Showing papers on "Marangoni effect published in 1994"

Nonlinear evolution equations for thin liquid films with insoluble surfactants

Abstract: The dynamics of a free‐liquid film with insoluble surfactants is followed until film rupture with a simple model based on three nonlinear evolution equations for the film thickness, the surfactants concentration and the tangential velocity of the fluid in the film. This model is derived asymptotically from the full Navier–Stokes equations for free films and incorporates the effect of van der Waals attraction, capillary forces and Marangoni forces due to gradients of surface tension. Different stability regimes are observed numerically for periodic and fixed boundary conditions and several initial conditions. Furthermore, the role of the relevant parameters (Hamaker constant, tension, Marangoni number) on the rupture time is assessed and comparison is made with the flow dynamics for a liquid film with insoluble surfactants on a solid substrate.

On a nonlinear thermocapillary effect in thin liquid layers

Abstract: Dilute aqueous solutions of long alcohol chains were recently found to cause a quadratic dependence of surface tension on the temperature without affecting other bulk properties of the liquid: σ = σ0 + αQ(T − T0)2, αQ > 0. The impact of such Marangoni instability on the behaviour of a thin liquid layer is studied in this work. We derive an equation describing a nonlinear spatiotemporal evolution of a thin film. The behaviour of the perturbed film in the absence of gravity, critically depends on whether the temperature T0, yielding a minimal surface tension, is attained on the surface of the film. When this is the case, a qualitatively new behaviour is observed: perturbations of the film interface may evolve into continuous steady patterns that do not rupture. Otherwise, the observed patterns due to the linear and quadratic Marangoni effects are qualitatively similar and result in the rupture of the film into separate drops.

Interaction between short‐scale Marangoni convection and long‐scale deformational instability

Abstract: Nonlinear evolution of two interacting modes of the Marangoni convection, a long‐scale deformational mode and a short‐scale stationary convective pattern, is considered. It is shown that the interaction between modes stabilizes surface deformation and leads to formation of various convective structures: stationary long‐scale modulated roll patterns, traveling and standing long waves, and can also cause chaotic convection (interfacial turbulence).

A three‐dimensional description of solitary waves and their interaction in Marangoni–Bénard layers

Abstract: A dissipation‐modified Boussinesq‐like system of equations governing three‐dimensional long wavelength Marangoni–Benard oscillatory convection in a shallow layer heated from the air side is presented. Solitary waves and their oblique and head‐on interactions are considered, thus leading to results that compare well with available experimental data.

Stability analysis of Benard-Marangoni convection in fluids with internal heat generation

Abstract: The effect of uniform distribution of internal heat generation on the stability of the Benard-Marangoni convection in a horizontal fluid layer with a deformable upper free surface is investigated. The stability analysis in this study is based on the linear stability theory. The eigenvalue equations obtained from the analysis are solved by using the fourth-order Runge-Kutta-Gill method with the shooting technique. The results indicate that the stability of Benard-Marangoni convection is significantly affected by internal heat generation in the fluid layer and by surface tension at the upper free surface. There are two different kinds of instability mode: the thermal mode and the surface tensile mode. At lower values of the Crispation number C, the instability is dominated by the thermal mode. At higher values of C, the system becomes more unstable and creates the surface tensile mode, which is induced by the surface tensile effect. The Crispation number C at the transition between the thermal and the surface tensile modes decreases as the value of internal heat generation increases and that of thermal buoyance decreases. The bond number Bo at the mode transition increases due to the existence of the internal heat generation. In addition, the system becomes more stable when the Biot number Bi of the upper free surface increases.

