Showing papers on "Marangoni effect published in 2001"

Fast drop movements resulting from the phase change on a gradient surface.

Abstract: The movement of liquid drops on a surface with a radial surface tension gradient is described here. When saturated steam passes over a colder hydrophobic substrate, numerous water droplets nucleate and grow by coalescence with the surrounding drops. The merging droplets exhibit two-dimensional random motion somewhat like the Brownian movements of colloidal particles. When a surface tension gradient is designed into the substrate surface, the random movements of droplets are biased toward the more wettable side of the surface. Powered by the energies of coalescence and collimated by the forces of the chemical gradient, small drops (0.1 to 0.3 millimeter) display speeds that are hundreds to thousands of times faster than those of typical Marangoni flows. This effect has implications for passively enhancing heat transfer in heat exchangers and heat pipes.

Evaporative instabilities in climbing films

Abstract: We consider flow in a thin lm generated by partially submerging an inclined rigid plate in a reservoir of ethanol{ or methanol{water solution and wetting its surface. Evaporation leads to concentration and surface tension gradients that drive flow up the plate. An experimental study indicates that the climbing lm is subject to two distinct instabilities. The rst is a convective instability characterized by flattened convection rolls aligned in the direction of flow and accompanied by free-surface deformations; in the meniscus region, this instability gives rise to pronounced ridge structures aligned with the mean flow. The second instability, evident when the plate is nearly vertical, takes the form of transverse surface waves propagating up the plate. We demonstrate that the observed longitudinal rolls are driven by the combined influence of surface deformations and alcohol concentration gradients. Guided by the observation that the rolls are flattened, we develop a quasi-two-dimensional theoretical model for the instability of the lm, based on lubrication theory, which includes the eects of gravity, capillarity and Marangoni stresses at the surface. We develop stability criteria for the lm which are in qualitative agreement with our experimental observations. Our analysis yields an equation for the shape of the interface which is solved numerically and reproduces the salient features of the observed flows, including the slow lateral drift and merging of the ridges.

Effects of surface active elements on weld pool fluid flow and weld penetration in gas metal arc welding

Abstract: This article presents a mathematical model simulating the effects of surface tension (Maragoni effect) on weld pool fluid flow and weld penetration in spot gas metal arc welding (GMAW). Filler droplets driven by gravity, electromagnetic force, and plasma arc drag force, carrying mass, thermal energy, and momentum, periodically impinge onto the weld pool. Complicated fluid flow in the weld pool is influenced by the droplet impinging momentum, electromagnetic force, and natural convection due to temperature and concentration gradients, and by surface tension, which is a function of both temperature and concentration of a surface active element (sulfur in the present study). Although the droplet impinging momentum creates a complex fluid flow near the weld pool surface, the momentum is damped out by an “up-and-down” fluid motion. A numerical study has shown that, depending upon the droplet’s sulfur content, which is different from that in the base metal, an inward or outward surface flow of the weld pool may be created, leading to deep or shallow weld penetration. In other words, it is primarily the Marangoni effect that contributes to weld penetration in spot GMAW.

Marangoni effect in laser deep penetration welding of steel

Abstract: In welding, the resulting weld-seam geometry may vary significantly although using constant process parameters and steels with the same material number. One likely reason for this are small variations in the concentration of sulfur, phosphorus, oxygen, and other chemical elements that are well within the tolerance of the standard of a specific alloy. These substances act as surfactants and even marginal changes strongly effect the temperature-dependent coefficient of surface tension. In simulations of conventional electric arc welding and laser heat conduction welding, the effect of the temperature-dependent coefficient of surface tension (Marangoni effect) has been identified as one of the primary driving forces of the liquid melt. In laser deep penetration welding simulations this effect has been widely neglected, so far. In this contribution, simulations of flow fields in the weld pool resulting from different temperature dependencies of the coefficient of surface tension are presented. The simulations...

Models for Marangoni drying

Abstract: Marangoni drying is a new ultra-clean drying process, which relies on surface-tension gradient forces, so-called Marangoni stresses. This method is of particular use in the semiconductor industry wherein obtaining ultra-clean surfaces is of paramount importance. The present work provides a mathematical description of this novel process involving four coupled partial differential equations, derived in the thin-layer approximation, for the film thickness, the concentration of chemicals in the air, at the air–liquid interface and in the bulk of the liquid film. Numerical solution of these equations yields prediction of typical profiles that accompany the spreading and drying processes. Particular attention is aimed at the prediction of the minimum film thickness as a function of system parameters with a view to optimizing the drying process.

