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.     

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.      

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.     

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.     

Evaporation of Falling and Shear-Driven Thin Films on Smooth and Grooved Surfaces

One of the most important tasks in development of modern gas turbine combustors is the reduction of NO_x emissions. An effective way to reduce the NO_x emission is using the lean premixed prevaporization (LPP) concept. An important phenomenon taking place in LPP chambers is the evaporation of thin fuel films. To increase the fuel evaporation rate, the use of microstructured walls has been suggested. The wall microstructures make use of the capillary forces to evenly distribute the liquid fuel over the wall, so that the appearance of uncontrolled dry patches can be avoided. Moreover, the wall structures promote the thin film evaporation characterized by ultra-high evaporation rates. An experimental setup was built for the investigation of thin liquid films falling down on the outer surface of vertical tubes with either a smooth or structured surface. In the first testing phase water is used, fuel like liquids will be used later on. The thin film can be heated from both sides, by hot oil flowing inside the tube, and by hot compressed air flowing in co-current direction to the thin film. The film is partly evaporated along the flow. Results for the wavy film structure at different Reynolds numbers are reported. For theoretical investigations a model describing the hydrodynamics and heat transfer due to evaporation of the gravity- and shear-driven undisturbed liquid film on structured surfaces was developed. For low Reynolds numbers or low liquid mass fluxes the wall surface is only partly covered with liquid and the heat transfer is shown to be governed by the evaporation of the ultra-thin film in the vicinity of the three-phase contact line. A numerical model for the solution of a two-dimensional free-surface flow of a liquid film over a structured wall was also developed. The Navier–Stokes equations are solved using the Volume of Fluid (VOF) technique. The energy equation is included in the model. The model is verified by comparison with data from the literature showing favorable agreement. In particular, the proposed model predicts the formation of capillary waves observed in the experiments. The model is used to investigate the flow of liquid on a structured wall. This calculation is the first step towards the modeling of a three-dimensional wavy flow of a gravity- and shear-driven film along a wall with longitudinal grooves. It is found that due to the Marangoni effect, a circulating flow arises within the cavity, thereby leading to an enhancement in the evaporation rate.     

Simulation and measurement of 3D shear-driven thin liquid film flow in a duct

Three-dimensional flow behavior of thin liquid film that is shear-driven by turbulent air flow in a duct is measured and simulated. Its film thickness and width are reported as a function of air velocity, liquid flow rate, surface tension coefficient, and wall contact angle. The numerical component of this study is aimed at exploring and assessing the suitability of utilizing the FLUENT-CFD code and its existing components, i.e. Volume of Fluid model (VOF) along with selected turbulence model, for simulating the behavior of 3D shear-driven liquid film flow, through a comparison with measured results. The thickness and width of the shear-driven liquid film are measured using an interferometric technique that makes use of the phase shift between the reflections of incident light from the top and bottom surfaces of the thin liquid film. Such measurements are quite challenging due to the dynamic interfacial instabilities that develop in this flow. The results reveal that higher air flow velocity decreases the liquid film thickness but increases its width, while higher liquid flow rate increases both its thickness and width. Simulated results provide good estimates of the measured values, and reveal the need for considering a dynamic rather than a static wall contact angle in the model for improving the comparison with measured values.     

Dislocation core spreading at interfaces between metal films and amorphous substrates

Experiments with transmission electron microscopy have shown that in a strong electron beam the contrast of dislocations may gradually disappear at an incoherent interface between a metal thin film and an amorphous substrate. There are reasons to believe that this phenomenon is caused by radiation-induced dislocation core spreading at the interface. A quantitative model accounting for this effect will be necessary for a better understanding of dislocation structures and plastic deformation in metal thin films. As a first step toward this objective, we develop a number of mathematical solutions for dislocation core spreading at an incoherent interface. For simplicity, we consider screw dislocations, and consider the interface to be characterized by a shear adhesive strength, τ₀, below which no core spreading occurs, and above which spreading takes place in a viscous manner. We determine the final equilibrium core width and the rate of core spreading for single or planar arrays of dislocations in a homogeneous bulk material or at the interface between a thin film and a semi-infinite substrate where the film and substrate may have the same, or different, elastic constants. Some of our solutions are analytic and others are based on an implicit finite difference method with a Gauss-Chebyshev quadrature scheme. The phenomenon of dislocation core spreading is expected to have a dramatic effect on the strength of crystalline films deposited on amorphous substrates.     

On the spreading radius of surface tension driven oil on deep water

The spread of a thin oil film by surface tension gradients from an oil source of unlimited mass on deep water is considered. A similarity solution for the velocity fields of the oil and water, the oil thickness and the rate at which each grow is obtained both for axisymmetric and the previously explored planar spreading. The dimensionless size of the spread, which is oil type independent, is shown to be 1.0754 and 1.4150 for axisymmetric and planar spreading respectively. It is further shown that the oil film equation of state, which relates surface tension to oil thickness, is unique to each oil or oil-surfactant mixture.     

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     

A new solution for the rotation-driven spreading of a thin fluid film

Lie groups are used to solve the equation governing the flow of a thin liquid film subject to centrifugal spreading and viscous resistance. A new implicit solution is found. It is shown how this relates to the previous known solutions for the spreading of an initially flat film, the steady state and a separable solution. New permissible forms for the film evolution are also studied, including solutions exhibiting finite time blow-up. Near the contact line, where the film height tends to zero, an approximate explicit solution is obtained which may be used to describe a film with any size contact angle.     

