Showing papers on "Marangoni effect published in 2000"

Rings and Hexagons Made of Nanocrystals: A Marangoni Effect

Abstract: By controlling solvent evaporation rates, it has been possible to form micrometer rings and hexagonal arrays made of nanocrystals of different sizes, shapes and materials. Such patterns are driven by surface tension gradients that induce Benard−Marangoni instabilities in the liquid films. The resulting self-assembled structures are consistent with theoretical prediction of hydrodynamic instabilities.

Experiments to simulate effect of Marangoni convection on weld pool shape

Abstract: Stationary welds of sodium nitrate (NaNO 3 , a high-Prandtl-number material) and gallium (Ga, a low-melting-point, low-Prandtl-number material) were made with a defocused CO 2 laser beam to simulate the effect of Marangoni convection on the shape of arc weld pools without a surface-active agent. A Peclet number representing the ratio of (heat transport by convection)/(heat transport by conduction) was defined as Pe = LV/a, where L is the pool surface radius, V the maximum outward surface velocity and a the thermal diffusivity. The Ga and NaNO 3 pools represented the low and high extremes of Pe, respectively, with commonly welded metals such as aluminum, steel and stainless steel falling in between. By going to these extremes, the effect of convection on the pool shape could be much more easily understood. For Ga, Pe was low because low V (weak Marangoni convection) and high a promoted conduction down into the pool, and the resultant pool bottom was concave. For NaNO 3 , however, Pe became high easily because high V (strong Marangoni convection) and very low a promoted outward convective heat transport, and the resultant pool bottom was shallow and flat. Reducing the beam diameter further increased V (even stronger Marangoni convection) and Pe. The fast outward surface flow turned and penetrated downward at the pool edge, resulting in a convex pool bottom. Both the flat and convex pool bottoms are a clear indication Marangoni convection dominated over gravity-induced buoyancy convection. It is proposed that, in the absence of both a surface-active agent and a significant electromagnetic force, the pool bottom convexity increases with increasing Pe. It was shown that, for a given material composition and welding process, the weld shape often reveals a good deal about the nature of weld pool convection.

The migration of a drop in a uniform temperature gradient at large Marangoni numbers

Abstract: The steady thermocapillary motion of a spherical drop in a uniform temperature gradient is treated in the situation where convective transport of energy is predominant in the drop phase as well as in the continuous phase, i.e., when the Marangoni numbers are large. It is assumed that the Reynolds numbers in both phases are large as well; to leading order, the velocity fields are given by a potential flow field in the continuous phase and Hill’s vortex inside the drop. The migration velocity of the drop is obtained by equating the rate at which work is done by the thermocapillary stress to the rate of viscous dissipation of energy. The analysis deals with an asymptotic situation wherein convective transport of energy dominates with conduction playing a role only where essential. This leads to thin thermal boundary layers both outside and within the drop. The method of matched asymptotic expansions is employed to solve the conjugate heat transfer problem in the two phases. It is shown that the demand for energy within the drop, necessary to increase its temperature at a steady rate as it moves into warmer surroundings, results in a large temperature difference between the surface of the drop and its interior. The variation of temperature over the drop surface is large as well, and leads to a linear increase of the migration velocity of the drop with increasing Marangoni number. This result is strikingly different from that for the limiting case when the viscosity and thermal conductivity inside the drop become negligible compared to the corresponding properties in the continuous phase. This limit, which holds for a gas bubble, is recovered correctly from the analysis.

Microgravity experiments and analysis of oscillatory thermocapillary flows in cylindrical containers

Abstract: Results are reported of thermocapillary flow experiments performed aboard the Spacelab. Oscillatory thermocapillary flows were investigated in open cylindrical containers filled with 2 cS kinematic viscosity (Prandtl number = 27 at 25 °C) silicone oil. The fluid was heated by a cylindrical cartridge heater placed at the symmetry axis of the container while the container sidewall was maintained at a lower temperature. Test containers with three different diameters of 1.2, 2.0 and 3.0 cm were used. The ratio of heater to test container diameter was fixed at 0.1. The liquid free-surface shape was either flat or concave. The flow and temperature fields were investigated for steady and oscillatory flows. Free-surface deformation was observed during oscillations. The conditions for the onset of oscillatory flow were determined. It is shown that the Marangoni number alone does not correlate the onset conditions. A new parameter, which represents free surface deformation, is derived for flat free surfaces and is shown to correlate the onset conditions well. Infrared images of free surface and oscillation frequencies are also presented.

