STABILITY OF ULTRATHIN LIQUID FILM EVOLUTION WITH SURFACTANT

针对固体基底上厚度小于100 nm的含活性剂超薄液膜演化过程, 基于润滑理论推导出包含分离压影响的液膜厚度和活性剂浓度的演化方程, 采用正则模态法导出了描述液膜线性稳定性的特征方程, 分析了多个特征参数对线性稳定性的影响, 数值模拟了液膜厚度和活性剂浓度演化历程, 对比了模拟所得非线性结果与线性分析预测结果的一致性.结果表明:范德华力具有促进扰动增长的作用, 较强的玻恩斥力促使扰动衰减, 使液膜趋于稳定;较小的毛细力数易使液膜凹陷处发生二次失稳, 并最终导致去润湿现象发生;液膜厚度和溶于液膜内部的活性剂浓度初值越大, 液膜稳定性越强, 液膜表面活性剂浓度影响则相反;增大吸附系数不利于液膜稳定性.     

Effect of surfactants on liquid loading in vertical wells

Most gas wells produce some amount of liquid. The liquid is either condensate or water. At high rates, the gas is able to entrain liquid to the surface; however, as gas well depletes, the liquid drops back in a gas well (called liquid loading) creating a back pressure on the reservoir formation. Addition of surfactants to the well to remove liquid is one of the common methods used in gas wells. Liquid loading in vertical gas wells with and without surfactant application was investigated in this study. Anionic, two types of amphoteric (amphoteric I and amphoteric II), sulphonate and cationic surfactants were tested in 2-inch and 4-inch 40-feet vertical pipes. Pressure gradient and liquid holdup are measured. Visual observation with a high speed camera was used to gain insight into the direction of foam flow in intermittent flow and foam film flow under annular flow conditions.Liquid loading is initiated when the liquid film attached to the wall in annular flow starts flowing downwards. Introduction of foam causes the gas velocity at which film reversal occurs to decrease; this shift increases with increasing surfactant concentration and it is more pronounced in 2-inch pipe than in 4-inch pipe. That is, the benefit of surfactants is much more pronounced in 2-inch pipe than in 4-inch pipe. The reason for postponement of liquid loading is reduction in the liquid holdup at low gas velocities which reduces the liquid holdup in foam flow compared to air-water flow. However, at higher gas velocities, the pressure drop in 2-inch compared to 4-inch pipe increases rapidly as the surfactant concentration increases. The selection of optimum concentration of the surfactant is a balance between the reductions in the gas velocity at which liquid loading occurs compared to increase in the frictional loss as the concentration increases. We provide guidelines about the selection of the surfactant concentration.Visual observations using high speed camera show differences in the behavior under foam flow conditions. Unlike air-water flow, the liquid film attached to the wall is replaced by thick foam capturing the gas bubbles. The type of roll waves which carry the liquid in 2-inch pipe is different than what was observed in 4-inch pipe. Compared to 4-inch pipe, the roll waves in 2-inch pipe are much thicker. This partly explains the differences in 2-inch versus 4-inch pipe behavior.     

Numerical study of condensing a small concentration of vapour inside a vertical tube

The purpose of this study is to analyse the combined heat and mass transfer of liquid film condensation from a small steam–air mixtures flowing downward along a vertical tube. Both liquid and gas stream are approached by two coupled laminar boundary layer. An implicit finite difference method is employed to solve the coupled governing equations for liquid film and gas flow together with the interfacial matching conditions. The effects of a wide range of changes of three independent variables (inlet pressure, inlet Reynolds number and wall temperature) on the concentration at exit tube, local Nusselt and Sherwood numbers, film thickness, accumulated condensate rate and temperature are carefully examined. The numerical results indicate that in the case of condensing a small concentration of vapours from a mixture, the resistance to heat and mass transfer by non-condensable gas becomes very intense. The comparisons of average Nusselt number and local condensate heat transfer coefficient with the literature results are in good agreement.     

