Showing papers on "Marangoni effect published in 1997"

Long-wavelength surface-tension-driven Bénard convection: experiment and theory

Abstract: Surface-tension-driven Benard (Marangoni) convection in liquid layers heated from below can exhibit a long-wavelength primary instability that differs from the more familiar hexagonal instability associated with Benard. This long-wavelength instability is predicted to be significant in microgravity and for thin liquid layers. The instability is studied experimentally in terrestrial gravity for silicone oil layers 0.007 to 0.027 cm thick on a conducting plate. For shallow liquid depths ( 0.024 cm), the system forms only the hexagonal convection cells. A two-layer nonlinear theory is developed to account properly for the effect of deformation on the interface temperature profile. Experimental results for the long-wavelength instability are compared to our two-layer theory and to a one-layer theory that accounts for the upper gas layer solely with a heat transfer coefficient. The two-layer model better describes the onset of instability and also predicts the formation of localized elevations, which the one-layer model does not predict. A weakly nonlinear analysis shows that the bifurcation is subcritical. Solving for steady states of the system shows that the subcritical pitchfork bifurcation curve never turns over to a stable branch. Numerical simulations also predict a subcritical instability and yield long-wavelength states that qualitatively agree with the experiments. The observations agree with the onset prediction of the two-layer model, except for very thin liquid layers; this deviation from theory may arise from small non-uniformities in the experiment. Theoretical analysis shows that a small non-uniformity in heating produces a large steady-state deformation (seen in the experiment) that becomes more pronounced with increasing temperature difference across the liquid. This steady-state deformation becomes unstable to the long-wavelength instability at a smaller temperature difference than that at which the undeformed state becomes unstable in the absence of non-uniformity.

Dynamic Surface Tension Effects in Impact of a Drop with a Solid Surface

Abstract: Recent research on free surface flows in the presence of surface-active species in which a fluid interface undergoes very large deformations, e.g., as in the deformation and breakup of drops in extensional flows under conditions of Stokes flow (Stone, H. A., and Leal, L. G., J. Fluid Mech. 220, 161 (1990)) (19) and the formation of drops from capillaries (Zhang, X., and Basaran, O. A., Phys. Fluids 7, 1184 (1995)) (20) has shown that dynamic surface tension (DST) effects can radically alter the dynamics compared to situations in which the fluid interface is clean. In this paper, we present results of an experimental study that examines the impact with a solid substrate of drops of Newtonian liquids containing two commonly used surfactants. In the experiments, an ultra high-speed video and associated image analysis system is used to monitor the dynamics of the impact process. On account of the extremely large deformations that a drop exhibits and the large-amplitude oscillations that it undergoes upon impacting and spreading on the substrate, DST plays a complex and dominant role in determining the dynamics and the asymptotic state that is approached at large times. A major consequence of the presence of surfactant is that on the one hand its accumulation on the fluid interface reduces the surface tension and thereby enhances the spreading of the drop across the substrate. On the other hand, the non-uniform distribution of surfactant along the fluid interface gives rise to Marangoni stresses that inhibit drop spreading. Given the fact that many liquids used in atomization coating applications ranging from the spraying of agricultural chemicals to painting of substrates contain surfactants and/or other surface-active species, the fundamental results to be reported in this paper have important practical ramifications.

A Theoretical Study of Instabilities at the Advancing Front of Thermally Driven Coating Films

Abstract: A thin liquid coating can spread vertically beyond the equilibrium meniscus position by the application of a temperature gradient to the adjacent substrate. So called super-meniscus films experience a surface shear stress which drives flow toward regions of higher surface tension located at the cooler end of the substrate. The Marangoni stresses responsible for this spreading process can also be used to coat horizontal surfaces rapidly and efficiently. Experiments in the literature have shown that in either geometry, the advancing front can develop a pronounced ridge with lateral undulations that develop into long slender rivulets. These rivulets, which prevent complete surface coverage, display a remarkable regularity in height, width, and spacing which suggests the presence of a hydrodynamic instability. We have performed a linear stability analysis of such thermally driven films to determine the most dangerous wavenumber. Our numerical solutions indicate the presence of an instability at the advancing front of films which develop a sufficiently thick capillary ridge. Our results for the film thickness profiles and spreading velocities, as well as the wavenumber corresponding to the most unstable mode, compare favorably with recent experimental measurements. An energy analysis of the perturbed flow reveals that the increased mobility in the thickened portions of the films strongly promotes unstable flow, in analogy with other coating processes using gravitational or centrifugal forces. Copyright 1997Academic Press

