Showing papers on "Marangoni effect published in 1992"
TL;DR: In this article, the spreading rate of a localized monolayer of insoluble surfactant on the surface of a thin viscous film, in the limit of weak capillarity and weak surface diffusion, was investigated.
Abstract: Lubrication theory and similarity methods are used to determine the spreading rate of a localized monolayer of insoluble surfactant on the surface of a thin viscous film, in the limit of weak capillarity and weak surface diffusion. If the total mass of surfactant increases as t(alpha), then at early times, when spreading is driven predominantly by Marangoni forces, a planar (axisymmetric) region of surfactant is shown to spread as t(1 + alpha)/3 (t(1 + alpha)/4) . A shock exists at the leading edge of the monolayer; asymptotic methods are used to show that a wavetrain due to capillary forces exists ahead of the shock at small times, but that after a finite time it is swamped by diffusive effects. For alpha < 1/2 (alpha < 1), the diffusive lengthscale at the shock grows faster than the length of the monolayer, ultimately destroying the shock; subsequently, spreading is driven by diffusion, and proceeds as t1/2. The asymptotic results are shown to be good approximations of numerical solutions of the governing partial differential equations in the appropriate limits. Additional forces are also considered: weak vertical gravity can also destroy the shock in finite time, while effects usually neglected from lubrication theory are important only early in spreading. Experiments have shown that the severe thinning of the film behind the shock can cause it to rupture: the dryout process is modelled by introducing van der Waals forces.
290 citations
TL;DR: In this paper, a study of the convection in acetone due jointly to the thermocapillary (Marangoni) and thermogravitational effects is presented, where the liquid (acetone) is submitted to a horizontal temperature difference.
Abstract: This paper presents a study of the convection in acetone due jointly to the thermocapillary (Marangoni) and thermogravitational effects. The liquid (acetone) is submitted to a horizontal temperature difference. Experiments and numerical simulations both show the existence of three different states : monocellular steady states, multicellular steady states and spatio-temporal structures. The results are discussed and compared with the linear stability analysis of Smith & Davis (1983).
145 citations
TL;DR: In this article, the authors investigated experimentally the flows induced by a localized surfactant (oleic acid) on thin glycerol films, where the initial motion of these markers is used to define the position of the timedependent convection front.
Abstract: We investigated experimentally the flows induced by a localized surfactant (oleic acid) on thin glycerol films. The oleic acid creates surface-tension gradients, which drive convention on the surface and within the film. Qualitative descriptions of the Lagrangian flow field were provided by flow-visualization experiments. Quantitative measurements of surface flows were conducted using dyed glycerol markers, where the initial motion of these markers is used to define the position of the timedependent ‘ convection front ’. The flow characteristics were found to depend largely upon the magnitude of a gravitational parameter, G, representing the ratio of gravitational to surface-tension gradient (Marangoni) forces. Small G (G 0. For this reason, surface markers may not be used to measure accurately the position of the droplet’s leading edge. Finally, simulations of the Lagrangian flows conducted using the theory of Gaver & Grotberg (1990) compare favourably with these experimental results in the limit of dilute surfactant concentrations, and thus experimental verification of that theory is provided by this work. The results of this study may be useful for understanding the behaviour of the lung’s thin-film lining after an aerosol droplet of insoluble exogenous surfactant lands upon its surface.
136 citations
TL;DR: In this paper, a mathematical model describing the evaporating meniscus in a capillary tube has been formulated incorporating the full three-dimensional Young-Laplace equation, Marangoni convection, London-van der Waals dispersion forces, and nonequilibrium interface conditions.
