Instability of Marangoni flow in the presence of an insoluble surfactant. Experiments

The stability and structure of solutocapillary Marangoni flow initiated by a localized concentration source in the presence of an adsorbed layer of insoluble surfactant is investigated experimentally. It has been established that the main axisymmetric flow becomes unstable with respect to azimuthally periodic disturbances which leads to the appearance of the surface flow with a multi-vortex structure. The structure of the secondary flow is investigated depending on the intensity of the main flow and on the surface density of the surfactant. It has been shown that the azimuthal wave number increases with the growth of the Marangoni number and decreases with the surface density of the surfactant. A threshold value of the surface density of the surfactant, at which the Marangoni flow does not occur, has been defined.     

活性剂浓度分布对液膜排液过程的影响

针对含不溶性活性剂的垂直液膜排液过程,考虑分离压和表面黏度的作用,应用润滑理论建立液膜厚度、活性剂浓度和表面速度的控制方程组,分析初始活性剂浓度及梯度对排液过程的影响.结果表明：当液膜表面不含活性剂时,其排液历程很短,很快发生破断.当液膜表面添加活性剂时,可以延长液膜存续时间.而当液膜表面活性剂浓度较低时,其诱发的Marangoni效应不足以克服重力的排液作用,其形成的"黑膜"不能稳定存在.随活性剂浓度增大,液膜表面流动速度减小,液膜表面更加"坚固",所形成的"黑膜"非常稳定.当考虑初始活性剂浓度梯度时,其影响主要体现在减缓排液初期的表面速度.     

平板马兰各尼流动中数的影响

本文提出了边界层充分发展情况下平板马兰各尼流动动量方程和能量方程的相似解,分析了流动与传热随Pr数的变化特征;由于在核沸腾中蒸汽气泡的一般直径大于估算边界层厚度,因而可以忽略表面张力影响,将这一结果用于气泡周界马兰各尼流动效应的初步分析.     

Marangoni flow and mass transfer of power-law non-Newtonian fluids over a disk with suction and injection

We scrutinize the approximate analytical solutions by the optimal homotopy analysis method (OHAM) for the flow and mass transfer within the Marangoni boundary layer of power-law fluids over a disk with suction and injection in the present paper. Concentration distribution on the surface of a disk varies in a power-law form. The non-Newtonian fluid flow is due to the surface concentration gradient without considering gravity and buoyancy. According to the conservation of mass, momentum and concentration, the governing partial differential equations are established, and the appropriate generalized Kármán transformation is found to reduce them to the nonlinear ordinary differential equations. OHAM is used to access the approximate analytical solution. The influences of Marangoni the number, suction/injection parameters and power-law exponent on the flow and mass transfer are examined.     

Influence of the surrounding pressure on acoustic properties of slightly compressible porous media permeated with air-filled bubbles

The effective wave velocity, attenuation, and nonlinear properties of slightly compressible porous media permeated with air-filled bubbles are studied numerically by employing the nonlinear Hooke’s law for different surrounding pressures. Numerical simulations show that the acoustic properties of porous media are greatly affected by the surrounding pressure if the shear modulus of the elastic medium is very small due to the fact that the acoustic wave propagation in porous media are strongly influenced by the nonlinear oscillation of bubbles; moreover, the oscillation of a bubble depends on the equilibrium bubble radius, which is affected by the surrounding pressures. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 490–496. The text was submitted by the authors in English.     

Dissipative hydrodynamic oscillators

Summary The oscillatory motion of a liquid-liquid interface induced by the Marangoni effect,i.e. the variation of surface tension with the concentration of a surfactant, is described as the harmonic oscillation of the surfactant concentration at the interface. Then, at vanishing damping, threshold values and parameter regions for sustainedlongitudinal (Marangoni-Lucassen) waves are given in terms of the transport coefficients of the two liquids. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Space experimental investigation on thermocapillary migration of bubbles

Results from a space experiment on bubble thermocapillary migration conducted on board the Chinese 22nd recoverable satellite were presented. Considering the temperature field in the cell was disturbed by the accumulated bubbles, the temperature gradient was corrected firstly with the help of the temperature measurement data at six points and numerical simulation. Marangoni number (Ma) of single bubble migrating in the space experiment ranged from 98.04 to 9288, exceeding that in the previous experiment data. The experiment data including the track and the velocity of two bubble thermocapillary migration showed that a smaller bubble would move slower as it was passed by a larger one, and the smaller one would even rest in a short time when the size ratio was large enough. Supported by the National Natural Science Foundation of China (Grant No. 10432060) and the Knowledge Innovation Program of Chinese Academy of Sciences (KJCX2-SW-L05, KACX2-SW-322)     