Marangoni Mechanism in Pulsed Laser Texturing of Magnetic Disk Substrates

Abstract: This paper proposes a mechanism for topographical features formed during pulsed laser texturing of Ni-P magnetic disk substrates. A salient feature of the process is the ability to raise a central peak in the irradiated spot, providing a low contact area bearing for the slider-head of a computer hard drive. Formation of topography is believed to involve gradient capillary forces acting at the surface of the molten pool (Marangoni effect). However, the central peak cannot be explained with thermo-capillary forces alone. Therefore, it is suggested that a compositional gradient due to the depletion of a surfactant at the molten surface provides the necessary condition to reverse the capillary force in the central region. This perspective is investigated using finite element modeling of the Lagrangian fluid mechanics coupled with heat and mass diffusion.

Thermocapillary motion of deformable drops at finite Reynolds and Marangoni numbers

Abstract: We present the results of numerical simulations of the three-dimensional thermocapillary motion of deformable viscous drops under the influence of a constant temperature gradient within a second liquid medium. In particular, we examine the effects of shape deformations and convective transport of momentum and energy on the migration velocity of the drop. A numerical method based on a continuum model for the fluid–fluid interface is used to account for finite drop deformations. An oct-tree adaptive grid refinement scheme is integrated into the numerical method in order to track the interface without the need for interface reconstruction. Interface deformations arising from the convection of energy at small Reynolds numbers are found to be negligible. On the other hand, deformations of the drop shape due to inertial effects, though small in magnitude, are found to retard the motion of the drop. The steady drop shapes are found to resemble oblate or prolate spheroids without fore and aft symmetry, with the d...

Thickening Factor in Marangoni Coating

Abstract: We have recently shown that a wire, and more generally a solid, drawn out of a solution containing surfactants entrains a thicker film than one drawn out of a pure liquid (Marangoni coating). The thickening factor, generally of order 2, was found to be independent of the capillary number (for surfactant concentration of the order of the cmc) but depends on the wire radius: the thinner the wire, the larger the thickening. After summarizing these results, we propose a model for understanding this effect, which is shown to result from a balance between convection and adsorption. Finally, a scaling form is proposed for the thickening factor.

Nonlinear evolution and secondary instabilities of Marangoni convection in a liquid–gas system with deformable interface

Abstract: The paper presents a theory of nonlinear evolution and secondary instabilities in Marangoni (surface-tension-driven) convection in a two-layer liquid–gas system with a deformable interface, heated from below. The theory takes into account the motion and convective heat transfer both in the liquid and in the gas layers. A system of nonlinear evolution equations is derived that describes a general case of slow long-scale evolution of a short-scale hexagonal Marangoni convection pattern near the onset of convection, coupled with a long-scale deformational Marangoni instability. Two cases are considered: (i) when interfacial deformations are negligible; and (ii) when they lead to a specific secondary instability of the hexagonal convection.In case (i), the extent of the subcritical region of the hexagonal Marangoni convection, the type of the hexagonal convection cells, selection of convection patterns – hexagons, rolls and squares – and transitions between them are studied, and the effect of convection in the gas phase is also investigated. Theoretical predictions are compared with experimental observations.In case (ii), the interaction between the short-scale hexagonal convection and the long-scale deformational instability, when both modes of Marangoni convection are excited, is studied. It is shown that the short-scale convection suppresses the deformational instability. The latter can appear as a secondary long-scale instability of the short-scale hexagonal convection pattern. This secondary instability is shown to be either monotonic or oscillatory, the latter leading to the excitation of deformational waves, propagating along the short-scale hexagonal convection pattern and modulating its amplitude.