Fundamentals of a liquid (soap) film tunnel

 The continuously running liquid film tunnel (LFT) is a novel device suitable for the study of two-dimensional flows. In this innovation, the films start from a reservoir, run over a horizontal or non-horizontal wire frame and get pulled/washed by a water sheet or by gravity of liquid film. How-ever, despite the simple design and widespread application of LFT, its working mechanisms are not well understood. In the present work, an experimental effort for explaining these mechanisms is reported. The results show that both film velocities and film flow rates increase with water sheet velocity up to a saturation level. This behavior is described via a force balance between the shear force produced by the water sheet and the opposing pulling force of reservoir and boundary layer frictions. The results also show that the average film thickness depends on the surfactant concentration. This is as predicted by a model based on Langmuir’s adsorption theory, in which the liquid film contains two external monolayers of surfactant and a slab of surfactant solution in between. When a film is drawn from the reservoir to the water sheet, the surfactant molecules start migrating from the former to the latter. To restore the thermodynamic equilibrium, the dragged film pulls more surfactant due to Marangoni elasticity, and thus a flow is established. The film flow soon reaches an equilibrium rate as required by the force balance mentioned above. Received: 15 August 1996/Accepted: 12 November 1996     

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.     

A two-phase boundary-layer model for laminar mixed-convection condensation with a noncondensable gas on inclined plates

A finite-volume-based numerical model for mixed-convection laminar film condensation from a flowing mixture of a vapor and a heavier noncondensable gas on inclined isothermal flat plates is presented. The full boundary layer equations for the liquid film and the vapor-gas mixtures (including liquid inertia and energy convection terms) are solved implicitly with appropriate liquid-mixture interface conditions. Results were obtained for three mixtures, covering wide ranges of liquid Prandtl number and free-stream gas concentration in the forced-convection, mixed-convection and free-convection flow regimes. The effects of liquid inertia were found to be significant only for low-Prandtl-number fluids and lower gas concentrations. The effects of liquid energy convection were found to be significant only for high-Prandtl-number fluids and to be most significant for mixed-convection condensation. Received on 3 March 1998     

Measurement of the liquid film thickness in micro tube slug flow

Slug flow is one of the representative flow regimes of two-phase flow in micro tubes. It is well known that the thin liquid film formed between the tube wall and the vapor bubble plays an important role in micro tube heat transfer. In the present study, experiments are carried out to clarify the effects of parameters that affect the formation of the thin liquid film in micro tube two-phase flow. Laser focus displacement meter is used to measure the thickness of the thin liquid film. Air, ethanol, water and FC-40 are used as working fluids. Circular tubes with five different diameters, D = 0.3, 0.5, 0.7, 1.0 and 1.3 mm, are used. It is confirmed that the liquid film thickness is determined only by capillary number and the effect of inertia force is negligible at small capillary numbers. However, the effect of inertia force cannot be neglected as capillary number increases. At relatively high capillary numbers, liquid film thickness takes a minimum value against Reynolds number. The effects of bubble length, liquid slug length and gravity on the liquid film thickness are also investigated. Experimental correlation for the initial liquid film thickness based on capillary number, Reynolds number and Weber number is proposed.     

Numerical study of evaporation by mixed convection of a binary liquid film flowing down the wall of two coaxial cylinders

Evaporation by mixed convection of a binary liquid film flowing down the external wall of a vertical cylinder has been investigated numerically. Two cases were considered: one where the cylinder wall is soaked with a liquid, and another where a liquid film flows along this wall. Heat, mass and momentum transfer in the liquid film and the vapor phase are modelled by mixed convection equations. In order to locate the liquid–vapor interface, a suitable coordinate transformation is carried out with suitable variables. The discretization of the dimensionless equations by an implicit difference scheme leads to a system of algebraic equations, which are solved by using Gauss algorithm for the momentum conservation equations and Thomas algorithm for the energy and diffusion conservation equations. The film thickness is calculated by the Newtons method. Results show, in particular, that the film thickness cannot be neglected and that the latent heat transfers are increasingly significant as the liquid film components become more volatile.     