Vertical water distribution during the drying of polymer films cast from aqueous emulsions

We present a systematic study of the vertical uniformity of water distribution during the drying of waterborne colloidal films, testing the predictions of a Peclet number Pe defined for this system. Pe indicates the relative contributions of water evaporation and Brownian diffusion in determining the concentration profile in the vertical direction (i.e. normal to the substrate). When Pe < 1, the water concentration in films cast from an alkyd emulsion is found via magnetic-resonance profiling to be uniform with depth, which is consistent with expectations. When Pe > 1, a gradient in the water concentration develops, with less water near the interface with air. The water profiles reveal that the alkyd particles do not coalesce immediately upon contact in close-packing. At later times, a concentrated surface layer develops, but particles are not coalesced in this layer to form a continuous “skin”, but rather the structure is likely to be that of a biliquid foam. Received 20 March 2002 and Received in final form 12 June 2002     

A hybrid numerical method for interfacial fluid flow with soluble surfactant

We address a significant difficulty in the numerical computation of fluid interfaces with soluble surfactant that occurs in the physically representative limit of large bulk Peclet number Pe. At the high values of Pe in typical fluid-surfactant systems, there is a transition layer near the interface in which the surfactant concentration varies rapidly, and large gradients at the interface must be resolved accurately to evaluate the exchange of surfactant between the interface and bulk flow. We use the slenderness of the layer to develop a fast and accurate ‘hybrid’ numerical method that incorporates a separate, singular perturbation analysis of the dynamics in the transition layer into a full numerical solution of the interfacial free boundary problem. The accuracy and efficiency of the method is assessed by comparison with a more ‘traditional’ numerical approach that uses finite differences on a curvilinear coordinate system exterior to the bubble, without the separate transition layer reduction. The traditional method implemented here features a novel fast calculation of fluid velocity off the interface.     

表面弹性对含可溶性活性剂垂直液膜排液的影响

针对含可溶性活性剂的垂直液膜排液过程,在考虑表面弹性作用的基础上,采用润滑理论建立了液膜厚度、表面速度、表面和内部活性剂浓度的演化方程组,通过数值计算分析了表面弹性和活性剂溶解度耦合作用下的液膜演化特征.结果表明：表面弹性是影响可溶性活性剂垂直液膜排液过程中必不可少的因素.排液初期,随表面弹性增加,液膜初始厚度增大,表面更趋于刚性化.随排液进行,弹性不同的液膜呈现不同的典型排液特征：当弹性较小时,液膜上部表面张力高,下部表面张力低,产生正向的马兰戈尼效应,与重力作用相抗衡.当弹性较大时,膜上部表面张力低,下部表面张力高,产生逆向的马兰戈尼效应,促使液膜排液加速,更易发生失稳.活性剂溶解度通过控制液膜表面的活性剂分子吸附量,进而影响表面弹性：当活性剂溶解度较大时,液膜厚度较小,很快发生破断;随溶解度降低,液膜稳定性增加,初始表面弹性也随之增大,并随液膜变薄逐渐接近极限膨胀弹性值.     

凹槽基底上含不溶性活性剂液膜的流动特性

针对凹槽基底上含不溶性活性剂液膜的流动过程,采用润滑理论建立液膜厚度和浓度演化模型,通过数值模拟得到液膜的流动特性及相关参数的影响规律.研究表明:含不溶性活性剂液膜在凹槽基底上流动时,重力和活性剂浓度梯度引起的Marangoni力对液膜的流动起促进作用,表面活性剂通过引起表层液体流动进而牵引内部液体运动,但其作用力相对重力较弱,重力起主导作用;与基底尺寸有关的粘性力则起阻碍作用;提高邦德数G和减小毛细力数C具有减弱液膜变形的作用;增大凹槽高度或减小凹槽斜度,均使Marangoni力增加,促使液膜变形加大.     