Lubrication theory for reactive spreading of a thin drop

Abstract: Solder drops spreading on metallic substrates are a reactive form of the wetting problem. A metallic component may diffuse in the liquid toward a metal substrate, where it is consumed by a reaction that forms a solid intermetallic phase. The resulting spatial variation in the composition of the drop may cause composition gradients along the free surface of the drop. Together with any thermal gradients along the free surface, Marangoni effects may, in turn, modify the bulk transport in the spreading drop. Motivated by this situation, we extend lubrication theory for the spreading of thin drops in the presence of gravity and thermocapillarity to include mass transport and solutocapillarity. We use an approximate solute profile in the drop to derive coupled evolution equations for the free surface shape and concentration field. Numerical solutions for the nonreactive (single component) drop agree well with previous theory. In the reactive case, we are only able to compute results for parameters outside of th...

Analysis of velocity data taken in Surface Tension Driven Convection Experiment in microgravity

Abstract: Some velocity field results from the Surface Tension Driven Convection Experiment (STDCE) that was conducted aboard the USML‐1 Spacelab in 1992 are reported. 10 cSt silicone oil was placed in an open circular container (10 cm wide×5 cm deep) and heated either by a cylindrical heater (1.11 cm diam) placed along the centerline or by a CO2 laser to induce thermocapillary flow. Tests were conducted under varieties of powers, laser beam diameters, and free‐surface shapes. The flow field was studied by flow visualization and the data were analyzed by a PIV technique. The results from the velocity measurement are presented and the effects of heating mode and free‐surface shape on the flow are discussed. The results are also compared with a numerical analysis conducted in conjunction with the experiment. Good agreement is shown.

Marangoni Convection With a Curved and Deforming Free Surface in a Cavity

Abstract: A finite-volume based computational model is developed to predict Marangoni convection in a cavity with a curved and deforming free surface. The two-dimensional incompressible continuity, momentum, and energy equations are solved on a staggered Cartesian grid. The free surface location is computed using the volume-of-fluid transport equation. Normal and tangential boundary conditions at the free surface are modeled using respectively a surface pressure and a continuum surface force technique. Computational predictions of thermocapillary flow in a shallow cavity are shown to be in good agreement with previously published asymptotic results. The new transient model is then used to study the influence of Marangoni number and Capillary number on thermocapillary flows in a cavity for different static contact angles. The flows are characterized by streamline and isotherm patterns. The influence of the dimensionless parameters on heat transfer rate at the cavity walls is exposed by examination of local Nusselt number profiles.

Drop motion with surfactant transfer in a homogeneous surrounding

Abstract: The influence of a soluble surfactant on the stationary motion of a drop in an infinite motionless homogeneous surfactant solution is considered when the surfactant undergoes a first‐order isothermal chemical reaction on the surface of the drop. The study is carried out for the asymptotic case of small Reynolds and Peclet numbers. First, the linear approximation is considered. It appears, in particular, that the hydrodynamical force acting on the drop provides either thrust or drag according to the parameter values. It also appears that the motion can be unstable and critical Marangoni numbers corresponding to instability thresholds of the motionless state of the fluids in the absence of buoyancy are provided. Emphasis is given to instability of the drop to its translations. A weakly nonlinear analysis past translational instability shows the possibility of multiple stationary states. On the one hand the hydrodynamical force dependence on the drop velocity can be nonmonotonous. Then, in particular, one ma...

On the instabilities of vertical falling liquid films in the presence of surface-active solute

Abstract: A linear-stability analysis is performed on a vertical falling film with a surface-active solute. It is assumed in the present model that the surfactant is soluble and volatile. In addition to the surface wave mode and the ‘wall wave’ mode which originate from the gravity-driven flow of the falling film itself, a new mode of instability related to the Marangoni effect induced by surface tension gradients is found for low Reynolds numbers and for moderate- or short-wavelength disturbances. The new mode is thought to be analogous to the thermocapillary instability examined first by Pearson (1958). The Marangoni instability of large-wavelength disturbances, revealed by Goussis & Kelly (1990) in a study of a liquid layer heated from below, may be completely suppressed in the present system by the effect of surface-excess concentration of the surfactant. The influence of the desorption of the solute and of its adsorption at the gas-liquid interface is determined for both the surface wave mode and the new wave mode. Desorption of the surfactant is shown to be responsible for the Marangoni instability of the new mode.