Droplets Speeding on Surfaces

Abstract: How fast a droplet will spread on a solid surface depends on the surface tension gradient and the wettability. The temperature dependence of the surface tension is exploited in a so-called Marangoni flow, but capillary forces can counteract this type of flow. Wasan et al. highlight the report by Danielet al., who have devised a method for harnessing the capillary flow such that it enhances the Marangoni flow. They achieve droplet speeds of up to 1.5 meters per second. The concept may be of interest in applications involving coatings, adhesion, and heat transfer.

The dynamics of a viscous soap film with soluble surfactant

Abstract: Nearly two decades ago, Couder (1981) and Gharib & Derango (1989) used soap films to perform classical hydrodynamics experiments on two-dimensional flows. Recently soap films have received renewed interest and experimental investigations published in the past few years call for a proper analysis of soap film dynamics. In the present paper, we derive the leading-order approximation for the dynamics of a flat soap film under the sole assumption that the typical length scale of the flow parallel to the film surface is large compared to the film thickness. The evolution equations governing the leading-order film thickness, two-dimensional velocities (locally averaged across the film thickness), average surfactant concentration in the interstitial liquid, and surface surfactant concentration are given and compared to similar results from the literature. Then we show that a sufficient condition for the film velocity distribution to comply with the Navier–Stokes equations is that the typical flow velocity be small compared to the Marangoni elastic wave velocity. In that case the thickness variations are slaved to the velocity field in a very specific way that seems consistent with recent experimental observations. When fluid velocities are of the order of the elastic wave speed, we show that the dynamics are generally very specific to a soap film except if the fluid viscosity and the surfactant solubility are neglected. In that case, the compressible Euler equations are recovered and the soap film behaves like a two-dimensional gas with an unusual ratio of specific heat capacities equal to unity.

Prandtl number effects for marangoni convection over a flat surface

Abstract: This paper presents a similarity solution for Marangoni flow over a flat surface for both the momentum equations and the energy equation assuming a developing boundary layer along a surface The analysis also shows how the heat transfer and flow rate vary with Prandtl number Since the Predicted boundary layer thickness would be less than the diameter of a typical Vapor bubble during nucleate boiling, the curvature effects can be neglected and this analysis can be used as a first estimate of the effect of Marangoni flow around a vapor bubble

Stability of thermocapillary flows with inclined temperature gradient

Abstract: The stability of a two-layer return thermocapillary flow in the presence of an inclined temperature gradient is investigated. Both a linear stability analysis and nonlinear simulations have been performed for an air–water system. It is found that a rather weak deviation of the mean temperature gradient from the vertical direction suppresses Pearson's instability mechanism and leads to the appearance of oblique hydrothermal waves. In a certain region of parameters, transverse convective rolls drifting with the mean flow appear.

Thermosolutal marangoni forced convection boundary layers

Abstract: An analysis is made for the forced convection thermal and solute concentration Marangoni boundary layers (thin dissipative layers) that can be formed along the surface, which separates two immiscible fluids in surface driven flows when the appropriately defined Reynolds number is large enough. Similarity equations for the case in which an external pressure gradient is imposed are derived. These equations are then solved numerically for some values of the involved parameters using very efficient numerical schemes known as Keller-box and superposition methods and the features of the flow and transport characteristics are analysed and discussed.

The Dynamics of Marangoni-Driven Local Film Drainage between Two Drops.

Abstract: A study of Marangoni-driven local continuous film drainage between two drops induced by an initially nonuniform interfacial distribution of insoluble surfactant is reported. Using the lubrication approximation, a coupled system of fourth-order nonlinear partial differential equations was derived to describe the spatio-temporal evolution of the continuous film thickness and surfactant interfacial concentration. Numerical solutions of these governing equations were obtained using the Numerical Method of Lines with appropriate initial and boundary conditions. A full parametric study was undertaken to explore the effect of the viscosity ratio, background surfactant concentration, the surface Peclet number, and van der Waals interaction forces on the dynamics of the draining film for the case where surfactant is present in trace amounts. Marangoni stresses were found to cause large deformations in the liquid film: Thickening of the film at the surfactant leading edge was accompanied by rapid and severe thinning far upstream. Under certain conditions, this severe thinning leads directly to film rupture due to the influence of van der Waals forces. Time scales for rupture, promoted by Marangoni-driven local film drainage were compared with those associated with the dimpling effect, which accompanies the approach of two drops, and implications of the results of this study on drop coalescence are discussed.