Air bubbles under vertical vibrations

This paper reports on an experimental study of the splitting instability of an air bubble a few centimetres in diameter placed in a sealed cylindrical cell filled with liquid and submitted to vertical oscillations. The response of the bubble to the oscillations is observed with a high-speed video camera. It is found that the bubble dynamics is closely associated with the acceleration of the cell Γ. For small acceleration values, the bubble undergoes minor shape deformations. With increasing acceleration values, these deformations are amplified and for sufficiently large Γ the bubble becomes toroidal. The bubble may then become unstable and split into smaller parts. The onset of bubble division is studied and its dependency on physical parameters such as the fluid viscosity, the fluid surface tension and the initial size of the bubble is presented. It is found that the criterion for the bubble splitting process is associated with a threshold based on the acceleration of the oscillations. Above this threshold, the number of bubbles present in the cell is observed to grow until a final steady state is reached. Data analysis reveals that the final bubble size may be characterized in terms of Bond number.     

Quasi-one-dimensional foam drainage

Foam drainage is considered in a froth flotation cell. Air flow through the foam is described by a simple two-dimensional deceleration flow, modelling the foam spilling over a weir. Foam microstructure is given in terms of the number of channels (Plateau borders) per unit area, which scales as the inverse square of bubble size. The Plateau border number density decreases with height in the foam, and also decreases horizontally as the weir is approached. Foam drainage equations, applicable in the dry foam limit, are described. These can be used to determine the average cross-sectional area of a Plateau border, denoted A, as a function of position in the foam. Quasi-one-dimensional solutions are available in which A only varies vertically, in spite of the two-dimensional nature of the air flow and Plateau border number density fields. For such situations the liquid drainage relative to the air flow is purely vertical. The parametric behaviour of the system is investigated with respect to a number of dimensionless parameters: K (the strength of capillary suction relative to gravity), α (the deceleration of the air flow), and n and h (respectively, the horizontal and vertical variations of the Plateau border number density). The parameter K is small, implying the existence of boundary layer solutions: capillary suction is negligible except in thin layers near the bottom boundary. The boundary layer thickness (when converted back to dimensional variables) is independent of the height of the foam. The deceleration parameter α affects the Plateau border area on the top boundary: weaker decelerations give larger Plateau border areas at the surface. For weak decelerations, there is rapid convergence of the boundary layer solutions at the bottom onto ones with negligible capillary suction higher up. For strong decelerations, two branches of solutions for A are possible in the K = 0 limit: one is smooth, and the other has a distinct kink. The full system, with small but non-zero capillary suction, lies relatively close to the kinked solution branch, but convergence from the lower boundary layer onto this branch is distinctly slow. Variations in the Plateau border number density (non-zero n and h) increase individual Plateau border areas relative to the case of uniformly sized bubbles. For strong decelerations and negligible capillarity, solutions closely follow the kinked solution branch if bubble sizes are only slightly non-uniform. As the extent of non-uniformity increases, the Plateau border area reaches a maximum corresponding to no net upward velocity of foam liquid. In the case of vertical variation of number density, liquid content profiles and Plateau border area profiles cease to be simply proportional to one another. Plateau border areas match at the top of the foam independent of h, implying a considerable difference in liquid content for foams which exhibit different number density profiles. Received 3 July 2001     

加热铂丝上运动汽泡产生的射流

目前很多水的核态沸腾都观察到了汽泡顶部射流的现象。本文分析了沿细丝运动的汽泡顶部产生射流的物理机理,并通过对汽泡和加热细丝周围温度场和速度场的数值求解来进行分析。结果显示:由汽泡前后表面的温度梯度引起的热射流很可能是流动的最主要原因。热射流能够推动汽泡前进。对比和试验的观测指出,不凝气体或者其他可能的机理将限制汽泡界面处的凝结换热,从而增大表面温度梯度,增强热射流。     

Theoretical investigation on resonance characteristics of a vapor bubble based on Laplace transform method

In the present paper, resonance characteristics of the vapor bubble oscillating in an acoustic field are investigated analytically. The analytical solution of the non-dimensional perturbation of the instantaneous bubble radius during the transient process in the initial oscillation stage is explicitly obtained and physically analyzed at the resonance situation based on the Laplace transform method. And the typical oscillation behaviors obtained from the analytical solution are thoroughly exhibited and analyzed in the time and frequency domains. In addition, the corresponding oscillation behaviors at the non-resonance situation are also investigated for the purpose of comparisons. Through our investigation, several essential conclusions can be drawn as follows: (1) The analytical solution of the non-dimensional perturbation of the instantaneous bubble radius can be divided into four terms according to the physical meaning. Among them, it is the term related to the acoustic field that causes the progressively violent bubble oscillation. (2) The vapor bubble with a smaller equilibrium radius could respond faster and more significantly to the acoustic field during the oscillation. (3) The bubble oscillation characteristics always exhibit significant differences at the resonance and non-resonance situations in both the time and frequency domains, even if the difference between the natural frequency of the oscillating vapor bubble and the angular frequency of the acoustic field is greatly small.     

