基底弹性对蒸发超薄液膜去润湿过程的影响

研究了基底的弹性变形对蒸发超薄膜的稳定性和去润湿动力学过程的影响. 基于长波近似, 得到了关于液体薄膜厚度的演化方程. 运用线性稳定性理论和数值模拟两种方法, 研究了基底弹性、范德华力以及液体蒸发等因素对液体薄膜的稳定性和去润湿过程的影响. 研究结果表明增大基底的弹性系数或者减小液体的表面张力, 都能加速液膜的破碎, 并且能够影响气液界面波的波长; 液体蒸发能促进气液界面扰动的增长, 有助于液膜的破裂.      

EFFECT OF TWO-DIMENSIONAL MICROPILLAR ARRAYED TOPOGRAPHY ON SPREADING OF INSOLUBLE SURFACTANT-LADEN DROPLET

针对二维微柱阵列壁面上含不溶性活性剂液滴的铺展过程,采用润滑理论建立了液膜厚度和浓度演化模型,采用数值计算方法得到了液滴的铺展特征及相关参数的影响. 研究表明：活性剂液滴在微柱阵列壁面上铺展时,在壁面凸起处衍生出隆起结构,壁面凹槽处衍生出凹陷结构,随时间持续,隆起和凹陷均向两侧移动,且数量不断增加. 活性剂液膜流经凸起时,隆起高度呈驼峰形变化. 增大预置液膜厚度或活性剂初始浓度,铺展区域隆起和凹陷数量增多,液滴铺展速度加快. 增加凹槽深度或减小斜度会使毛细力作用增强,液膜破断可能性加大;增大凹槽宽度可加速活性剂液滴的铺展,加剧液膜表面波动幅度.     

Effects of surfactant on liquid film thickness in the Bretherton problem

The effects of insoluble and soluble surfactant on the motion of a long bubble propagating through a capillary tube are investigated computationally using a finite-difference/front-tracking method. Emphasis is placed on the effects of surfactant on the liquid film thickness between the bubble and the tube wall. The numerical method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier–Stokes equations. A non-linear equation of state is used to relate surface tension coefficient to surfactant concentration at the interface. Computations are first performed for soluble cases and then repeated for the corresponding clean and insoluble cases for a wide range of governing non-dimensional parameters in order to investigate the effects of surfactant and surfactant solubility. The computed film thickness for the clean case is found to be in a good agreement with Taylor’s law indicating the accuracy of the numerical method. We found that both the insoluble and soluble surfactant generally have a thickening effect on the film thickness, which is especially pronounced at low capillary numbers. This thickening effect strengthens with increasing sensitivity of surface tension to interfacial surfactant coverage mainly due to the enhanced Marangoni stresses along the liquid film. It is also observed that film thickening shows a non-monotonic behavior for variations in Peclet number. The validity of insoluble surfactant assumption is assessed for various non-dimensional numbers and it is demonstrated that insoluble assumption is valid only when capillary number is very low, i.e., Ca ≪ 1 and when surface tension is highly sensitive to interfacial surfactant coverage, i.e., the elasticity number is large.     

Non-linear analysis of creeping flow on the inclined permeable substrate plane subjected to an electric field

The effect of an externally applied electric field on the stability of a thin fluid film over an inclined porous plane is analyzed using linear and non-linear stability analysis in the long wave limit. The principle aim of this study is to illustrate the influence of electric field on the non-linear stability of a thin liquid layer flow down incline substrate when the plane is porous. The driving force for the instability under an electric field is an electrostatic force exerted on the free charges accumulated at the dividing interface. The coupled non-linear evolution equations for the local film thickness and the interfacial charge for two-dimensional disturbances are derived to analyze the effect of long-wave instabilities. The method of multiple scales is applied to obtain approximate solutions and analyze the stability criteria. Numerical simulations of this system of non-linear evolution equations are performed. It is found that the permeability parameter as well as the inclination of the plane plays a destabilizing role in the stability criteria, while the damping influence is observed for increasing of the electrical conductivity in both linear and non-linear behavior.     