Quasi-steady-state flows in a liquid film in a gas: Comparison of two methods of describing waves

The motion of thin films of a viscous incompressible liquid in a gas under the action of capillary forces is studied. The surface tension depends on the surfactant concentration, and the liquid is nonvolatile. The motion is described by the well-known model of quasi-steady-state viscous film flow. The linear-wave solutions are compared with the solution using the Navier-Stokes equations. Situations are studied where a solution close to the inviscid two-dimensional solutions exists and in the case of long wavelength, the occurrence of sound waves in the film due to the Gibbs surface elasticity is possible. The behavior of the exact solutions near the region of applicability of asymptotic equations is studied, and nonmonotonic dependences of the wave characteristics on wavenumber are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 103–111, May–June, 2007.     

Influence of coolant injector configuration on film cooling effectiveness for gaseous and liquid film coolants

An experimental investigation is conducted to bring out the effects of coolant injector configuration on film cooling effectiveness, film cooled length and film uniformity associated with gaseous and liquid coolants. A series of measurements are performed using hot air as the core gas and gaseous nitrogen and water as the film coolants in a cylindrical test section simulating a thrust chamber. Straight and compound angle injection at two different configurations of 30°–10° and 45°–10° are investigated for the gaseous coolant. Tangential injection at 30° and compound angle injection at 30°–10° are examined for the liquid coolant. The analysis is based on measurements of the film-cooling effectiveness and film uniformity downstream of the injection location at different blowing ratios. Measured results showed that compound angle configuration leads to lower far-field effectiveness and shorter film length compared to tangential injection in the case of liquid film cooling. For similar injector configurations, effectiveness along the stream wise direction showed flat characteristics initially for the liquid coolant, while it was continuously dropping for the gaseous coolant. For liquid coolant, deviations in temperature around the circumference are very low near the injection point, but increases to higher values for regions away from the coolant injection locations. The study brings out the existance of an optimum gaseous film coolant injector configuration for which the effectiveness is maximum.     

Lattice Boltzmann study of the interaction between a single solid particle and a thin liquid film

The isothermal single-component multi-phase lattice Boltzmann method(LBM) combined with the particle motion model is used to simulate the detailed process of liquid film rupture induced by a single spherical particle.The entire process of the liquid film rupture can be divided into two stages.In Stage 1,the particle contacts with the liquid film and moves into it due to the interfacial force and finally penetrates the liquid film.Then in Stage 2,the upper and lower liquid surfaces of the thin film are driven by the capillary force and approach to each other along the surface of the particle,resulting in a complete rupture.It is found that a hydrophobic particle with a contact angle of 106.7° shows the shortest rupture duration when the liquid film thickness is less than the particle radius.When the thickness of the liquid film is greater than the immersed depth of the particle at equilibrium,the time of liquid film rupture caused by a hydrophobic particle will be increased.On the other hand,a moderately hydrophilic particle can form a bridge in the middle of the liquid film to enhance the stability of the thin liquid film.     

Measurement of liquid film thickness in a micro parallel channel with interferometer and laser focus displacement meter

In the present study, liquid film thicknesses in parallel channels with heights of H = 0.1, 0.3 and 0.5 mm are measured with two different optical methods, i.e., interferometer and laser focus displacement meter. Ethanol is used as a working fluid. Liquid film thicknesses obtained from two optical methods agree very well. At low capillary numbers, dimensionless liquid film thickness is in accordance with Taylor’s law. However, as capillary number increases, dimensionless liquid film thickness becomes larger than Taylor’s law for larger channel heights. It is attributed to the dominant inertial effect at high capillary numbers. Using channel height H for dimensionless liquid film thickness δ₀/H and hydraulic diameter D_h = 2H as the characteristic length for Reynolds and Weber numbers, liquid film thickness in a parallel channel can be predicted well by the circular tube correlation previously proposed by the authors. This is because curvature differences between bubble nose and flat film region are identical in circular tubes and parallel channels.     

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.      

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.     

Untersuchung der laminaren Zweistoffgrenzschichtströmung längs eines verdunstenden Flüssigkeitsfilms

A contribution for clarifying the physical process in the evaporating part of a film-evaporation combustion-chamber is presented. Experimental and theoretical investigations are carried out for a flat vaporizing liquid film. The binary laminar boundary-layer flow including heat and mass transfer is calculated taking into account variable fluid properties. It is shown analytically and numerically and confirmed by the experiments, that the equations for momentum, energy and mass concentration yield “similar solutions” and that furthermore a 1/√x?law for the local evaporation velocity and a constant distribution of temperature and mass concentration at the film surface is obtained. The boundary-layer parameters and the influence of evaporation mass-flow are computed. A comparison with the experimental results shows good agreement.     