Three‐dimensional numerical simulation of Marangoni instabilities in liquid bridges: influence of geometrical aspect ratio

Abstract: Oscillatory Marangoni convection in silicone oil–liquid bridges with different geometrical aspect ratios is investigated by three-dimensional and time-dependent numerical simulations, based on control volume methods in staggered cylindrical non-uniform grids. The three-dimensional oscillatory flow regimes are studied and compared with previous experimental and theoretical results. The results show that the critical wavenumber (m), related to the azimuthal spatio-temporal flow structure, is a monotonically decreasing function of the geometrical aspect ratio of the liquid bridge (defined as the ratio of length to diameter). For this function, a general correlation formula is found, which is in agreement with the previous experimental findings. The critical Marangoni number and the oscillation frequency are decreasing functions of the aspect ratio; however, the critical Marangoni number, based on the axial length of the bridge, does not change much with the aspect ratio. For each aspect ratio investigated, the onset of the instability from the axisymmetric steady state to the three-dimensional oscillatory one is characterized by the appearance of a standing wave regime that exhibits, after a certain time, a second transition to a travelling wave regime. The standing wave regime is more stable for lower aspect ratios since it lasts for a long time. This behaviour is explained on the basis of the propagation velocity of the disturbances in the liquid phase. For this velocity, a general correlation law is found as a function of the aspect ratio and of the Marangoni number. Copyright © 2001 John Wiley & Sons, Ltd.

“Marginal pinching” in soap films

Abstract: We discuss the behaviour of a thin soap film facing a frame element: the pressure in the Plateau border around the frame is lower than the film pressure, and the film thins out over a certain distance λ(t), due to the formation of a well-localized pinched region of thickness h(t) and extension w(t). We construct a hydrodynamic theory for this thinning process, assuming a constant surface tension: Marangoni effects are probably important only at late stages, where instabilities set in. We find λ(t) ~ t1/4, and for the pinch dimensions, h(t) ~ t−1/2 and w(t) ~ t−1/4. These results may play a useful role for the discussion of later instabilities leading to a global film thinning and drainage, as first discussed by K. Mysels under the name "marginal regeneration".

Topological defects after a quench in a Bénard-Marangoni convection system.

Abstract: We report experimental evidence of the fact that, in a Benard-Marangoni conduction-convection transition, the density of defects in the emerging structure scales as a power law in the quench time needed for the control parameter to ramp through the threshold. The obtained scaling exponents differ from the ones predicted and observed in the case in which the defects correspond to zeros in the amplitude of the global two-dimensional field.

Thermocapillary migration of long bubbles in polygonal tubes. I. Theory

Abstract: Thermocapillary migration of long gas bubbles in cylinders of regular-polygonal or rectangular cross sections is studied. An imposed axial temperature gradient produces a gradient of surface tension leading to a steady migration of the bubble towards the hotter region. A leading order approximation for the bubble migration speed is found by computing the volume flux of liquid through the corner regions of the cylinder, which provide a parallel channel for the flow of fluid driven by the Marangoni stress. A global mass balance is used to relate the dimensionless bubble speed to the modified capillary number Δσ*=γTβa/σ, where β is the temperature gradient, a the tube length scale, σ the mean surface tension, and γT the temperature coefficient of surface tension. The dimensionless bubble speed is found to be linear in this parameter at leading order. The approximation is improved by accounting for the deposition of a thin film on the cylinder walls at small capillary number. A modified Landau–Levich equation...