Abstract: A mathematical model describing the evaporating meniscus in a capillary tube has been formulated incorporating the full three-dimensional Young-Laplace equation, Marangoni convection, London-van der Waals dispersion forces, and nonequilibrium interface conditions. The results showed that varying the dimensionless superheat had no apparent effect on the meniscus profile. However, varying the dispersion number produced a noticeable change in the meniscus profile, but only at the microscopic level near the tube wall. No change in the apparent contact angle was observed with changes in the dimensionless superheat or dispersion number. In all cases, the dimensionless mean curvature was asymptotic to a value equal to that for a hemispherical meniscus. The local interfacial mass flux and total mass transfer rate increased dramatically as the dispersion number was increased, suggesting that surface coatings can play an important role in improving or degrading capillary pumping. The model also predicted that the local capillary pressure remains constant and equal to 2{sigma}/r{sub c} regardless of changes in the dimensionless superheat and dispersion number. It should be noted that the results in this study are theoretical in nature and require experimental verification.
105 citations
TL;DR: In this paper, Rayleigh's theory of the instability of a free liquid cylinder due to surface tension is applied and the width-to-length ratio of the weld pool has to exceed 1/2 pi to avoid humping.
Abstract: The conjecture which explains the humping phenomenon in terms of Marangoni convection is discussed and rejected. Instead, Rayleigh's theory of the instability of a free liquid cylinder due to surface tension is applied. The width-to-length ratio of the weld pool has to exceed 1/2 pi to avoid humping. The growth time of a disturbance is found to be approximately the same as the growth time of a hump. The analysis of a bounded cylinder provides a new stability criterion which allows the introduction of a bounding function to distinguish between arc and laser welding. The weld pool dimensions are estimated in terms of a simple heat conduction model. The threshold value predicted theoretically for the travel speed above which humping commences agrees well with the experimental value. It decreases with increasing power, which is in qualitative agreement with experimental results.
102 citations
01 Jun 1992-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this paper, the free surface temperature of weld pools appears to be limited by Marangoni convection, rather than heat losses due to vaporization, and a realistic allowance for the temperature dependence of the surface tension.
Abstract: By combining a mathematical model of the welding arc and of the weld pool, calculations are presented to describe the free surface temperature of weld pools for spot welding operations. The novel aspects of the treatment include the calculation of the heat and current fluxes falling on the free weld pool surface from first principles, a realistic allowance for heat losses due to vaporization, and a realistic allowance for the temperature dependence of the surface tension. The most important finding reported in this article is that the free surface temperature of weld pools appears to be limited by Marangoni convection, rather than heat losses due to vaporiza-tion. Furthermore, it was found that once thermocapillary flow can produce high enough surface velocities (>25 cm/s), the precise nature of the relationship between temperature and surface tension will become less important.
75 citations
TL;DR: In this paper, the authors reviewed the phenomena by which wetting and the Marangoni effect participate or may participate in iron and steelmaking processes, and the concept of wetting conventionally defined for the system of gas-liquid-solid was applied to the systems of liquid 1-liquid 2-solid, liquid-solid 1-solid 2 and gas liquid 1 liquid 2.
Abstract: This article reviews the phenomena by which wetting and the Marangoni effect participate or may participate in iron and steelmaking processes. The concept of wetting conventionally defined for the system of gas-liquid-solid was applied to the systems of liquid 1-liquid 2-solid, liquid-solid 1-solid 2 and gas-liquid 1-liquid 2. In these systems, local corrosions of refractories at the interfaces of gas-slag and metal-slag, slag foaming, bubble dispersion into metal phase, and interaction of inclusions with solidification fronts were described in relation to the wetting and the Marangoni effect. Rates of reactions of gas-metal, and metal-slag were briefly introduced as examples of possible participation of the Marangoni effect.
65 citations
TL;DR: It is shown that the equation has a Liapunov functional, and this fact is exploited to demonstrate that the Marangoni effect can stabilize the destabilizing effect of gravity, allowing for the existence of stable localized axisymmetric solutions for a wide range of parameter values.
Abstract: We study a 2-D nonlinear evolution equation which describes the 3-D spatiotemporal behavior of the air-liquid interface of a thin liquid film lying on the underside of a cooled horizontal plate. We show that the Marangoni effect can stabilize the destabilizing effect of gravity (the Rayleigh-Taylor instability) allowing for the existence of stable localized axisymmetric solutions for a wide range of parameter values. Various properties of these structures are discussed.
