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Showing papers on "Marangoni effect published in 2009"


Journal ArticleDOI
TL;DR: In this article, the formation of deposits during the drying of nanoliter colloidal drops on a flat substrate is investigated numerically and experimentally, and a finite element numerical model is developed that solves the Navier-Stokes, heat and mass transport equations in a Lagrangian framework.
Abstract: An efficient way to precisely pattern particles on solid surfaces is to dispense and evaporate colloidal drops, as for bioassays The dried deposits often exhibit complex structures exemplified by the coffee ring pattern, where most particles have accumulated at the periphery of the deposit In this work, the formation of deposits during the drying of nanoliter colloidal drops on a flat substrate is investigated numerically and experimentally A finite-element numerical model is developed that solves the Navier–Stokes, heat and mass transport equations in a Lagrangian framework The diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet–air interface Laplace stresses and thermal Marangoni stresses are accounted for The particle concentration is tracked by solving a continuum advection–diffusion equation Wetting line motion and the interaction of the free surface of the drop with the growing deposit are modeled based on criteria on wetting angles Numerical results for evaporation times and flow field are in very good agreement with published experimental and theoretical results We also performed transient visualization experiments of water and isopropanol drops loaded with polystyrene microspheres evaporating on glass and polydimethylsiloxane substrates, respectively Measured evaporation times, deposit shapes and sizes and flow fields are in very good agreement with the numerical results Different flow patterns caused by the competition of Marangoni loops and radial flow are shown to determine the deposit shape to be either a ring-like pattern or a homogeneous bump

297 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a pragmatic engineering model to study aspects of the SLM process using an enthalpy formulation and accounting for shrinkage and laser light penetration, and investigate the importance of evaporation for a set of process parameters relevant to production.

271 citations


Journal ArticleDOI
TL;DR: In this article, a small droplet of water sitting on top of a heated superhydrophobic surface is considered, and a toroidal convection pattern develops in which fluid is observed to rise along the surface of the spherical droplet and to accelerate downwards in the interior towards the liquid/solid contact point.
Abstract: We consider a small droplet of water sitting on top of a heated superhydrophobic surface. A toroidal convection pattern develops in which fluid is observed to rise along the surface of the spherical droplet and to accelerate downwards in the interior towards the liquid/solid contact point. The internal dynamics arise due to the presence of a vertical temperature gradient; this leads to a gradient in surface tension which in turn drives fluid away from the contact point along the interface. We develop a solution to this thermocapillary-driven Marangoni flow analytically in terms of streamfunctions. Quantitative comparisons between analytical and experimental results, as well as effective heat transfer coefficients, are presented.