分离压对波状基底上活性剂液滴铺展过程的影响

针对波状基底上含不溶性活性剂液滴的铺展过程,引入受活性剂浓度影响的分离压模型,应用润滑理论建立了液滴高度和活性剂浓度演化方程组,通过数值计算方法得到了分离压作用下含活性剂液滴过程的演化特征. 研究表明:分离压作用下的液滴演化时间显著缩短,铺展速率加快,铺展前沿处衍生出的子波结构明显减少,铺展更加稳定;分离压对液滴铺展稳定性的影响与活性剂关联强度密切相关,减小引力强度系数α₁有利于促进液滴的铺展,而减小斥力强度系数α₂则起抑制作用,且放大了液滴的演化扰动能量,致使液滴铺展呈现不稳定特征;增加基底高度D或波数k均使液滴铺展速率减慢.      

二维微柱阵列壁面对活性剂液滴铺展的影响

针对二维微柱阵列壁面上含不溶性活性剂液滴的铺展过程,采用润滑理论建立了液膜厚度和浓度演化模型,采用数值计算方法得到了液滴的铺展特征及相关参数的影响. 研究表明:活性剂液滴在微柱阵列壁面上铺展时,在壁面凸起处衍生出隆起结构,壁面凹槽处衍生出凹陷结构,随时间持续,隆起和凹陷均向两侧移动,且数量不断增加. 活性剂液膜流经凸起时,隆起高度呈驼峰形变化. 增大预置液膜厚度或活性剂初始浓度,铺展区域隆起和凹陷数量增多,液滴铺展速度加快. 增加凹槽深度或减小斜度会使毛细力作用增强,液膜破断可能性加大;增大凹槽宽度可加速活性剂液滴的铺展,加剧液膜表面波动幅度.      

界面剪切力作用下波状液膜流的水动力稳定性

液膜流的水动力稳定性作为保障其高效传热传质性能的重要因素之一,受多种因素的制约和影响. 当气液界面处存在因气流流动而产生剪切力作用时,剪切力将通过改变界面处的边界条件,从而影响液膜流动的稳定性. 基于边界层理论,采用积分法建立了剪切力作用下降液膜表面波演化方程,分析了界面剪切力对水动力稳定性的影响. 研究表明,正向剪切力为不稳定性因素,反向剪切力在较小雷诺数时为不稳定因素,在大雷诺数时为稳定性因素;正向剪切力使临界波数和临界波速增大,反向剪切力使其减小;剪切力对临界波速的影响在不同雷诺数下也有所不同.      

Two-fluid modeling in analyzing the interfacial stability of liquid film flows

The area-averaged two-fluid model formulation of a separated two-phase flow system is used to investigate interfacial stability of liquid film flows. The analysis takes into account the effects of phase change at the interface as well as the dynamic effects of the adjacent vapor flow on the interfacial stability. Wave formation and instability criteria are established in terms of the generalized fluid and flow parameters. The criteria are applied to investigate the stability of laminar liquid film flow with interfacial shear and phase change. The influence of various dimensionless parameters characterizing film thickness, gravity, phase change and interfacial shear are studied with respect to the neutral stability, temporal growth factor and the wave propagation velocity. The results of the present study indicate that the interfacial stability analysis developed within the frame of the two-fluid model formulation proves to be quite accurate as judged by comparing its results with the available experimental data and with the results of much longer and more complex analytical investigations which are valid only for the liquid film free of interfacial shear.     

Surfactant effects on the Rayleigh instability in capillary tubes – non-ideal systems

In a previous work, the instability of a liquid film deposited on the inner walls of a capillary under the presence of insoluble surfactant was analyzed; for that purpose the surface tension was related to the interfacial concentration of surfactant by a linear equation. In general, that assumption is valid when just trace amounts of surfactant are present. The present work extends previous analysis by considering a non-linear surface equation of state derived from the Frumkin adsorption isotherm. This equation of state account not only for the existing quantities of surfactant but also for non-ideal interactions between adsorbed molecules. Except for the equation of state, both the model and the numerical technique employed do not differ from those used in the preceding work. The new predictions here presented show that a linear surface equation of state gives reasonable results for strong surfactants. However, the action of weaker surfactants strongly depends on other parameters: the initial concentration and the type and strength of interaction between adsorbed molecules. Thus, the use of a linear equation of state in these circumstances might give erroneous results.     