Effects of Marangoni convection on transient droplet evaporation

Abstract: Results from a computational model of transient droplet vaporization are presented In this model, axisymmetric flows around translating single component droplets are assumed The governing equations are expressed in finite volume form and solved numerically for transient velocity, species and temperature profiles Fully variable properties in the gas and liquid phases are allowed (except for liquid densities, which are held constant), and pressures of 1 and 10 atm are considered A unique feature of the calculations is the inclusion of surface-tension gradients resulting from droplet surface temperature variations Results show that surface-tension gradients significantly affect droplet internal temperature and velocity fields even when initial droplet Reynolds numbers, based on droplet diameters and free-stream conditions, are as large as 50 When surface-tension gradients are allowed at high initial Reynolds numbers (SO), droplet internal circulation rates are found to be initially increased f

The effect of a uniform magnetic field on the onset of steady Marangoni convection in a layer of conducting fluid with a prescribed heat flux at its lower boundary

Abstract: In this paper a combination of analytical and numerical techniques are used to analyze the effect of a uniform vertical magnetic field on the onset of steady Marangoni convection in a horizontal layer of quiescent, electrically conducting fluid with a uniform vertical temperature gradient subject to a prescribed heat flux at its rigid lower boundary. Critical Marangoni numbers for the onset of instability are calculated which are significantly different from those calculated previously in the case of an isothermal lower boundary. Analytical results for the behavior of the critical Marangoni number in the asymptotic limit of large magnetic field strength are also obtained. It is concluded that the magnetic field always has a stabilizing effect on the onset of steady Marangoni convection, but that when the free surface is deformable situations with a sufficiently large Marangoni number will always have unstable modes no matter how strong the applied magnetic field is.

Bénard-Marangoni instability in a viscoelastic Jeffreys' fluid layer

Abstract: Coupled buoyancy (Benard) and thermocapillary (Marangoni) convection in a thin fluid layer of a viscoelastic fluid are studied. The viscoelastic fluid is modeled by Jeffreys' constitutive equation. The lower surface of the layer is in contact with a rigid heat-conducting plate while its upper surface is subject to a temperature-dependent surface tension. The critical temperature difference between both boundaries corresponding to the onset of convection is calculated. The role of the various viscometric coefficients is discussed. In the appendix it is shown that Jeffreys' constitutive relation is easily derived from thermodynamic considerations based on extended irreversible thermodynamics.

Comments on the numerical investigation of Rayleigh and Marangoni convection in a vertical circular cylinder

Abstract: Convection in a cylindrical container was simulated with a three‐dimensional, time‐dependent code. For the case of purely Rayleigh convection, a completely rigid cylinder with adiabatic vertical walls and conducting horizontal walls was considered. The calculations showed that the individual velocity components could be in a transient state, while the total heat transfer was steady. This occurred in cases where the maximum azimuthal component of velocity was very small in magnitude, in comparison to the other two components, and this component decreased in time. On the other hand, the total kinetic energy along with the heat transfer reached a steady value. Consequently the present results have been shown to be at variance with the calculations of Neumann [J. Fluid Mech. 214, 559 (1990)]. Marangoni convection was modeled with a free flat surface on the upper side, assuming the superimposed second layer to be passive. The numerically obtained critical Marangoni numbers and flow patterns were compared favorably to earlier results from linearized stability. In addition, flow structural changes for supercritical Marangoni numbers were illustrated. Interestingly, axisymmetric disturbances led to nonsymmetric bifurcation diagrams, but three‐dimensional disturbance calculations led to symmetry in the bifurcation plots. Another very interesting result was the observed transition from three‐dimensional to two‐dimensional patterns as the Marangoni number was increased. Large computational requirements precluded a detailed parametric study. The special case of Prandtl number equal to 6.7 (corresponding to water), and in the case of Marangoni convection, a surface Biot number of unity was assumed.