153 citations


Journal ArticleDOI
TL;DR: In this paper, a series of experiments performed in a cylindrical PVT-cell at a pressure range of pi 10-50 bar, where a fixed volume of CO2 gas was brought into contact with a column of distilled water, was shown that the mass transfer rate across the interface is much faster than that predicted by Fickian diffusion and increases with increasing initial gas pressure.
Abstract: Concern over global warming has increased interest in quantification of the dissolution of CO2 in (sub-)- surface water. The mechanisms of the mass transfer of CO2 in aquifers and of transfer to surface water have many common features. The advantage of experiments using bulk water is that the underlying assumptions to the quantify mass-transfer rate can be validated. Dissolution of CO2 into water (or oil) increases the density of the liquid phase. This density change destabilizes the interface and enhances the transfer rate across the interface by natural convection. This paper describes a series of experiments performed in a cylindrical PVT- cell at a pressure range of pi ) 10-50 bar, where a fixed volume of CO2 gas was brought into contact with a column of distilled water. The transfer rate is inferred by following the gas pressure history. The results show that the mass-transfer rate across the interface is much faster than that predicted by Fickian diffusion and increases with increasing initial gas pressure. The theoretical interpretation of the observed effects is based on diffusion and natural convection phenomena. The CO2 concentration at the interface is estimated from the gas pressure using Henry's solubility law, in which the coefficient varies with both pressure and temperature. Good agreement between the experiments and the theoretical results has been obtained. tion of CO2 in the atmosphere, geological storage of CO2 is considered. 2-4 When CO2 is injected into an aquifer, the competition between viscous, capillary, and buoyancy forces determines the flow pattern. Eventually, due to buoyancy forces CO2 will migrate upward and be trapped under the cap rock due to capillary forces. In this case an interface between a CO2- rich phase and brine exists. Subsequently, CO2 starts to dissolve into water by molecular diffusion when it is in contact with the brine. The dissolution of CO2 increases the density of brine. 5 This density increase together with temperature fluctuations in the aquifer (which may be only partially compensated by pressure gradients 6 ) destabilize the CO2-brine interface and accelerate the transfer rate of CO2 into the brine by natural convection. 5-10 The occurrence of natural convection signifi- cantly increases the total storage rate in the aquifer since convection currents bring the fresh brine to the top. Hence, the quantification of CO2 dissolution in water and understanding the transport mechanisms are crucial in predicting the potential and long-term behavior of CO2 in aquifers. Unfortunately there are only a few experimental data in the literature, involving mass transfer between water and CO2 under elevated pressures. Weir et al. 11 were the first to point out the importance of natural convection for sequestration of CO2. Yang and Gu 8 performed experiments in bulk where a column of CO2 at high pressure was in contact with water. The procedure was similar to the established approach in which the changes in gas pressure relate the gas to the transfer rate. 12-15 A modified diffusion equation with an effective diffusivity was used to describe the mass-transfer process of CO2 into the brine. Good agreement between the experiments and the model was observed by choosing effective diffusion coefficients 2 orders of mag- nitude larger than the molecular diffusivity of CO2 into water. However, the authors pointed out that the accurate modeling of the experiments should consider natural convection effects. Farajzadeh et al. 9,10 reported experimental results for the same system, in a slightly different geometry, showing initially enhanced mass transfer followed by a classical diffusion behavior in long times. A physical model based on Fick's second law and Henry's law was used to interpret the experimental data. It was found that the mass-transfer process cannot be modeled with a modified Fick's second law with a single effective diffusion coefficient for the CO2-water system at high pressures. Nevertheless, the initial stages and later stages of the experiments can be modeled individually with the described model. Arendt et al. 16 applied a Schlieren method and a three- mode magnetic suspension balance connected to an optical cell to analyze the mass transfer of the CO2-water system up to 360 bar. Good agreement between their model (linear superposi- tion of free conVection and Marangoni convection) and the experiment was obtained. The addition of surfactant suppressed the Marangoni convection in their experiments, while in the experiments of ref 9, addition of surfactant did not have a significant effect on the transfer rate of CO2. A similar mass- transfer enhancement was observed for the mass transfer between a gaseous CO2-rich phase with two hydrocarbons (n- decane and n-hexadecane) 9,10 due to the fact that CO2 increases the hydrocarbon density. 17 The effect becomes less significant with increasing oil viscosity. This has implications for oil recovery. Indeed in geological storage of CO2 the early time behavior is governed by diffusion before the onset of the natural

122 citations


Journal ArticleDOI
TL;DR: In this paper, a three-dimensional heat transfer model is developed to simulate the cladding process that include the different physical phenomena such as heat transfer, phase changes, addition of powder particles and fluid flow due to Marangoni-Rayleigh-Benard convection.

113 citations


Journal ArticleDOI
TL;DR: Theoretical description and numerical simulation of an evaporating sessile drop are developed and several dynamical stages of the convection characterized by different number of vortices in the drop are demonstrated.
Abstract: Theoretical description and numerical simulation of an evaporating sessile drop are developed. We jointly take into account the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the drop, and the diffusion of vapor in air. A shape of the rotationally symmetric drop is determined within the quasistationary approximation. Nonstationary effects in the diffusion of the vapor are also taken into account. Simulation results agree well with the data of evaporation rate measurements for the toluene drop. Marangoni forces associated with the temperature dependence of the surface tension generate fluid convection in the sessile drop. Our results demonstrate several dynamical stages of the convection characterized by different number of vortices in the drop. During the early stage the array of vortices arises near a surface of the drop and induces a nonmonotonic spatial distribution of the temperature over the drop surface. The initial number of near-surface vortices in the drop is controlled by the Marangoni cell size which is similar to that given by Pearson for flat fluid layers. This number quickly decreases with time resulting in three bulk vortices in the intermediate stage. The vortices finally transform into the single convection vortex in the drop existing during about 1/2 of the evaporation time.

