Showing papers on "Marangoni effect published in 1999"

Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows

Abstract: The dynamic behaviour and stability of a two-dimensional immiscible droplet subject to shear or pressure-driven flow between parallel plates is studied under conditions of negligible inertial and gravitational forces. The droplet is attached to the lower plate and forms two contact lines that are either fixed or mobile. The boundary-integral method is used to numerically determine the flow along and dynamics of the free surface. For surfactant-free interfaces with fixed contact lines, the deformation of the interface is determined for a range of capillary numbers, droplet to displacing fluid viscosity ratios, droplet sizes and flow type. It is shown that as the capillary number or viscosity ratio or size of the droplet increases, the deformation of the interface increases and above critical values of the capillary number no steady shape exists. For small droplets, and at low capillary numbers, shear and pressure-driven flows are shown to yield similar steady droplet shapes. The effect of surfactants is studied assuming a fixed amount of surfactant that is subject to convective–diffusive transport along the interface and no transport to or from the bulk fluids. Increasing the surface Peclet number, the ratio of convective to diffusive transport, leads to an accumulation of surfactant at the downstream end of the droplet and creates Marangoni stresses that immobilize the interface and reduce deformation. The no-slip boundary condition is then relaxed and an integral form of the Navier-slip model is used to examine the effects of allowing the droplet to slip along the solid surface in a pressure-driven flow. For contact angles less than or equal to 90°, a stable droplet spreads along the wall until a steady shape is reached, when the droplet translates across the wall at a constant velocity. The critical capillary number is larger for these droplets compared to those with pinned contact lines. For contact angles greater than 90°, the wetted area between a stable droplet and the wall decreases until a steady shape is reached. The critical capillary number for these droplets is less than that for pinned droplets. Above the critical capillary number the droplet completely detaches for a contact angle of 120°, or part of it is pinched off leaving behind a smaller attached droplet for contact angles less than or equal to 90°.

Thermocapillary migration of bubbles and drops at moderate to large Marangoni number and moderate Reynolds number in reduced gravity

Abstract: Results from experiments on the thermocapillary migration of air bubbles and Fluorinert drops in a Dow–Corning silicone oil aboard a NASA Space Shuttle mission are presented and discussed. The experiments cover a wider range of Marangoni and Reynolds numbers than that attained in a prior flight experiment. The data are consistent with earlier results, and are compared with theoretical predictions. Large air bubbles were found to deform slightly in shape to oblate spheroids while the deformation of even the largest drops was within the uncertainty of the size measurements.

The development of transient fingering patterns during the spreading of surfactant coated films

Abstract: The spontaneous spreading of an insoluble surfactant monolayer on a thin liquid film produces a complex waveform whose time variant shape is strongly influenced by the surface shear stress. This Marangoni stress produces a shocklike front at the leading edge of the spreading monolayer and significant film thinning near the source. For sufficiently thin films or large initial shear stress, digitated structures appear in the wake of the advancing monolayer. These structures funnel the oncoming flow into small arteries that continuously tip-split to produce spectacular dendritic shapes. A previous quasisteady modal analysis has predicted stable flow at asymptotically long times [Phys. Fluids A 9, 3645 (1997)]. A more recent transient analysis has revealed large amplification in the disturbance film thickness at early times [O. K. Matar and S. M. Troian, "Growth of nonmodal transient structures during the spreading of surfactant coated films," Phys. Fluids A 10, 1234 (1998)]. In this paper, we report results of an extended sensitivity analysis which probes two aspects of the flow: the time variant character of the base state and the non-normal character of the disturbance operators. The analysis clearly identifies Marangoni forces as the main source of digitation for both small and large wave number disturbances. Furthermore, initial conditions which increase the initial shear stress or which steepen the shape of the advancing front produce a larger transient response and deeper corrugations in the film. Disturbances applied just ahead of the deposited monolayer rapidly fall behind the advancing front eventually settling in the upstream region where their mobility is hampered. Recent findings confirm that additional forces which promote film thinning can further intensify disturbances [O. K. Matar and S. M. Troian, "Spreading of surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures," Chaos 9, 141 (1999). The transient analysis presented here corroborates our previous results for asymptotic stability but reveals a source for digitation at early times. The energy decomposition lends useful insight into the actual mechanisms preventing efficacious distribution of surfactant.

