力的作用、激动剂的浓度改变共同参与了剪应力信号转导。     

Effect of the adsorption-desorption process intensity on solutal convection near a drop in a horizontal channel

The interaction between gravity convection and Marangoni convection in a horizontal rectangular channel filled with a liquid containing a surfactant and a drop of another liquid is numerically investigated. For large Schmidt numbers the occurring oscillatory regime of solutal convection is analyzed. In the model with a surface phase the effect of the adsorption and desorption processes on the convective flow structure is determined. The corresponding initial and boundary value problem is solved using a difference method.     

Structure and stability of the interface between magnetic and conventional fluids. Model of a three-component medium

The structure of a flat interphase boundary between a magnetic suspension and a conventional immiscible fluid is investigated within the framework of the model of a three-component medium taking the dependence of the free energy of the system on the concentration gradients into account. It is shown that for certain values of the constitutive parameters the bulk magnetic particle concentration increases significantly inside the interfacial layer, i.e., the particles are significantly adsorbed on the interface. The dependence of the surface tension on the magnetic field strength is determined. It is shown that for certain problem parameters this dependence qualitatively corresponds to that obtained experimentally and described in the phenomenological theory developed by Golubyatnikov and Subkhankulov in 1986. In the case of strong particle adsorption the dependence of the surface tension on the magnetic particle concentration on the phase interface is significantly nonlinear. A refined model of the interface as a two-dimensional continuum with surface magnetization is constructed. Constitutive equations, conditions on the interface, and necessary stability conditions are obtained.     

Oscillatory behaviour in melting of a GaSb/InSb/GaSb system

The effect of coexistence of Marangoni and natural convections was studied numerically in melting of a GaSb/InSb/GaSb sandwich sample. Fluid flow and concentration fields are oscillatory when the solutal natural convection coexists with the thermal Marangoni convection. The coexistence of solutal and thermal natural convections, without Marangoni convection, however, does not lead to fluid flow oscillations in spite of the existence of two flow cells in opposite directions. The conclusion is that not the presence of two opposite flow cells but the flow structure itself, due to the presence of a free surface, is responsible for such an oscillatory behaviour.