105 citations


Journal ArticleDOI
Rafael Tadmor1
15 Apr 2009
TL;DR: A view of the Marangoni effect from the perspectives of all three possible interfaces as motion inducing agents is given.
Abstract: A view of the Marangoni effect from the perspectives of all three possible interfaces as motion inducing agents is given. Arguments are made that it is required and sufficient that surface tension gradient at the substrate surface induce the flow while the liquid vapor surface tension gradient is unable to induce a flow on its own; that the flow is toward a lower interface potential at the wall liquid interface; and that this is an appropriate way of viewing the Marangoni effect is demonstrated with examples.

97 citations


Journal ArticleDOI
16 Feb 2009-Langmuir
TL;DR: The results of the numerical simulations indicate that, depending on the value of system parameters, the droplet exhibits a variety of different behaviours, which include spreading, evaporation-driven retraction, contact line pinning, and "terrace" formation.
Abstract: We consider the dynamics of a slender, evaporating droplet containing nanoparticles. We use lubrication theory to derive a coupled system of equations that govern the film thickness and the concentration of nanoparticles. These equations account for capillarity, Marangoni stresses, evaporation, and disjoining pressure; the nanoparticle-induced structural component of the disjoining pressure is also considered. Contact line singularities are avoided through the adsorption of ultrathin films wherein evaporation is suppressed by the disjoining pressure; a similar approach has recently been used by Ajaev [J. Fluid Mech. 2005, 528, 279-296] who has built on the previous work of Moosman and Homsy [J. Colloid Interface Sci. 1980, 73, 212-223]. The results of our numerical simulations indicate that, depending on the value of system parameters, the droplet exhibits a variety of different behaviours, which include spreading, evaporation-driven retraction, contact line pinning, and "terrace" formation.

95 citations


Journal ArticleDOI
06 Jan 2009-Langmuir
TL;DR: Experimental results where mesoscale 2D well-ordered surface corrugation patterns are formed during solvent evaporation from polystyrene/toluene solutions are presented.
Abstract: Film formation through the drying of polymer solutions is a widely used process in laboratories and in many industrial applications such as coatings. One of the main goals of these applications is to control the film surface morphology. In many cases, evaporation has been found to yield corrugated patterns on the free surface of films. This has been interpreted in terms of either mechanical or hydrodynamic instabilities. In this article, we present experimental results where mesoscale 2D well-ordered surface corrugation patterns are formed during solvent evaporation from polystyrene/toluene solutions. The transformation of Benard-Marangoni instabilities into surface corrugation is studied during the entire drying process using particle tracking, 3D morphology analyses, etc. We show that the corrugation wavelength is controlled by the Benard-Marangoni instability, whereas the corrugation amplitude is controlled by a mechanism that involves a high evaporation rate.

86 citations


Journal ArticleDOI
TL;DR: The generation of directed self-propelled motion of a droplet of aniline oil with a velocity on the order of centimeters per second on an aqueous phase is reported.
Abstract: We report the generation of directed self-propelled motion of a droplet of aniline oil with a velocity on the order of centimeters per second on an aqueous phase. It is found that, depending on the initial conditions, the droplet shows either circular or beeline motion in a circular Petri dish. The motion of a droplet depends on volume of the droplet and concentration of solution. The velocity decreases when volume of the droplet and concentration of solution increase. Such unique motion is discussed in terms of Marangoni-driven spreading under chemical nonequilibrium. The simulation reproduces the mode of motion in a circular Petri dish.

86 citations


Journal ArticleDOI
TL;DR: In this paper, both the experiment and the finite volume method (FVM) are utilized to investigate the thermal phenomena during continuous laser keyhole welding, and it has been found that the shape and size of the molten pool in the workpiece are affected by welding parameters such as welding speed and the incident laser power.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the time evolution of a thin liquid film flowing down a heated solid porous substrate using the Navier-Stokes and Darcy-Brinkman equations in the film and the porous layer.
Abstract: The time evolution of a thin liquid film flowing down a heated solid porous substrate is investigated. Using the Navier–Stokes and Darcy–Brinkman equations in the film and the porous layer, respectively, the problem is reduced to the study of the evolution equation for the free surface of the liquid film derived through a long-wave approximation. A linear stability analysis of the base flow is performed and the critical Reynolds and Marangoni numbers are obtained. A nonlinear analysis using continuation techniques shows that the base flow yields to stationary surface structures ranging from surface waves to large amplitude structures resembling sliding drops or ridges. It is also shown under what conditions the porous layer can be replaced by an effective slip boundary condition at the liquid-solid interface. Then, the corresponding slip length is calculated from the porous layer characteristics (thickness, porosity, and Darcy number).