Linear stability analysis of an insoluble surfactant monolayer spreading on a thin liquid film

Abstract: Recent experiments by several groups have uncovered a novel fingering instability in the spreading of surface active material on a thin liquid film. The mechanism responsible for this instability is yet to be determined. In an effort to understand this phenomenon and isolate a possible mechanism, we have investigated the linear stability of a coupled set of equations describing the Marangoni spreading of a surfactant monolayer on a thin liquid support. The unperturbed flows, which exhibit simple linear behavior in the film thickness and surfactant concentration, are self-similar solutions of the first kind for spreading in a rectilinear geometry. The solution of the disturbance equations determines that the rectilinear base flows are linearly stable. An energy analysis reveals why these base flows can successfully heal perturbations of all wavenumbers. The details of this analysis suggest, however, a mechanism by which the spreading can be destabilized. We propose how the inclusion of additional forces acting on the surfactant coated spreading film might give rise to regions of adverse mobility gradients known to produce fingering instabilities in other fluid flows.

Surfactant-induced retardation of the thermocapillary migration of a droplet

Abstract: A neutrally buoyant droplet in a fluid possessing a temperature gradient migrates under the action of thermocapillarity. The drop pole in the high-temperature region has a reduced surface tension. The surface pulls away from this low-tension region, establishing a Marangoni stress which propels the droplet into the warmer fluid. Thermocapillary migration is retarded by the adsorption of surfactant: surfactant is swept to the trailing pole by surface convection, establishing a surfactant-induced Marangoni stress resisting the flow (Barton & Subramanian 1990).The impact of surfactant adsorption on drop thermocapillary motion is studied for two nonlinear adsorption frameworks in the sorption-controlled limit. The Langmuir adsorption framework accounts for the maximum surface concentration Γ′∞ that can be attained for monolayer adsorption; the Frumkin adsorption framework accounts for Γ′∞ and for non-ideal surfactant interactions. The compositional dependence of the surface tension alters both the thermocapillary stress which drives the flow and the surfactant-induced Marangoni stress which retards it. The competition between these stresses determines the terminal velocity U′, which is given by Young's velocity U′0 in the absence of surfactant adsorption. In the regime where adsorption–desorption and surface convection are of the same order, U′ initially decreases with surfactant concentration for the Langmuir model. A minimum is then attained, and U′ subsequently increases slightly with bulk concentration, but remains significantly less than U′0. For cohesive interactions in the Frumkin model, U′ decreases monotonically with surfactant concentration, asymptoting to a value less than the Langmuir velocity. For repulsive interactions, U′ is non-monotonic, initially decreasing with concentration, subsequently increasing for elevated concentrations. The implications of these results for using surfactants to control surface mobilities in thermocapillary migration are discussed.

Porous Media and the Bénard–Marangoni Problem

Abstract: The Rayleigh–Benard instability for a clear fluid has its equivalent for a liquid saturated porous matrix. The phenomenological Darcy momentum law cannot give rise by itself to an instability analogous to that of Benard–Marangoni, but the Brinkman model at least allows it. A critical Marangoni number exists leading to cellullar patterns and, for realistic values of the permeability, it is proportional to the inverse of this last parameter.

Thermocapillary flow in a Hele-Shaw cell

Abstract: We formulate a simple theoretical model that permits one to investigate surface-tension-driven flows with complex interface geometry The model consists of a Hele-Shaw cell filled with two different fluids and subjected to a unidirectional temperature gradient The shape of the interface that separates the fluids can be arbitrarily complex If the contact line is pinned, ie unable to move, the problem of calculating the flow in both fluids is governed by a linear set of equations containing the characteristic aspect ratio and the viscosity ratio as the only input parameters Analytical solutions, derived for a linear interface and for a circular drop, demonstrate that for large aspect ratio the flow field splits into a potential core flow and a thermocapillary boundary layer which acts as a source for the core An asymptotic theory is developed for this limit which reduces the mathematical problem to a Laplace equation with Dirichlet boundary conditions This problem can be efficiently solved utilizing a boundary element method It is found that the thermocapillary flow in non-circular drops has a highly non-trivial streamline topology After releasing the assumption of a pinned interface, a linear stability analysis is carried out for the interface under both transverse and longitudinal temperature gradients For a semi-infinite fluid bounded by a freely movable surface long-wavelength instability due to the temperature gradient across the surface is predicted The mechanism of this instability is closely related to the long-wave instability in surface-tension-driven Benard convection A linear interface heated from the side is found to be linearly stable The possibility of experimental verification of the predictions is briefly discussed