63 citations
TL;DR: The effect of surfactants on the motion and deformation of liquid drops in Poiseuille flow through circular tubes at low Reynolds numbers is examined in this article, where the boundary integral method is used in conjunction with a convective-diffusion equation to determine the distribution of the surfactant on the deformed surface of the drop.
Abstract: The effect of surfactants on the motion and deformation of liquid drops in Poiseuille flow through circular tubes at low Reynolds numbers is examined Assuming no bulk transport of surfactant, the boundary integral method is used in conjunction with a convective–diffusion equation to determine the distribution of surfactant on the deformed surface of the drop The velocity and shape of the drop as well as the extra pressure loss due to the presence of the drop are calculated Increasing the surface Peclet number is found to produce large variations in surfactant concentration across the surface of the drop The resulting interfacial tension gradients lead to tangential (Marangoni) stresses that oppose surface convection and retard the motion of the drop as a whole For large Peclet numbers, Marangoni stresses immobilize the surface of the drop, leading to a significant increase in the extra pressure loss required to move the drop through the tube The accumulation of surfactant near the trailing end of the drop partially lowers the interfacial tension on that side, thereby requiring larger deformations to satisfy the normal stress balance At the same time, the increase in interfacial area associated with drop deformation causes an overall dilution of the surfactant, which, in turn, counteracts the effect of convective transport of surfactant at large Peclet numbers The effects of these coupled responses are studied over a wide range of the dimensionless parameters
63 citations
01 Apr 1992
TL;DR: In this paper, it was shown that the Marangoni elasticity induced by the isothermal transfer of a surface active solute between two adjacent immiscible bulks could result in convective motion.
Abstract: Sternling and Scriven1 showed that the Marangoni elasticity induced by the isothermal transfer of a surface active solute between two adjacent immiscible bulks could result in convective motion.
45 citations
TL;DR: In this article, the influence of the type of lateral walls on the multiplicity of steady states is considered, and it is shown that "no-slip" lateral walls lead to hysteresis effects and typically restrict the number of stable flow patterns (with respect to'slippery' sidewalls) through the occurrence of saddle node bifurcations.
Abstract: Multiple steady flow patterns occur in surface-tension/buoyancy-driven convection in a liquid layer heated from below (Rayleigh-Benard-Marangoni flows). Techniques of numerical bifurcation theory are used to study the multiplicity and stability of two-dimensional steady flow patterns (rolls) in rectangular small-aspect-ratio containers as the aspect ratio is varied. For pure Marangoni flows at moderate Biot and Prandtl number, the transitions occurring when paths of codimension 1 singularities intersect determine to a large extent the multiplicity of stable patterns. These transitions also lead, for example, to Hopf bifurcations and stable periodic flows for a small range in aspect ratio. The influence of the type of lateral walls on the multiplicity of steady states is considered. 'No-slip' lateral walls lead to hysteresis effects and typically restrict the number of stable flow patterns (with respect to 'slippery' sidewalls) through the occurrence of saddle node bifurcations. In this way 'no-slip' sidewalls induce a selection of certain patterns, which typically have the largest Nusselt number, through secondary bifurcation.
TL;DR: In this paper, the authors take a look at experiments in both heat-transfer and mass-transfer-driven Marangoni systems to discern nonlinear behavior of the type associated with solitary wave interactions.
Abstract: Recent studies have elucidated the possibility of solitary wave behavior in Marangoni–Benard instability flows. The present paper takes a look at experiments in both heat‐transfer‐ and mass‐transfer‐driven Marangoni systems to discern nonlinear behavior of the type associated with solitary wave interactions. Direct observation of phase shifts incurred by two Marangoni waves having undergone a head‐on collision are reported. Analysis of experiments exhibiting wave reflection at a solid wall and obliquely interacting waves in Marangoni instability flows also show remarkable similarities with nonlinear behavior in Korteweg–de Vries systems.