浓度边界层中成长汽泡的界面特性

对于双组分池内核态沸腾，热边界层中生成的汽泡，同时也处于浓度边界层中．本文建立了边界展中汽泡表面张力模型，对温度和浓度引起的表面张力变化进行分析．结果表明，表面张力从汽泡顶部到底部是递增的，从而形成液体沿界面自上而下的Marangoni流．通过汽泡底部微层相界面方程的求解，探讨了微层变形特征，由此分析汽泡脱离机理．微层变形与文献[1]中指出的接触线的变化从本质上是一致的．     

Evaluation of Nusselt number and effectiveness for a vertical shell-coiled tube heat exchanger with air bubble injection into shell side

Air bubble injection was employed to increase the heat transfer rate (Nusselt number) of a vertical shell and coiled tube heat exchanger in this article. Hot and cold water flowed into the coil side and shell side of heat exchanger, respectively, and air bubbles were injected inside the shell side of heat exchanger via a memorable method. Bubbles' vertical movement due to buoyancy forcing through the heat exchanger can enhance the heat transfer rate by mixing the thermal boundary layer, increasing the turbulence level of the fluid flow and increasing the shell-side fluid Reynolds number.     

Structural and dynamic properties of polyoxyethylene sorbitan monooleate micelle in water dispersion studied by pulsed field gradient NMR

The diffusion phenomenon of a nonionic surfactant, polyoxyethylene sorbitan monooleate (POE-SMO), micelle in aqueous solution was investigated by pulsed field gradient nuclear magnetic resonance (PFG NMR) with a high gradient strength of 17.4 T/m at the diffusion timet _d varied from 3 to 300 ms. This high gradient strength allowed us to measure the slow self-diffusion coefficient of POE-SMO micelle, and the short diffusion time below 10 ms showed the restricted diffusion of the micelle. At the shortt _d the self-diffusion of the micelle was restricted and the restricted sizes were 1.8, 1.5, and 0.8 μm for the POE-SMO concentration of 100, 200 and 300 mM, respectively, and 0.6 μm for the POE-SMO only. The possible reason of this restriction was assumed to be the formation of a spatial network or a micellar clustering. Furthermore, a proton exchange between water molecule and surfactant OH group on the micelle surface was proposed. With respect to this proposal, the residence time of the proton at the micelle surface and the thickness of the surface were investigated from proton self-diffusion coefficients by PFG NMR.     

微重力下凝结和沸腾着的汽泡周围流场

1引言尽管对沸腾换热已有大量的研究，但对沸腾过程中驱动汽泡外流动的机理仍没有透彻理解，通常认为，汽泡外流动是由液体自然对流引起的。但是，近来的微重力实验表明［‘］；在没有自然对流的微重力场中，沸腾换热同样很剧烈。为了弄清正常重力和微重力环境中驱动换热的机理，很有必要作进一步的研究。本文数值分析了微重力环境下驱动壁面汽泡周围液体流动的基本机理，深入分析了Marangoni效应的影响，同时考虑表面凝结和蒸发过程的作用。2理论模型汽泡外流动可由二维层流N－S方程及烙方程来描述，流动是由Marangoni边界条件驱动，该条…     

Skin formation and bubble growth during drying process of polymer solution

When a polymer solution with volatile solvent is dried, skins are often formed at the surface of the solution. It has been observed that after the skin is formed, bubbles often appear in the solution. We conducted experiments to clarify the relation between the skin formation and the bubble formation. We measured the time dependence of the thickness of the skin layer, the size of the bubbles, and the pressure in the solution. From our experiments, we concluded that i) the gas in the bubble is a mixture of solvent vapor and air dissolved in the solution, ii) the bubble nucleation is assisted by the pressure decrease in the solution covered by the skin layer, and iii) the growth of the bubbles is diffusion limited, mainly limited by the diffusion of air molecules dissolved in the solution.