Origin of waves in surface-tension-driven convection

Abstract: A fluid layer heated from one side ~and cooled from the opposite! gets into motion, no matter how small the imposed temperature difference DT between the end walls is. Two unbalanced forces set up a global flow. The first one arises from the change of the surface forces with temperature, also called the Marangoni effect. The second one is gravity, acting upon the density variations with temperature. The two main experimental parameters, the temperature difference DT and the depth of the fluid layer h, can be expressed in terms of two nondimensional numbers: the Marangoni number Ma and the Rayleigh number Ra. We use the following definitions for Ra and Ma:

Inertial Bénard–Marangoni convection

Abstract: Two-dimensional surface-tension-driven Benard convection in a layer with a free-slip bottom is investigated in the limit of small Prandtl number using accurate numerical simulations with a pseudospectral method complemented by linear stability analysis and a perturbation method. It is found that the system attains a steady state consisting of counter-rotating convection rolls. Upon increasing the Marangoni number Ma the system experiences a transition between two typical convective regimes. The first one is the regime of weak convection characterized by only slight deviations of the isotherms from the linear conductive temperature profile. In contrast, the second regime, called inertial convection, shows significantly deformed isotherms. The transition between the two regimes becomes increasingly sharp as the Prandtl number is reduced. For sufficiently small Prandtl number the transition from weak to inertial convection proceeds via a subcritical bifurcation involving weak hysteresis. In the viscous zero-Prandtl-number limit the transition manifests itself in an unbounded growth of the flow amplitude for Marangoni numbers beyond a critical value Mai. For Ma

The generation of two-dimensional vortices by transverse oscillation of a soap film

Abstract: An experimental investigation of the dynamics of horizontal soap films stretched over circular or square boundaries undergoing periodic transverse oscillations at frequencies in the range 20–200 Hz is reported. Concomitant with modes of transverse flexural oscillations, it was observed that two-dimensional vortices in the plane of the film are excited. The vortices may be either (i) large, scaling with the size of the cavity or (ii) small, localized at a wavelength or half-wavelength of the membrane modes. In the experiments a stable generation of one, two, …, ten pairs of counter-rotating vortices were observed in finite regions of amplitude-frequency parameter space. The circulation strength of vortices in a given vortex pattern increases with increasing external forcing and with decreasing soap film thickness. A theoretical model based on the wave-boundary interaction of excited Marangoni waves reveals a vorticity generation mechanism active in vibrating soap films. This model shows that vorticity is generated throughout the entire liquid volume by viscous diffusion, and qualitatively reproduces many steady vortex patterns observed in the experiment. However, the model cannot explain the existence of the sometimes intense vortices observed far from the film boundary that do not appear to be generated by diffusive processes.

Liquid coating from a surfactant solution

Abstract: A solid drawn out of a pure wetting liquid comes out coated with a layer of liquid, of thickness given by the Landau equation (for small coating velocities). If the solid is drawn from a solution containing surfactants, we show that the film is thicker than predicted by Landau: when drawing the solid, a gradient of surface concentration appears, provoking a Marangoni flow and thus a thickening of the film. The thickening factor we measure is found to reflect a balance between convection (responsible for the gradient) and absorption from the volume (which tends to erase the gradient).

The anomalous wake accompanying bubbles rising in a thin gap: a mechanically forced Marangoni flow