Effects of insoluble surfactants on the nonlinear deformation and breakup of stretching liquid bridges

Abstract: During the emission of single drops and the atomization of a liquid from a nozzle, threads of liquid are stretched and broken. A convenient setup for studying in a controlled manner the dynamics of liquid threads is the so-called liquid bridge, which is created by holding captive a volume of liquid between two solid disks and pulling apart the two disks at a constant velocity. Although the stability of static bridges and the dynamics of stretching bridges of pure liquids have been extensively studied, even a rudimentary understanding of the dynamics of the stretching and breakup of bridges of surfactant-laden liquids is lacking. In this work, the dynamics of a bridge of a Newtonian liquid containing an insoluble surfactant are analyzed by solving numerically a one-dimensional set of equations that results from a slender-jet approximation of the Navier–Stokes system that governs fluid flow and the convection-diffusion equation that governs surfactant transport. The computational technique is based on the method-of-lines, and uses finite elements for discretization in space and finite differences for discretization in time. The computational results reveal that the presence of an insoluble surfactant can drastically alter the physics of bridge deformation and breakup compared to the situation in which the bridge is surfactant free. They also make clear how the distribution of surfactant along the free surface varies with stretching velocity, bridge geometry, and bulk and surface properties of the liquid bridge. Gradients in surfactant concentration along the interface give rise to Marangoni stresses which can either retard or accelerate the breakup of the liquid bridge. For example, a high-viscosity bridge being stretched at a low velocity is stabilized by the presence of a surfactant of low surface diffusivity (high Peclet number) because of the favorable influence of Marangoni stresses on delaying the rupture of the bridge. This effect, however, can be lessened or even negated by increasing the stretching velocity. Large increases in the stretching velocity result in interesting changes in their own right regardless of whether surfactants are present or not. Namely, it is shown that whereas bridges being stretched at low velocities rupture near the bottom disk, those being stretched at high velocities rupture near the top disk.

A New Technique for the Spontaneous Growth of Colloidal Nanoparticle Superlattices

Abstract: The spontaneous growth of thin films of carboxylic acid derivatized colloidal gold particles electrostatically immobilized at the hydrosol-organic solution interface onto moistened hydrophilic substrates is demonstrated. Immersion of the substrates up to the interface of the biphasic mixture leads to superlattice formation by an extremely fast climbing mechanism, the process apparently driven by surface tension gradients at the substrate surface (Marangoni growth). This approach shows promise for development in the deposition of superlattice films of different surface-modified colloidal nanoparticles as well as salts of fatty lipids.

Auto-oscillation of surface tension.

Abstract: Long-time auto-oscillation of the surface tension can evolve when in an aqueous system a diethyl phthalate droplet is placed under the free water surface. The experimental conditions for development of surface tension auto-oscillations are described. Based on a theoretical analysis the mechanism of these auto-oscillations is proposed. The mechanism of the auto-oscillations results from a switching between diffusion and convection transfer of diethyl phthalate in the solution. A periodic Marangoni flow on the water surface resulting from a surface layer instability is discussed. The solubility of the amphiphile in the water and its surface activity are the main characteristics that determine the system behavior.

Time-independent square patterns in surface-tension-driven Benard convection

Abstract: The transition between hexagonal and square patterns is investigated in laboratory experiments on surface-tension-driven Benard (Marangoni) convection in a fluid of Prandtl number 81. As the Marangoni number M is increased, an ideal hexagonal pattern is supplanted by a defect-free square pattern; the transition occurs gradually with patterns of mixed hexagonal, pentagonal, and square symmetry arising at intermediate values of M. An elementary topological process associated with two-dimensional patterns governs local changes in morphology; the dynamics are relaxational with all patterns becoming stationary with M fixed for a sufficiently long time. The transition is hysteretic and depends strongly on the pattern wave number.

Control of long-wavelength Marangoni Bénard convection

Abstract: A nonlinear feedback control strategy for delaying the onset and eliminating the subcritical nature of long-wavelength Marangoni–Benard convection is investigated based on an evolution equation. A control temperature is applied to the lower wall in a gas–liquid layer otherwise heated uniformly from below. It is shown that, if the interface deflection is assumed to be known via sensing as a function of both horizontal coordinates and time, a control temperature with a cubic-order polynomial dependence on the deflection is capable of delaying the onset as well as eliminating the subcritical instability altogether, at least on the basis of a weakly nonlinear analysis. The analytical results are supported by direct numerical simulations. The control coefficients required for stabilization are O(1) for both delaying onset indefinitely and eliminating subcritical instability. In order to discuss the effects of control, a review is made of the dependence of the weakly nonlinear subcritical solutions without control upon the various governing parameters.

Marginal regeneration and the Marangoni effect

Abstract: On the basis of experimental observations described earlier, we have proposed that marginal regeneration is caused by surface tension gradients at the borders of mobile foam films. Marginal regeneration is the rate-determining mechanism in the drainage of such films, and, as such, a determining factor in the persistence (or long-term stability) of foams. Marangoni flows are caused by surface tension gradients, and these set off the exchange of thicker for thin film elements along the borders, while the total film area remains the same. In this paper we present simulations of the drainage of liquid in a vertical soap film, and show that it is realistic to expect large surface tension gradients along the lower border of the film under the conditions which lead to marginal regeneration. Copyright 1999 Academic Press.