Thermocapillary migration of a bidisperse suspension of bubbles

Abstract: We consider the thermocapillary motion of a well-mixed suspension of non-conducting spherical bubbles of negligible viscosity in a viscous conducting liquid under conditions of vanishingly small Reynolds and Marangoni numbers. Acrivos, Jeffrey & Saville showed that when all the bubbles are of identical size, the ensemble-averaged migration velocity U 1 of a test bubble of radius a, within the suspension equals U 1 (0) [1-3/2c 1 +O(c 1 2 )], where c 1 is the volume fraction of the bubbles and U 1 (0) is the thermocapillary velocity of a single bubble given by Young, Goldstein & Block

Active Drops and Drop Motions due to Nonequilibrium Phenomena

Abstract: The influence of nonequilibrium phenomena such as heat and mass transfer and chemical reactions on the behavior of a drop with the surface tension sensitive to the temperature and composition is considered in linear and weakly nonlinear approximations. Particular attention is paid to the case of a drop in a homogeneous surrounding when due to the thermo(soluto)-hydrodynamical instability spontaneous breakdown of the radial symmetry of temperature and/or concentration distributions and thus translatory drop motion occur.

Boundary effects on the Bénard-Marangoni instability under an electric field

Abstract: This article theoretically studies the Benard-Marangoni instability problem for a liquid layer with a free upper surface, which is heated from below by a heating coil through a solid plate in ana.c. electric field. The boundary effects of the solid plate, which include its thermal conductivity, electric conductivity and thickness, have great influences on the onset of convective instability in the liquid layer. The stability analysis in this study is based on the linear stability theory. The eigenvalue equations obtained from the analysis are solved by using the fourth order Runge-Kutta-Gill's method with the shooting technique. The results indicate that the solid plate with a higher thermal or electric conductivity and a bigger thickness tends to stabilize the system. It is also found that the critical Rayleigh numberR c, the critical Marangoni numberM c, and the criticala.c. Rayleigh numberE ac become smaller as the intensity of thea.c. electric field increases.

Effect of surface tension on the stability of a binary fluid layer under reduced gravity

Abstract: A temperature gradient imposed across a binary fluid layer with a nonzero Soret coefficient will induce a solute concentration gradient. The ratio of these two gradients is proportional to the separation ratio χ, a property of the fluid. Similarly, the ratio of the thermal and solutal Marangoni numbers, which are nondimensional increments in surface tension due to changes in temperature and concentration, is also proportional to the separation ratio. As a consequence, the stability of a given binary fluid layer with a free surface under zero gravity depends only on the temperature difference, ΔT, imposed across the layer or, equivalently, on the thermal Marangoni number, M, albeit the dependence, is rather complicated. When the gravity is nonzero but of small magnitude, such that the buoyancy effects are not dominant, the stability characteristics of the layer are functions of two parameters, M and R, the thermal Rayleigh number. In this paper, the stability of such a binary layer under zero and reduced g...

The chaotic evolution of patterns in Benard-Marangoni convection with square symmetry

Abstract: We present the results of a Benard-Marangoni convection experiment in a square container with small aspect ratio. When the control parameters are slightly changed, a sequence of bifurcations is observed. Moreover, in some measurable region of parameter space, a chaotic behaviour is evidenced. We show that these dynamics can be explained by assuming that the system is close to a codimension two (Takens-Bogdanov) bifurcation after taking into account the symmetries of the system. The dynamical model deduced from these simple observations reflects many of the features present in the experiment. The characteristics of the chaotic regime are also compared with those of the model.

Transient Motion of a Gas Bubble in a Thermal Gradient in Low Gravity

Abstract: The transient motion of a gas bubble induced by thermocapillary action in a low gravity environment is numerically investigated at low to moderate Marangoni numbers for the special case of high Prandtl number fluids. It was found that for Marangoni numbers greater than unity, the distance traveled by the bubble is a better scale to predict the approach to steady-state velocities than is the scaling factor R 2 /α.