Abstract: A novel wake structure, observed as penny-shaped air bubbles rise at moderate Reynolds number through a thin layer of water bound between parallel glass plates inclined at a shallow angle relative to the horizontal, is reported. The structure of the wake is revealed through tracking particles suspended in the water. The wake completely encircles the rising bubble, and is characterized by a reverse surface flow or ‘edge jet’ which transports fluid in a thin boundary layer along the bubble surface from the tail to the nose at speeds which are typically an order of magnitude larger than the bubble rise speed. A consistent physical explanation for the wake structure is proposed. The wake is revealed to be a manifestation of the three-dimensionality of the flow in the suspending fluid. The bubble surface advances through a rolling motion, thus generating regions of surface divergence and convergence at, respectively, the leading and trailing edges of the bubble. A nose-to-tail gradient in surfactant concentration is thus established, and the associated surface tension gradient drives the edge jet. The dependence of the wake structure on the suspending fluid is examined experimentally. Surfactants play an anomalous role in the reported flow, serving to promote rather than suppress surface motions. The wake structure is an example of a mechanically forced Marangoni flow, and so represents a mechanical analogue of that accompanying thermocapillary drop motion in microgravity. A theoretical model is developed which reproduces the salient features of the flow, and on the basis of which an estimate is made of the mechanically induced surface tension gradient along the bubble surface.

The effect of uniform internal heat generation on the onset of steady Marangoni convection in a horizontal layer of fluid

Abstract: In this paper we use a combination of analytical and numerical techniques to analyse the effect of uniform internal heat generation on the onset of steady Marangoni convection in a horizontal layer of quiescent fluid heated from below. We obtain for the first time the closed form analytical solution for the onset of steady Marangoni convection and give a comprehensive description of the stability characteristics of the layer both when the lower boundary is conducting and when it is insulating to temperature perturbations. We also present asymptotically- and numerically-calculated results for the linear growth rates of the steady modes. In particular, we show that the effect of increasing the internal heat generation is always to destabilise the layer and give asymptotic expressions for the critical Marangoni number and critical wavenumber in the limit of large internal heat generation.

Linear stability of two-dimensional combined buoyant-thermocapillary flow in cylindrical liquid bridges

Abstract: The combined buoyant-thermocapillary flow in cylindrical liquid bridges of unit aspect ratio is calculated by a mixed finite-difference\char21{}Chebyshev-collocation method. Gravity is assumed to be parallel or antiparallel to the cylinder's axis. For dominating thermocapillarity the two-dimensional basic flow is unique at the onset of instability. It is shown that additional buoyant body forces act stabilizing on the axisymmetric flow in high Prandtl number fluids for both heating and cooling from below. For heating from below, the onset of time-dependent convection is delayed to higher Marangoni numbers than for cooling from below, in agreement with previously unexplained experimental findings. In the absence of thermocapillary effects two axisymmetric convective solutions bifurcate from the conducting basic state. This perfect pitchfork bifurcation is perturbed by weak thermocapillary forces. The linear stability of all three axisymmetric base states is investigated numerically for Pr=4, a Prandtl number typical for model experiments.

On the induction criterion of the Marangoni convection at the gas/liquid interface

Abstract: Some spreading solutes were found to be effective in enhancing the absorption rate by provoking interfacial turbulence at the gas−liquid surface. In this work, the induction criterion of the Marang...

Correlation between experimental results and numerical solutions of the Navier–Stokes problem for noncoalescing liquid drops with Marangoni effects

Abstract: Experiments show that, when two drops are brought in contact and pushed toward each other in the presence of temperature differences, coalescence is inhibited. Axisymmetric numerical solutions of the Navier–Stokes problem have been obtained to give an explanation of the phenomenon, assuming that a thin air film exists between the contacting drops and that, provided that well-defined dynamic conditions prevail on the liquid surfaces, the film experiences a suitable pressure that balances the pressure in the drops. The numerical results agree with the experimental ones, qualitatively explain why an air film between the drops could be created by Marangoni effects and show that the suppression of coalescence is obtained as long as films sufficiently large exhibit excess pressures of the same order of magnitude of the pressure needed to deform the drops.

Interaction of Reaction-Diffusion Fronts and Marangoni Flow on the Interface of a Deep Fluid

Abstract: It is shown that interfacial solitary structures (spots) generated by a bistable chemical reaction can be stabilized by Marangoni flow preventing the spread of a dynamically favorable state with a higher surface tension. The solutions are constructed using the method of matched asymptotic expansions to resolve the singularity at a sharp interface between the alternative states, and to compute the self-induced flow velocity advecting the domain boundary. {copyright} {ital 1997} {ital The American Physical Society}