Numerical Simulation of Thermocapillary Drop Motion with Internal Circulation

Abstract: The thermocapillary motion of drops in zero gravity is analyzed numerically. When convective transport is important, the internal circulation in the drop has a profound effect on the temperature distribution in its vicinity and hence on its migration speed. For sufficiently large values of the Marangoni number number Ma, for steady motion of the drop, the temperature difference on the drop surface and its scaled speed increase with Ma. This is in contrast to (1) existing computational results for liquid drops whose scaled speed decreases with Ma and (2) asymptotic results for gas bubbles whose scaled speed is independent of Ma when it is large.

Marangoni effect in microbubble systems

Abstract: This work explores the application of the Marangoni effect in micro systems involving small gas or vapor bubbles in a liquid environment subjected to a temperature gradient. The Marangoni effect characterizes the variation of surface tension along the bubble surface resulting from the temperature gradient around the bubble, thus driving the bubble toward the higher temperature region. This phenomenon is more pronounced as the bubble becomes smaller and the temperature gradient becomes steeper, both of which can be achieved in microbubble systems. Potential applications based on the Marangoni effect include linear bubble actuators, dynamic microvalves, and hot-spot locators. The optimum bubble size for these applications is expected to be of the order of 10 mu m. A smaller bubble may be difficult to introduce into the working system and maintain its size. Presented for illustration is a feasibility analysis for both a noncondensable gas bubble and a vapor bubble situated above a microheater. The analysis y...

A tutorial on the Rayleigh–Marangoni–Bénard problem with multiple layers and side wall effects

Abstract: A brief review in the form of a tutorial is presented on convective instabilities that arise from thermocapillary and buoyancy effects. This tutorial primarily focuses on the effect of multiple layers and side walls on the nature of the convective flows and associated patterns. A comprehensive explanation of the physics of this type of convection is followed by a discussion of the mathematical features of bifurcation associated with the problem and some of the recent experimental studies.

Instabilities of dynamic thermocapillary liquid layers with magnetic fields

Abstract: We present a linear-stability analysis for the transition from a steady, two-dimensional thermocapillary convection in a liquid-metal layer to a periodic, three-dimensional flow involving hydrothermal waves which propagate in the direction normal to the plane of the base flow. There is a uniform magnetic field applied parallel to the free surface in the plane of the base flow, and there is a linear temperature gradient along the free surface in the base flow. The ratio of the layer's length to its depth, 2L, is large. The magnetic Reynolds number is small. A key parameter is λ, the ratio of the large Hartmann number based on depth to L

Investigation of thermocapillary convection in a three-liquid-layer system

Abstract: This paper presents the first experimental results on Marangoni–Benard instability in a symmetrical three-layer system. A pure thermocapillary phenomenon has been observed by performing the experiment in a microgravity environment where buoyancy forces can be neglected. This configuration enables the hydrodynamic stability of two identical liquid–liquid interfaces subjected to a normal gradient of temperature to be studied. The flow is driven by one interface only and obeys the criterion based on the heat diffusivity ratio proposed by Scriven & Sternling (1959) and Smith (1966). The measured critical temperature difference for the onset of convection is compared to the value obtained from two-dimensional numerical simulations. The results of the simulations are in reasonable agreement with the velocimetry and the thermal experimental data for moderate supercriticality. Numerically and experimentally, the convective pattern exhibits a transition between different convective regimes for similar temperature gradients. Their common detailed features are discussed.

A model for Marangoni drying

Abstract: We propose a simple theoretical model for the movement of a thin liquid film on a flat plate that is vertically withdrawn from a large liquid reservoir in the presence of a surface tension gradient. This problem is relevant to Marangoni drying—a technique that is used in the semiconductor industry for the purpose of water removal from wafers. Due to the smallness of the capillary number the fluid flow can be described by the classical Landau–Levich equation with an additional term accounting for the Marangoni effect. A numerical solution of this equation shows that the thickness of the residual film is a monotonically decreasing function of the surface tension gradient, thereby providing an explanation of the Marangoni drying process.

Marangoni flow in liquid crystal interfaces

Abstract: This letter presents the equation of capillary hydrodynamics for interfaces between viscous isotropic fluids and nematic liquid crystals (NLCs) to establish the existence of a new class of Marangoni flow. The interfacial stress balance equation involves the surface divergence of the surface stress tensor. It is shown that the anisotropic elastic contribution to the surface stress tensor gives rise to bending stresses and tangential forces. When the tensor order parameter that describes the NLC structure has surface gradients, a tensor order parameter-driven Marangoni flow is predicted. The strength of the predicted effect is proportional to the nematic–isotropic interaction energy characteristic of the interface, and the direction of flow is from low energy regions towards high energy regions.