Journal ArticleDOI
TL;DR: An excellent surfactant mass conservation without any additional mass correction scheme is obtained and the differences in using a linear and a nonlinear equation of state, respectively, on the flow dynamics of a freely oscillating droplet are demonstrated.

Journal ArticleDOI
TL;DR: In this paper, the spreading kinetics of aqueous solutions of sodium dodecyl sulfate and trimethyl ammonium bromide along the interface between thick layers of water and decane has been investigated by means of two different optical visualization techniques (dye tracer and laser shadowgraphy).
Abstract: Marangoni-driven spreading at gas-liquid interfaces has been studied extensively over the past years but so far the spreading kinetics along the interface between immiscible liquids has not been investigated systematically. In this study, the spreading kinetics of aqueous solutions of sodium dodecyl sulfate and dodecyl trimethyl ammonium bromide along the interface between thick layers of water and decane has been investigated by means of two different optical visualization techniques (dye tracer and laser shadowgraphy). The spreading kinetics follows a power law where the radius r as function of time t scales as r(t)∝t3/4 indicating large similarities with Marangoni-driven spreading at air-liquid interfaces. The existing scaling law for spreading at air-liquid interfaces is based on the balance between an interfacial tension gradient and the viscous stress in the fluid layers beneath the interface. When the viscous dissipation in the two boundary layers below and above the interface is factored into the scaling law, quantitative agreement with experimental data is obtained. Marangoni-driven spreading along an interface is a fast transport mechanism. The velocity of the leading edge lies within the range of group velocities of capillary waves.

Journal ArticleDOI
TL;DR: In this paper, a 2D axisymmetric model of a molten pool created by a laser heat source has been developed, which solves the coupled equations of a laminar fluid flow and heat transfer to demonstrate the flow behavior in the pool.
Abstract: A pulse laser (Nd:YAG) interaction with an AZ91 magnesium alloy has been experimentally and numerically studied. A two-dimensional (2D) axisymmetric model of a molten pool created by a laser heat source has been developed. The elaborated model solves the coupled equations of a laminar fluid flow and heat transfer to demonstrate the flow behavior in the pool. This model takes into account the coupled effects of buoyancy and Marangoni forces, the thermophysic variation properties with temperature, and the radiation and convection heat losses. Concerning numerical results, the molten temperature distribution, velocity field and molten shape were discussed. It was noted that the Marangoni flow significantly alters the characteristics of the thawing and solidifying processes, and makes the molten pool wider and shallower. On the other hand, the experimental results showed that the material thermal properties have significant effects on the transport phenomena which takes place in the molten pool, and consequently on the formation as well as the shape of the pool. Finally, a comparison between the numerical and experimental results exhibited a good agreement.

Journal ArticleDOI
TL;DR: In this paper, a theoretical description of the evaporation of sessile drops is proposed and the linear dependency of the rate on droplet's base radius is described as well as the interfacial temperature.

Journal ArticleDOI
TL;DR: In this article, the results of an experimental study of convective instabilities in a horizontal liquid layer with free upper surface under the action of an inclined temperature gradient, i.e., when horizontal and vertical temperature gradients are applied at the same time, are presented.
Abstract: We present the results of an experimental study of convective instabilities in a horizontal liquid layer with free upper surface under the action of an inclined temperature gradient, i.e., when horizontal and vertical temperature gradients are applied at the same time. Silicone oil of 10 cSt (Prandtl number Pr=102) was employed as the test fluid. We investigated the layers with different thicknesses to examine the influence of gravity on the formation of the convective patterns. It is found out that the system behavior appreciably depends on the dynamic Bond number, which shows a relation of buoyancy and thermocapillary forces. In the case of small dynamic Bond numbers, when the influence of buoyancy is minimal, four different flow patterns, according to the combination of the vertical and horizontal Marangoni numbers, have been found: steady parallel flow, Benard–Marangoni cells, drifting Benard–Marangoni cells, and longitudinal rolls. At larger dynamic Bond number, when the influence of buoyancy becomes...