Numerical simulation of annular two-phase flow considering the four involved mass transfers

In the present study, a numerical model is developed for simulation of annular two-phase flow considering bubbly flow regime in the liquid film along with the four involved mechanisms of mass transfer those are evaporation, entrainment, deposition and condensation. In the numerical approach, liquid film accompanied by fine nucleated bubbles are simulated with innovative model named suction model, the whole domain containing liquid film and the vapor core is simulated by volume of fluid model. While the vapor and the entrained droplets are treated as homogeneous flow. The interface between the liquid and the vapor is traced by level set formulation. The model is then validated by experimental models of Lee & Lee and Stevanovic et al. and shows a good precision such that it predicts the experimental results of Stevanivic et al. Better than their own numerical model. This issue is due to the least possible simplifying assumptions along with considering the effect of boiling in liquid film and all mechanisms of mass transfer in the fluid flow.     

Dispersion in annular climbing film flow

The dispersion of a tracer injected as a pulse into a climbing liquid film is investigated for a series of water and air flow rates, and for a number of different electrolyte tracers. It is found that at all flow rates the observed concentration distribution depends on the nature of the tracer. This observation is explained in terms of two effects: molecular diffusion in a viscous sub-layer and ion fractionation associated with droplet formation at the gas-liquid interface. The overall dispersive characteristics of the system are described in terms of a mathematical model assuming dispersed plug flow in both the film and entrained droplets with interchange between these phases. This model is fitted to experimental tracer concentration distributions using a non-linear least-squares regression procedure. The parameter values obtained from the fitting procedure are studied to determine trends with flow rates and tracer properties. Values for a film dispersion parameter, $\text{P}{}_{\mathrm{f}}$, are found to correlate significantly with the molecular diffusion coefficients of the tracers. Consistent values for an ion fractionation coefficient, $\text{k}{}_{\mathrm{if}}$, are also obtained.     

Primary instabilities of liquid film flow sheared by turbulent gas stream

Evolution of excited waves on a viscous liquid film has been investigated experimentally for the annular gas–liquid flow in a vertical tube. For the first time the dispersion relations are obtained experimentally for linear waves on liquid film surface in the presence of turbulent gas flow. Both cocurrent and countercurrent flow regimes are investigated. As an example of comparison with theory, the experimental data are compared to the results of calculations based on the Benjamin quasi-laminar model for turbulent gas flow. The calculation results are found to be in good agreement with experiments for moderate values of film Reynolds number.     

Simultaneous entrainment of oil and water droplets in high Reynolds number gas turbulence in horizontal pipe flow

We develop a 1D cross sectional concentration profile model for oil and water droplets that coexist in the turbulent gas phase (of Re ∼ 10⁶) in near horizontal stratified pipe flows. Entrainment of the oil and water mixture from a liquid film near the bottom of the pipe into the gas is modeled based on earlier single-fluid entrainment correlations. A Gamma distribution for the droplet sizes based on the breakup of liquid filaments, is adopted. An explicit algebraic–exponential formula for the total concentration profile for either phase can then be derived.     

Convective heat and mass transfer from a falling film to a laminar gas stream

A numerical study has been made of convective heat and mass transfer from a falling film to a laminar gas stream between vertical parallel plates. The effects of gas-liquid phase coupling, variable thermophysical properties, and film vaporization have been considered. Simultaneous mass, momentum and heat transfer between liquid film and gas stream is numerically studied by solving the respective governing equations for the liquid film and gas stream together. The influences of the inlet liquid temperature and liquid flowrate on the cooling of liquid film are examined for air-water and air-ethanol systems. Results show that the heat transfer from the gas-liquid interface to the gas stream is predominantly determined by the latent heat transfer connected with film evaporation. Additionally, better liquid film cooling is noticed for the system having a higher inlet liquid temperature or a lower liquid flowrate.