TL;DR: In this paper, the governing equations for momentum, energy and electric transport are solved numerically to obtain the unsteady development of an axially symmetric gas tungsten arc weld pool.
TL;DR: In this article, the authors present results on more realistic events involving simultaneous Marangoni and buoyancy flows, where the fluid flow along the interface is directed towards the wall, and the expected behavior for a negative capillarity gradient is shown.
Abstract: so that the fluid flow along the interface is directed towards the wall. Events involving negative as well as positive capillarity gradients of various values and in the absence of buoyancy currents have been modeled in the course of this work. Below, we present results on more realistic events involving simultaneous Marangoni and buoyancy flows. For example, Fig. 3 depicts the expected behavior for a negative capillarity gradient, that is
TL;DR: In this article, the conditions that enable a drop of one liquid to spread on the surface of an immiscible second liquid were first stated in 1865 by Carlo Marangoni, but within the next few years other authors had independently arrived at the same conclusion.
TL;DR: In this paper, numerical simulations of thermocapillary convection of low-Prandtl number melts in a rectangular cavity subject to a horizontal temperature gradient under zero gravity are performed.
TL;DR: In this article, a semi-empirical model of mass transfer accompanied by interfacial turbulence is proposed which accounts for the linear dependence of the mass transfer coefficients on the driving force under interfacial turbulent conditions.
TL;DR: In this paper, a catamaran was used to carry out in situ measurements of physical and dynamical properties of slick and clean sea surfaces, and the surface tension and wave-damping rate were found to vary across the slick.
Abstract: A fully instrumented catamaran was used to carry out in situ measurements of physical and dynamical properties of slick and clean sea surfaces. The surface tension and wave-damping rate were found to vary across the slick. The latter is further associated with the Marangoni effect. In addition to wave suppression, the augmentation of wind speed and the reduction of wind stress by slicks were recorded. The formation of slick bands was also observed. Finally, surface films influence air-sea transfers and other interfacial processes were discussed.
TL;DR: In this article, the behavior of a lenticular nitroethane droplet at the free surface is studied experimentally, and it is shown that the motion is rectilinear and uniform.
TL;DR: In this paper, the effect of surface tension on the stability of a double-diffusive layer is considered using linear stability analysis, where the surface tension is assumed to vary linearly with temperature and solute concentration.
Abstract: The effect of surface tension on the stability of a double‐diffusive layer is considered using linear stability analysis. The surface tension is assumed to vary linearly with temperature and solute concentration. The eigenvalue problem is solved by the Galerkin method. Results show that the predicted stability boundary based on Marangoni effects alone is completely altered in the presence of buoyancy effects induced by low gravity levels (∼10−5 g). At reduced gravity levels, salt‐finger instability may onset in the overstable mode due to the stabilizing effect of surface tension. Fluid properties in terms of the Prandtl and the Lewis numbers have a profound effect on the stability conditions; opposite stability characteristics are found in salt solutions and in molten metals. In the diffusive case, the competition between the surface‐tension and the double‐diffusive effects can generate bimodal marginal stability curves, thus resulting in the simultaneous occurrence of two instability modes with different wave numbers and oscillation frequencies.
TL;DR: In this article, the authors observed two stages in the spreading of large, flat, droplets of silicone oils (degree of polymerization N < 20) deposited on bare silicon wafers, and interpreted these results in terms of Marangoni driven instabilities induced by the surface tension gradient generated at the drop edge by liquid evaporation.
Abstract: We have observed two stages in the spreading of large, flat, droplets of silicone oils (degree of polymerization N < 20) deposited on bare silicon wafers : i) at first, the drop contour is perfectly circular and the drop radius R increases with time as R∼t0.15, ii) below a critical thickness hc, a rim is formed at the contact line and the contour develops spectacular festoons. At the same time, the spreading speeds up and the radius increases as R∼t1/3. We have interpreted these results in terms of Marangoni driven instabilities induced by the surface tension gradient generated at the drop edge by liquid evaporation.