Microchannel membrane separation applied to confined thin film desorption

The concept of a confined thin film to enhance the desorption process is based on a reduced mass diffusion resistance. A wide thin film is formed into a microchannel by using a porous membrane as one wall of the channel enabling vapor extraction along the flow. Heat added to the channel results in vapor generation and subsequent extraction through the membrane. This experimental study investigates the performance of vapor extraction as a function of confined thin film thickness, pressure difference across the membrane and inlet concentration to the microchannel. In addition, heat added to the system was varied and results are presented in terms of the wall superheat temperature relative to the inlet saturated conditions of the binary fluid. The test section was equipped with a transparent window to observe bubble formation and vapor extraction. Results show that the performance, measured by the vapor release rate, increases for reduced channel thickness, for increased pressure difference across the membrane, and for lower inlet concentration. Results show that lower wall superheat correspond to higher heat transfer coefficients. Trends of Nusselt number and Sherwood number versus both channel Reynolds number and the product of the Reynolds number and Schmidt number are presented. Bubble formation in the channel does not degrade overall performance provided a critical heat flux condition does not occur.     

Magnetohydrodynamic Rayleigh problem for magnetic prandtl number close to one

Summary In this paper the solutions for indicial motion of an infinite flat plate are discussed. It is assumed that the fluid is incompressible and has constant viscosity and electric conductivity. It is also assumed that both the solid and fluid are semi-infinite or that the solid is thin with fluids on both sides. The conductivity of the wall is assumed in one case to be much greater than the conductivity of the fluid and in a second case to be much less than that of the fluid. In the limit the first case corresponds to a perfectly conducting wall; the second, to a perfectly insulated wall. The distributions of the velocity, magnetic field current, and vorticity are calculated. In the case where the magnetic diffusivity becomes larger than the viscous diffusivity, we show that there is a spreading of the layer in which the magnetic field changes and also a shrinking of the viscous layer. Both layers are very thick in comparison with the non-magneto-hydrodynamic case. This is due to diffusion of the Alfvén wave carrying the vorticity and the current.     

Dynamic contact angle for etting of a surface by a van der waals fluid

We consider the creeping motion of a thin layer of a nonvolatile viscous fluid spreading due to capillary forces over a rigid surface covered by a thin homogeneous film (microfilm). The influence of van der Waals forces on the asymptotic slope of the free boundary of the layer is studied in the region of large thickness, where capillary forces dominate. A solution of the problem of the slope angle is obtained for the entire possible range of the microfilm thickness. In the limit of small thickness of the microfilm, this solution is in agreement with the well-known solution of the problem of the dynamics of wetting of a dry surface in the presence of a precursory film and van der Waals forces. The role of the condition at the end of the precursory film is studied. Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences. Tyumen' 625000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika. Vol. 41, No. 4, pp. 101–105, July–August. 2000.     

The flow of thin liquid films around corners

Situations arise where it is required to strip a moving liquid film from a boundary wall. The need to sample wet steam isokinetically is one such situation. Equally it is sometimes desirable for a film not to separate from a boundary wall as in, for example, liquid separators. A theoretical analysis is developed to examine the radial stress distribution within a uniformly thin liquid film flowing around a sharp bend of fixed radius. The results of the analysis are discussed in the light of experimental observations. The controlling parameters in the film flow are identified and are evaluated for a given situation.     

Wavy wall influence on the hydrodynamic instability of a liquid film flowing along an inclined plane

The film dynamic of a thin liquid along an inclined and wavy wall was numerically depicted in a weighted-residual integral boundary layer equation. A qualitative and quantitative analysis was initially carried out and accurate comparisons were obtained from experimental data on film instability along a flat and inclined as well as a wavy wall. To pinpoint the effect of waviness on film instability, 20 wavy wall periods in the computational CFD domain were considered. Several waviness parameters were studied and shown to have taken on a major role in the film instability process. Finally, a wide range of main wall inclination angles was taken into account, and consequent numerical data permitted identification of a threshold angle value. For wall angles higher than the threshold angle, the film behaved as though no corrugations were present. For lower angles, the film was repeatedly altered during the acceleration and deceleration phases.     

Heat transfer in droplet-laden turbulent channel flow with phase transition in the presence of a thin film of water

We present results of a numerical study of turbulent droplet-laden channel flow with phase transition. Previous studies of the same system did not take into account the presence of gravity. Here, we do so introducing a thin film of water at the bottom wall and permitting droplets to fall into and merge with it. We treat the carrier phase with the Eulerian approach. Each droplet is considered separately in the Lagrangian formulation, adopting the point–particle approximation. We maintain the film thickness constant by draining water from the bottom wall to compensate for (a) the droplets that fall onto the film and (b) evaporation/condensation. We also maintain on average the total mass of water in the channel by inserting new droplets at the top wall to compensate for the water that has been drained from the bottom wall. We analyze the behavior of the statistically averaged gas and droplet quantities focusing on the heat exchange between the two phases. We increase (a) the initial droplet diameter keeping the same initial droplet volume fraction and (b) the initial number of droplets in the channel keeping their diameter the same. In both parameter studies we find that droplets grow less than in the reference case. In case (a) this is explained by the larger velocity with which they travel to the bottom wall and in case (b) by the lower rate of condensation of vapor due to the presence of neighboring droplets.     

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.     

The slow rotation of an axisymmetric solid submerged in a fluid with a surfactant surface layer—II. The rotating solid in a bounded fluid

This paper extends the work in Shail (1979) on the problem of an axisymmetric submerged solid rotating slowly and steadily in a fluid whose surface is covered with a surfactant film. The bulk fluid is of finite extent, and both asymptotic and numerical results (the latter in the case of a thin circular disk) are given for boundary effects on the resistive torque and surface velocity profile when the container is a right circular cylinder and the fluid is of finite depth.     

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.