Journal ArticleDOI
TL;DR: In this paper, a model for the interaction between these phases and the surface tension obeys a nonlinear equation of state is developed for the breakup of viscous liquid jets that contain surfactant, that is potentially above the critical micelle concentration.
Abstract: The breakup of viscous liquid jets that contain surfactant, that is potentially above the critical micelle concentration (CMC) is considered here within the long-wave approximation. The soluble surfactant is assumed to be present in three phases: as an interfacial species, bulk monomers and micelles. A model is developed for the interaction between these phases and the surface tension which obeys a nonlinear equation of state. The effects of the equation of state and the reservoir of surfactant created by micelles on breakup are investigated. The long-wave approximation naturally leads to a system of coupled one-dimensional equations that are solved numerically. It is demonstrated that jet breakup and satellite formation are critically affected by the presence of high surfactant concentrations above the CMC. This manifests itself by the formation of unusually large satellites. We present extensive numerical evidence that the mechanism for this phenomenon centres on the interplay between Marangoni stresses and the nonlinear surfactant equation of state; the latter exhibits a plateau at high interfacial concentrations.

Journal ArticleDOI
TL;DR: In this paper, the transient drop rise velocity has been investigated in the system toluene(d)/acetone(s)/water(c) for different initial solute concentrations and different drop diameters.

Journal ArticleDOI
TL;DR: In this article, the impact of Marangoni convection on the extraction efficiency during the drop formation stage is investigated in the system toluene/acetone/water for different initial solute concentrations and different drop diameters.

Journal ArticleDOI
TL;DR: In this article, it was shown that the welding parameters and material properties responsible for the formation of unusual, wavy fusion boundaries can be identified from heat and fluid flow calculations and confirmed by independent experiments.

Journal ArticleDOI
TL;DR: In this paper, the surface deformation of the gas-liquid interface was calculated using the level set approach and coupled with heat-transfer and diffusion equations to obtain more information about the acting forces and the coating development.
Abstract: Pure titanium was treated by free electron laser (FEL) radiation in a nitrogen atmosphere. As a result, nitrogen diffusion occurs and a TiN coating was synthesized. Local gradients of interfacial tension due to the local heating lead to a Marangoni convection, which determines the track properties. Because of the experimental inaccessibility of time-dependent occurrences, finite element calculations were performed, to determine the physical processes such as heat transfer, melt flow, and mass transport. In order to calculate the surface deformation of the gas-liquid interface, the level set approach was used. The equations were modified and coupled with heat-transfer and diffusion equations. The process was characterized by dimensionless numbers such as the Reynolds, Peclet, and capillary numbers, to obtain more information about the acting forces and the coating development. Moreover, the nitrogen distribution was calculated using the corresponding transport equation. The simulations were compared with cross-sectional micrographs of the treated titanium sheets and checked for their validity. Finally, the process presented is discussed and compared with similar laser treatments.

Journal ArticleDOI
TL;DR: In this article, the heat transfer of water and ethanol mixture vapours was investigated on a vertical surface with large and nonhomogeneous temperature gradients, and the authors showed that the local heat transfer coefficients (HTCs) were varied along the surface for the nonhomogenous temperature gradient on condensing surface.

Journal ArticleDOI
TL;DR: In this article, a new flow expansion model for mass transfer is proposed for data analysis, which considers the overall mass transfer coefficient ratio (k 1/k2) which includes diffusion and convection effects instead of the pure ratio of diffusivities (D1/D2) under the condition of growing drops.

Journal ArticleDOI
TL;DR: In this article, a lubrication-type dynamical model is developed of a molten, pulsed-laser-irradiated metallic film, and the heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically.
Abstract: In this paper the lubrication-type dynamical model is developed of a molten, pulsed-laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the three-dimensional long-wave evolution partial differential equation for the film height. To get insights into dynamics of dewetting, we study the two-dimensional (2D) version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam intensity, the film optical thickness, the reflectivity, and the Biot and Marangoni numbers, are elucidated. It is observed that the film stability is promoted for such parameter variations that increase the heat production in the film. In the numerical simulations the impacts of different irradiation modes are investigated. In particular, we obtain that in the interference heating mode the spatially periodic irradiation results in a spatially periodic film rupture with the same or nearly equal period. The 2D model qualitatively reproduces the results of the experimental observations of a film stability and spatial ordering of a resolidified nanostructures.