TL;DR: In this article, a new equation for the evolution of film thickness is presented, which, in addition to van der Waals dispersive forces and surface tension, includes flow effects arising from surface tension gradients.
01 Jan 1992
TL;DR: In this article, a linear stability analysis is presented for the evolution of film thickness which, in addition to van der Waals dispersive forces and surface tension, includes flow effects arising from surface tension gradients.
Abstract: A new equation is presented for the evolution of film thickness which, in addition to van der Waals dispersive forces and surface tension, includes flow effects arising from surface tension gradients. The effect of surfactant is quantified in terms of its adsorption at the liquid-gas interface. A linear stability analysis shows that the dynamics of evaporating/condensing thin films in the presence of surfactant are entirely different from isothermal films with surfactant and non-isothermal films without surfactant. Thus, flows driven by surface tension gradients originating from surfactant concentration variations, i.e. Marangoni flows, are in a direction opposite to that of similar flows originating from surface temperature variations, i.e. thermocapillary flows. The former usually dominate; they are destabilizing for condensing films and stabilizing for evaporating films.. In flow through porous media, the dominantly-wetting phase fills small-size pores and flows along the walls of larger pores as a continuous thin film. The bulk of the large pores is occupied by less-wetting and non-wetting phases. The wall films are subject to hydrodynamic, surface instabilities. Under certain flow conditions (Gauglitz & Radke 1988), and for specific pore throat-to-body ratios (Ransohoff et al. 1987), they "snap-off" to form free films, called lamellae, which block the pore-throat entrance to the incoming non-wetting phase. In enhanced oil recovery (EOR) operations which utilize injected gas to displace the oil, the problem of an efficient sweep of the reservoir arises since the gas flows preferentially through the top of the formation or through high-permeability zones. One of the ways of slowing down the advance of the gas and redistributing it over a larger cross section of the reservoir is to render part or all of the gas phase discontinuous. To achieve this goal, the lamellae are stabilized by surfactant which is injected in the form of dilute aqueous solutions. The non-uniform gas-in-water dispersion, which is stabilized by surfactant in porous media, is called a foam, although its texture and features are quite different from those of common bulk foams outside porous media. The wall films (figure l a) are bounded in the transverse direction by the inside pore wall and a gas-liquid interface. Their stability is of primary importance to foam formation. The stability of the free films (figure la), which span the pore and have two gas-liquid interfaces, determines the rate of foam collapse. Film stability is a result of the interplay of viscous, capillary and intermolecular (disjoint pressure) forces. Variations of surfactant concentration and temperature at the gas-liquid interface add surface-tension gradients to the factors influencing film stability. Flows induced by surface-tension gradients due to surfactant excess concentration variations are known as Marangoni flows (Sternling & Scriven 1959); those arising from interfacial temperature variations are known as thermocapillary flows (Pearson 1958).
TL;DR: In this paper, the authors examined the appearance of surface waves governed by Burgers and Korteweg -de Vries equations in a shallow viscous heated fluid and established the range of parameters for which the above-mentioned equations appear.
Abstract: We examine the appearance of surface waves governed by Burgers and Korteweg — de Vries equations in a shallow viscous heated fluid We consider waves triggered by a surface-tension variation induced by both temperature and concentration gradients We also establish the range of parameters for which the above-mentioned equations appear
TL;DR: In this article, the onset of Marangoni-Benard instability under microgravity conditions is studied experimentally using a sounding rocket (TEXUS 21) launched in the microgravity program developed by the European Space Agency.
TL;DR: In this paper, the generation and growth of surface water waves by the wind and including modified boundary conditions appropriate for the presence of surfactants at the surface are reconsidered using linear instability theory to describe the process.