The mathematics of foam

Abstract: The aim of this thesis is to derive and solve mathematical models for the flow of liquid in a foam. A primary concern is to investigate how so-called `Marangoni stresses' (i.e. surface tension gradients), generated for example by the presence of a surfactant, act to stabilise a foam. We aim to provide the key microscopic components for future foam modelling. We begin by describing in detail the influence of surface tension gradients on a general liquid flow, and various physical mechanisms which can give rise to such gradients. We apply the models thus devised to an experimental configuration designed to investigate Marangoni effects. Next we turn our attention to the flow in the thin liquid films (`lamellae') which make up a foam. Our methodology is to simplify the field equations (e.g. the Navier-Stokes equations for the liquid) and free surface conditions using systematic asymptotic methods. The models so derived explain the `stiffening' effect of surfactants at free surfaces, which extends considerably the lifetime of a foam. Finally, we look at the macroscopic behaviour of foam using an ad-hoc averaging of the thin film models.

The slow motion of a single gas bubble in a non-Newtonian fluid containing surfactants

Abstract: The drag force experienced by bubbles, rising freely in an inelastic shear-thinning fluid is calculated. In particular, the effect of contaminants is considered when the continuous phase can be represented by the power-law or the three parameter Carreau models. Two cases are examined in order to take into account the effect of surfactants: (a) interfacial mass transfer is taken into account via a perturbation around the thermodynamic equilibrium values using Gibbs elasticity, (b) a continuous distribution of impurities over the whole interface (uniform retardation) leading to Marangoni stresses. The relations obtained are based on perturbation methods around the Newtonian solution. The drag force can be evaluated via the rheological model parameters, the physical properties of the system and the concentration of impurities in the fluid. The presence of contamination was found to increase the drag resulting in a decrease of the rise velocity. Inversely, the effect of shear thinning is to decrease the drag, thus leading to a balance between both effects.

Visualization and model development of Marangoni convection in NH3–H2O system

Abstract: The objectives of this paper are to obtain experimental data of surface tension and interfacial tension, and to develop a new model of Marangoni convection for the best selection of heat transfer additive in ammonia–water absorption systems. The basic mechanism of Marangoni convection in absorption systems was reviewed from the viewpoints of the surface tension and the interfacial tension gradients. Marangoni convection was successfully visualized using a shadow graphic method. The solubility limits of the additives in ammonia–water solution ranged from 500 to 3000 ppm depending on the heat transfer additives. These values are much higher than those in LiBr–H2O solution in which the solubility ranged from 70 to 400 ppm. The temperature gradient of the surface tension should not be a criterion for Marangoni convection inducement in NH3–H2O system. The concentration and temperature gradients of the interfacial tension should not be a criterion for Marangoni convection inducement in NH3–H2O system. The magnitude of the interfacial tension did not affect the occurrence of Marangoni convection either. It was found that addition of the heat transfer additive beyond the solubility limit assisted Marangoni convection occurrence, but should not be a criterion for Marangoni convection inducement. It was proposed that the radical-out model should be a criterion for Marangoni convection inducement within the solubility limit in NH3–H2O system.

Linear stability of thermocapillary convection in cylindrical liquid bridges under axial magnetic fields

Abstract: The stability of axisymmetric steady thermocapillary convection of electrically conducting fluids in half-zones under the influence of a static axial magnetic field is investigated numerically by linear stability theory. In addition, the energy transfer between the basic state and a disturbance is considered in order to elucidate the mechanics of the most unstable mode. Axial magnetic fields cause a concentration of the thermocapillary flow near the free surface of the liquid bridge. For the low Prandtl number fluids considered, the most dangerous disturbance is a non-axisymmetric steady mode. It is found that axial magnetic fields act to stabilize the basic state. The stabilizing effect increases with the Prandtl number and decreases with the zone height, the heat transfer rate at the free surface and buoyancy when the heating is from below. The magnetic field also influences the azimuthal symmetry of the most unstable mode.

Stability of the axisymmetric buoyant-capillary flows in a laterally heated liquid bridge

Abstract: The axisymmetric steady-states solutions of buoyant-capillary flows in a cylindrical liquid bridge are calculated by means of a pseudo-spectral method. The free surface is undeformable and laterally heated. The working fluid is a liquid metal, with a Prandtl number value Pr=0.01. Particular care was taken to preserve the physical regularity in our model, by writing appropriate flux boundary conditions. The location and nature of the bifurcations undergone by the flows are investigated in the space of the dimensionless numbers (Marangoni, Ma∈[0,600]; Rayleigh, Ra∈[0,5×104]). Saddle-node and Hopf bifurcations are found. By analyzing the steady state structures and the energy budgets, the saddle-node bifurcations are observed to play a determinant role. Only two sets of stable steady-states, connected by saddle-nodes, are allowed by the coupling of buoyancy and capillarity. Most of the solutions of the explored part of the (Ma, Ra) plane belong to these states.