Journal ArticleDOI
Prashant Bahadur1, Preeti Yadav1, Kumud Chaurasia1, Aisha Leh1, Rafael Tadmor1 
15 Apr 2009
TL;DR: In this paper, it was shown that the Marangoni flow is induced at the solid-vapor interface as opposed to the air-liquid interface, which is true even for the case of water drop and alcohol drop on a glass surface.
Abstract: We study experimentally six different systems in which Marangoni flow is induced by two chemically different drops on a solid surface in air. In such systems one drop seems to chase away the other. We show that in all the systems studied, the Marangoni flow is induced at the solid-vapor interface as opposed to the air-liquid interface. This is true even for the case of water drop and alcohol drop on a glass surface (which corresponds to the "tears of wine" classical case). Thus we explain the drop motion as a result of an interfacial tension gradient which takes place primarily at the air-surface region and less, if at all, at the two other interfaces in the problem: the liquid-substrate or liquid-air interfaces. Then we follow the motion of drops on surfaces and find that it is discontinuous, i.e. characterized by stops and jumps as in a stick slip mechanism. We explain this behavior by an increase in the Laplace pressure that creates a higher anchoring pinning effect at the front edge of the moving drop. The understanding of this process has implications for passively separating mixed liquids.

Journal ArticleDOI
TL;DR: In this paper, the authors study the Marangoni effects in the mixture of two Newtonian fluids due to the thermo-induced surface tension heterogeneity on the interface and obtain the corresponding governing equations defined by a modified Navier-Stokes equations coupled with phase field and energy transport.
Abstract: In this paper, we study the Marangoni effects in the mixture of two Newtonian fluids due to the thermo-induced surface tension heterogeneity on the interface. We employ an energetic variational phase field model to describe its physical phenomena, and obtain the corresponding governing equations defined by a modified Navier-Stokes equations coupled with phase field and energy transport. A mixed Taylor-Hood finite element discretization together with full Newton’s method are applied to this strongly nonlinear phase fieldmodel on a specific domain. Under different boundary conditions of temperature, the resulting numerical solutions illustrate that the thermal energy plays a fundamental role in the interfacial dynamics of two-phase flows. In particular, it gives rise to a dynamic interfacial tension that depends on the direction of temperature gradient, determining the movement of the interface along a sine/cosine-like curve. AMS subject classifications: 65B99, 65K05, 65K10, 65N12, 65N22, 65N30, 65N55, 65Z05

Journal ArticleDOI
TL;DR: In this article, Thiele et al. studied the linear stability of free surface films of polymer mixtures on solid substrates with respect to lateral perturbations and showed that an increase in the film thickness either exponentially decreases the lateral instability or entirely stabilizes the film.
Abstract: We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. Thiele, S. Madruga, and L. Frastia, Phys. Fluids 19, 122106 (2007)]. To this aim, the linearized bulk equations and boundary equations are solved using continuation techniques for several different cases of energetic bias at the surfaces corresponding to linear and quadratic solutal Marangoni effects. For purely diffusive transport, an increase in the film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. Including convective transport leads to a further destabilization as compared to the purely diffusive case. In some cases the inclusion of convective transport and the related widening of the range of available film configurations (it is then able to change its surface profile) change the stability behavior qu...

Journal ArticleDOI
TL;DR: In this article, a linear stability problem for surface-tension-driven convection in a layer of a binary mixture is studied in the presence of both thermocapillary and solutocapelle effects.
Abstract: We consider surface-tension-driven convection in a layer of a binary mixture. A linear stability problem is studied in the presence of both thermocapillary and solutocapillary effects. Assuming the Lewis and Biot numbers to be small, we develop the long wave theory and find both monotonic and oscillatory modes. Three various modes of oscillatory convection exist depending on the ratio between the small parameters. In the case of finite but sufficiently small values of the Biot and Lewis numbers, linear stability thresholds are determined numerically. The numerical results agree well with those found analytically.

Journal ArticleDOI
TL;DR: In this article, the surface wave and film thickness of the heated falling liquid film were experimentally investigated using thermal imaging technique and a film thickness metering system, and it was found that the lateral Marangoni flow (MF I) and the streamwise MARangoni Flow (MF II) make the heated film thick, while the Marangani flow in the surface waves (MF III) reinforces the wave and makes the film thin.