Abstract: The generation and growth of surface water waves by the wind and including modified boundary conditions appropriate for the presence of surfactants at the surface are reconsidered using linear instability theory to describe the process. The new features of our work are the inclusion of both surfactants and a wind drift layer. We allow a coupled mean flow in both the air and water; the depth-dependent mean flow is considered to be wind-induced. The complex wave frequencies are determined numerically. Uncontrolled numerical errors associated with a direct numerical solution of the Orr-Sommerfeld equation for the coupled mean flow are avoided by solving an associated equation obtained by a Riccati transformation of the original equation, allowing a straightforward and efficient determination of the eigenvalues of the linear stability problem. A different aspect of our analysis is the change of surface boundary conditions due to contamination of the surface, notably, the change of tangential stress at the surface due to surface tension gradients induced by the film (known as the Marangoni effect). Comparisons are made with previous work on both film-free and contaminated surfaces. The dominant effect of introducing film boundary conditions is a large change in the wave number of the most unstable wave with an attendant reduction in the growth rate. Implications for wind wave growth on the ocean are discussed.
TL;DR: For a liquid layer parametrically excited with a time harmonically varying heat flux imposed normal to the free surface, threshold values for the onset of convective thermocapillary instability are provided in this article.
Abstract: For a liquid layer parametrically excited with a time harmonically varying heat flux imposed normal to the free surface, threshold values for the onset of convective thermocapillary instability are provided. Both the critical Marangoni number and the critical wave number are given as functions of the Prandtl number. Also provided here are some numerical estimates for possible experimental test of the theoretical predictions.
TL;DR: In this article, an improved fluid flow and heat transfer modeling of float-zone growth by introducing a RF heating model so that an ad hoc heating temperature profile is not necessary was provided. But the numerical results showed that the thermocapillary convection occurring inside the molten zone tends to increase the convexity of the melt-crystal interface and decrease the maximum temperature of the molten zones, while the natural convection tends to reduce the stability of the liquid zone by increasing its height.
Abstract: The present work provides an improved fluid flow and heat-transfer modeling of float-zone growth by introducing a RF heating model so that an ad hoc heating temperature profile is not necessary. Numerical simulations were carried out to study the high-temperature float-zone growth of titanium carbide single crystal. The numerical results showed that the thermocapillary convection occurring inside the molten zone tends to increase the convexity of the melt-crystal interface and decrease the maximum temperature of the molten zone, while the natural convection tends to reduce the stability of the molten zone by increasing its height. It was found that the increase of induced heating due to the increase of applied RF voltage is reduced by the decrease of zone diameter. Surface tension plays an important role in controlling the amount of induced heating. Finally, a comparison of the computed shape of the free surface with a digital image obtained during a growth run showed adequate agreement.
01 Aug 1992
TL;DR: The analysis of wave interaction experiments in both heat transfer-driven and mass-transfer-driven high supercritical Marangoni number convection flows provides strong evidence of solitary wave behavior as mentioned in this paper.
Abstract: The analysis of wave interaction experiments in both heat-transfer-driven and mass-transfer-driven high supercritical Marangoni number convection flows provides strong evidence of solitary wave behavior. Wave reflections at a solid wall and oblique wave interactions are qualitatively similar to KdV type interactions in purely gravity-driven (free-surface and internal) solitary wave systems. It is anticipated that the results reported here will motivate new experiments designed to directly test for the existence of solitary waves and solitons in Marangoni-Benard systems.
TL;DR: In this article, the convective instability problem in ac and dc electric field was studied theoretically, where the critical ac electric Rayleigh number, the critical rayleigh number and the critical Marangoni number become smaller as electric field increases.
Abstract: The convective instability problem in ac and dc electric field is studied theoretically. Linearized perturbation equations are solved by the Galerkin method where the critical ac or dc electric Rayleigh number, the critical Rayleigh number and the critical Marangoni number are expressed as eigen values. It is found that the critical ac electric Rayleigh number, the critical Rayleigh number and the critical Marangoni number become smaller as electric field increases in the case of ac electric field. However, in the case of dc electric field, the critical dc electric Rayleigh number, the critical Rayleigh number and the critical Marangoni number increase with increasing electric field when nondimensional parameters S and K are small while the critical dc electric Rayleigh number, the critical Rayleigh number and the critical Marangoni number decrease with increasing electric field when S and K are large.