Onset of oscillatory interfacial instability and wave motions in Bénard layers

Abstract: Publisher Summary This chapter describes the onset of oscillatory interfacial instability and wave motions in Benard layers. An account of the basic equations and approximations needed to study Benard convection with heat or mass transfer and Marangoni stresses is presented. According to Pearson's theory, a liquid layer open to passive air is unstable to a well-defined short-wave planform of steady cellular convection for a critical value of the Marangoni number when the heating is from the liquid side. It is shown that that oscillatory instability is possible for gradients of the opposite sense if due account is taken of the dynamics of both the upper and lower phases as for the case of an interface between two liquids with transport from either side. It is found that when the Rayleigh numbers of two layers are very different from one another, the onset of instability in one of the layers drives the other, and hence the appearance of two counter-rotating cells. It is observed that when both Rayleigh numbers approach a common value, for about the same critical wavenumbers, the situation is more complex. The nonlinear waves and dissipative solitons are also elaborated.

Measurement and computation of hydrodynamic coupling at an air/water interface with an insoluble monolayer

Abstract: The coupling between a bulk vortical flow and a surfactant-influenced air/water interface has been examined in a canonical flow geometry through experiments and computations. The flow in an annular region bounded by stationary inner and outer cylinders is driven by the constant rotation of the floor and the free surface is initially covered by a uniformly distributed insoluble monolayer. When driven slowly, this geometry is referred to as the deep-channel surface viscometer and the flow is essentially azimuthal. The only interfacial property that affects the flow in this regime is the surface shear viscosity, μs, which is uniform on the surface due to the vanishingly small concentration gradient. However, when operated at higher Reynolds number, secondary flow drives the surfactant film towards the inner cylinder until the Marangoni stress balances the shear stress on the bulk fluid. In general, the flow can be influenced by the surface tension, σ, and the surface dilatational viscosity, κs, as well as μs. However, because of the small capillary number of the present flow, the effects of surface tension gradients dominate the surface viscosities in the radial stress balance, and the effect of μs can only come through the azimuthal stress. Vitamin K1 was chosen for this study since it forms a well-behaved insoluble monolayer on water and μs is essentially zero in the range of concentration on the surface, c, encountered. Thus the effect of Marangoni elasticity on the interfacial stress could be isolated. The flow near the interface was measured in an optical channel using digital particle image velocimetry. Steady axisymmetric flow was observed at the nominal Reynolds number of 8500. A numerical model has been developed using the axisymmetric Navier–Stokes equations to examine the details of the coupling between the bulk and the interface. The nonlinear equation of state, σ(c), for the vitamin K1 monolayer was measured and utilized in the computations. Agreement was demonstrated between the measurements and computations, but the flow is critically dependent on the nonlinear equation of state.

Motion of a drop in a vertical temperature gradient at small Marangoni number the critical role of inertia

Abstract: When a drop moves in a uniform vertical temperature gradient under the combined action of gravity and thermocapillarity at small values of the thermal Peclet number, it is shown that inclusion of inertia is crucial in the development of an asymptotic solution for the temperature field. If inertia is completely ignored, use of the method of matched asymptotic expansions, employing the Peclet number (known as the Marangoni number) as the small parameter, leads to singular behaviour of the outer temperature field. The origin of this behaviour can be traced to the interaction of the slowly decaying Stokeslet, arising from the gravitational contribution to the motion of the drop, with the temperature gradient field far from the drop. When inertia is included, and the method of matched asymptotic expansions is used, employing the Reynolds number as a small parameter, the singular behaviour of the temperature field is eliminated. A result is obtained for the migration velocity of the drop that is correct to O(Re 2 log Re)

Diffuse-interface modelling of thermocapillary flow instabilities in a Hele-Shaw cell

Abstract: In this paper we present the results of a diffuse-interface model for thermocapillary or Marangoni flow in a Hele-Shaw cell. We use a Galerkin-type spectral element discretization, based on Gauss–Lobatto quadrature, for numerical implementation of the governing equations resulting from the diffuse-interface model. The results are compared to classical results for a linear and circular fixed interface. It is found that the diffuse-interface solution converges to the classical solution in the sharp-interface limit. The results are sufficiently accurate if the interfacial thickness is only small compared to the size of the thermocapillary boundary layer, even if the interfacial thickness used is much larger than the real interfacial thickness. We also consider freely movable interfaces with a temperature gradient perpendicular to the interface. It will be shown that this situation can lead to a destabilizing Marangoni convection.