Interfacial instability of ferrofluid flow under the influence of a vacuum magnetic field

This study is to numerically test the interfacial instability of ferrofluid flow under the presence of a vacuum magnetic field. The ferrofluid parabolized stability equations(PSEs) are derived from the ferrofluid stability equations and the Rosensweig equations, and the characteristic values of the ferrofluid PSEs are given to describe the ellipticity of ferrofluid flow. Three numerical models representing specific cases considering with/without a vacuum magnetic field or viscosity are created to mathematically examine the interfacial instability by the computation of characteristic values. Numerical investigation shows strong dependence of the basic characteristic of ferrofluid Rayleigh-Taylor instability(RTI) on viscosity of ferrofluid and independence of the vacuum magnetic field.For the shock wave striking helium bubble, the magnetic field is not able to trigger the symmetry breaking of bubble but change the speed of the bubble movement. In the process of droplet formation from a submerged orifice, the collision between the droplet and the liquid surface causes symmetry breaking. Both the viscosity and the magnetic field exacerbate symmetry breaking. The computational results agree with the published experimental results.     

Surfactant spreading on a thin weakly viscoelastic film

A mathematical model is presented for surfactant-driven thin weakly viscoelastic film flows on a flat, impermeable plane. The Oldroyd-B constitutive relation is used to model the viscoelastic fluid. Lubrication theory and a perturbation expansion in powers of the Weissenberg number (We) are employed, which give rise to non-linear coupled evolution equations governing the transport of insoluble surfactant and thin liquid film thickness. Spreading on a Newtonian film is recovered to leading order and corrections to viscoelasticity are obtained at order We. These equations are solved numerically over a wide range of viscosity ratio (ratio of solvent viscosity to the sum of solvent and polymeric viscosities), pre-existing surfactant level and Peclet number (Pe). The effect of viscoelasticity on surfactant transport and fluid flow is investigated and the mechanisms underlying this effect are explored. Shear stress, streamwise normal stress and the temporal rate of change of extra shear stress generated from gradients in surfactant concentration dominate thin viscoelastic film flows whereas only shear stresses play a role in Newtonian thin film flows. Our results also reveal that, for weak viscoelasticity, the influence of viscosity ratio on the evolution of surfactant concentration and film thickness can be significant and varies considerably, depending on the concentration of pre-existing surfactant and surfactant surface diffusivity.     

切应力协同下受热过冷层流液膜的破断特性

针对界面切应力协同下受热过冷层流液膜流动的破断过程, 建立了不同气液流向下的临界液膜厚度和最小润湿量的理论模型, 分析了不同驱动力作用下, 接触角、流体温度、界面切应力和壁面热流密度对液膜破断特性的影响. 研究表明: 临界液膜厚度和最小润湿量均随壁面热流密度的增加而增大; 重力驱动下的接触角影响在不同热流密度下有所不同, 流体温度在不同驱动力下对最小润湿量的影响截然相反; 同向切应力驱动下临界液膜厚度和最小润湿量随切应力增加而减小; 在重力和切应力协同驱动下, 同向切应力对最小润湿量的影响与重力和切应力所起作用的相对大小有关, 反向切应力使得临界液膜厚度和最小润湿量有所增大.      

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.     

Influence of a sureactant on the instability of a falling liquid film

The hydrodynamic instability of a film flow of a weak solution containing a soluble volatile surfactant is investigated. Diffusion of the surfactant in the liquid, its evaporation into the boundary gas medium, and the adsorption and desorption processes in the near-surface layer are taken into account. A system of evolutionary equations is derived and a steady-state solution film flow along a vertical surface and the stability of this flow are investigated for the simultaneous action of body and capillary forces and the Marangoni effect. Hydrodynamic and diffusion instability modes are detected and their properties are investigated for constant and variable surfactant concentration in the adsorbed sublayer. Moscow, Madrid. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 56–67, July–August, 2000. The work was carried out with support from the Russian Foundation for Basic Research (project No. 97-01-00153) and the Spanish Ministry of Higher Education (program DGICYT (Spain), project No. PB 96-599).     

Linear instability of ultra-thin liquid films flowing down cylindrical fibre

The stability characteristics of an ultra-thin layer of a viscous liquid flowing down a cylindrical fibre are investigated by a linear theory. The film with the thickness less than 100 nm is driven by an external force and under the influence of the van der Waals forces. The results show that, when the relative film thickness decreases, the curvature of the fibre depresses the development of the linear perturbations, whereas the van der Waals forces promote the instabilities. This competition results in a non-monotonous dependence of the growth rate on the relative film thickness. The critical curves are also obtained to describe the transition from the absolute instability to the convective instability, indicating that the van der Waals forces can enlarge the absolutely unstable region. Furthermore, the surface tension can cause the development of the absolute instability, whereas the external force has an opposite effect.     

Linear instability of ultra-thin liquid films flowing down cylindrical fibre

The stability characteristics of an ultra-thin layer of a viscous liquid flowing down a cylindrical fibre are investigated by a linear theory. The film with the thickness less than 100 nm is driven by an external force and under the influence of the van der Waals forces. The results show that, when the relative film thickness decreases, the curvature of the fibre depresses the development of the linear perturbations, whereas the van der Waals forces promote the instabilities. This competition results in a non-monotonous dependence of the growth rate on the relative film thickness. The critical curves are also obtained to describe the transition from the absolute instability to the convective instability, indicating that the van der Waals forces can enlarge the absolutely unstable region. Furthermore, the surface tension can cause the development of the absolute instability, whereas the external force has an opposite effect.     

Experimental evaluation of Marangoni stress and surfactant concentration at interface of contaminated single spherical drop using spatiotemporal filter velocimetry

Spatiotemporal filter velocimetry (SFV) was extended to Lagrangian measurements with boundary-fitted measurement areas, and was applied to flows about single spherical drops of glycerol-water solution falling in stagnant silicon oil under clean and contaminated conditions to examine its applicability to the estimation of the Marangoni stress and surfactant concentration at a moving interface. Effects of bulk concentration of surfactant on the velocity field, the Marangoni stress and the surface concentration of surfactant were discussed from the measured data. As a result, we confirmed that accurate velocity distribution in the vicinity of the interface measured by SFV enables us to evaluate interfacial velocity and interfacial shear stresses and to estimate the Marangoni stress, interfacial tension and surfactant concentration at the interface with the assumption of negligible surface viscosity. The flow inside the drop and the interfacial velocity become weak due to the Marangoni stress caused by the gradient of surfactant concentration at the interface as the bulk concentration of surfactant increases. These results demonstrate that SFV is of great use in experimental analysis of adsorption and desorption kinetics at a moving interface.     

Measurements of the stabilisation of liquid film flow by the soluble surfactant sodium dodecyl sulfate (SDS)

Gravity-driven film flow of aqueous solutions of SDS is studied experimentally and the evolution of small-amplitude, regular inlet disturbances is investigated. With the addition of SDS, strong attenuation of non-linear growth is observed, with traveling waves remaining relatively small in height and near-sinusoidal over an impressive parametric range. The critical Reynolds number of the primary instability rises by an order of magnitude. Maximum stabilization is observed at small surfactant loadings (characterized by surface tension 60–65 mN/m) and the critical Reynolds number gradually decreases with further addition of surfactant. Observations are interpreted by the competing effects of surface elasticity -which increases with the adsorbed SDS and intensifies Marangoni stresses- and surfactant mass transfer between bulk and interface -which also increases with the amount of SDS and mitigates interfacial gradients and Marangoni stresses.     

Interfacial slippage effect on the spontaneous instability of soft thin viscoelastic films

Based on the continuum mechanics and the bifurcation theory, a three-dimensional theoretical model for a soft thin viscoelastic film bonded to a rigid substrate is investigated. Considering the effect of interfacial slippage and the competition among van der Waals interaction potential energy, strain energy, and surface energy, a set of three-dimensional governing equations of the spontaneous instability is derived, and the analytical results of time-dependent critical conditions are obtained. Furthermore, the phase diagram of instability due to van der Waals interaction and the variation of the dimensionless characteristic wavenumber and the critical interaction stiffness with the critical time are discussed by considering the effect of interfacial slippage.     

Weakly nonlinear stability analysis of a falling film with countercurrent gas flow

Weakly nonlinear stability analysis of a falling film with countercurrent gas–liquid flow has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear and nonlinear stability solutions for the film flow system. The results show that both supercritical stability and subcritical instability are possible for a film flow system when the gas flows in the countercurrent direction. The stability characteristics of the film flow system are strongly influenced by the effects of interfacial shear stress when the gas flows in the countercurrent direction. The effect of countercurrent gas flow in a falling film is to stabilize the film flow system.