Visualization of Marangoni convection in simulated weld pools

Abstract: A transparent pool of NaNO3 (10 mm in diameter) was heated with a defocused CO2 laser beam to simulate Marangoni convection in arc weld pools without a surface-active agent. The flow patterns were revealed clearly by flow vi- sualization with a laser light-cut tech- nique, the surface temperature profiles were measured immediately below the pool surface, and a device for measuring the beam diameter was developed. The observed Marangoni convection was ex- pected to resemble that in welding be- cause the Marangoni number was close to those in welding. Two counterrotating cells were observed in the meridian plane of the pool. The maximum veloc- ity was at the pool surface, the outward surface flow was much faster than the in- ward return flow and the centers of the cells were near the pool edge. These characteristics suggest Marangoni con- vection dominates in the pool over grav- ity-induced convection. Increasing the beam power (from 0.5 to 5.4 W) and re- ducing the beam diameter (from 5.9 to 1.5 mm) both made Marangoni convec- tion stronger. The latter, however, had a significantly greater effect; the surface flow was so much stronger as to make the return flow penetrate deeper into the pool. The results of physical simulation provided interesting insights for under- standing the significant effect of Marangoni convection on the weld pool shape, as will be presented in a follow- up report. pool is of practical interest in welding. It can have a dramatic effect on the pene- tration depth of the resultant weld (Ref. 1). Marangoni convection in a weld pool without a surface-active agent is illus- trated in Fig. 1. The surface-active agent of a liquid, e.g., S in liquid steel, is a ma- terial that can significantly reduce the surface tension of the liquid and even change its temperature dependence. As shown by the velocity profile, fluid flow near the pool surface is outward, with the maximum velocity vs located at and tan- gent to the pool surface, where the sub- script, s, denotes the tangent direction. The outward-pointing shear stress at the pool surface, τns (= -∝∂vs/∂n>0), is in- duced by the surface-tension gradients along the pool surface ∂γ/∂s (> 0), where n denotes the normal direction, ∝ is the viscosity and γ is the surface tension. These surface-tension gradients ∂γ/∂s(=∂T/∂s x ∂γ/∂T) are induced both by the temperature gradients along the pool surface ∂T/∂s (<0) and the temperature dependence of the surface tension ∂γ/∂T (<0). The fluid is pulled along the pool surface from the center (where tempera- ture is high and the surface tension is low) to the edge (where temperature is low and the surface tension is high). Herein, the outward flow along the pool surface will be called the surface flow and the in-

Effects associated with bubble formation in optical trapping

Abstract: Heating of absorbing particles in a liquid medium by an optical trapping beam may lead to bubble formation. Powerful currents, which we identify as due to Marangoni convection, can be observed in the vicinity. At the micron size scale such surface tension effects can be very powerful, whereas normal thermal convection is negligible. Similar effects cause bubbles to be attracted to regions of higher temperature, providing a very powerful means of trapping bubbles, which are repelled by optical forces in a Gaussian beam. Measurements of the temperature required for bubble formation show that it occurs above the boiling point of the surrounding liquid, in reasonable agreement with nucleation theories.

Voltammetry of Electroactive Oil Droplets. Part II: Comparison of Experimental and Simulation Data for Coupled Ion and Electron Insertion Processes and Evidence for Microscale Convection

Abstract: Modelling electrochemical processes at the three phase junction between electrode–aqueous electrolyte–oil droplet presents a considerable challenge due to the complexity of simultaneous electron transfer between electrode and droplet, ion uptake or expulsion between droplet and aqueous phase, the interaction of redox centers at high concentration, and transport processes accompanying the electrochemical process. For the case of oxidation of para-tetrahexylphenylenediamine (THPD) microdroplet deposits on basal plane pyrolytic graphite electrodes or random arrrays of microelectrodes (RAM) three models may be envisaged which proceed via A) exchange of ions between droplet and aqueous electrolyte with the electrochemical process commencing at the electrode–oil interface, B) rapid electron transport over the oil–aqueous electrolyte interface and the electrochemical process commencing from the oil–aqueous electrolyte interface inwards, and C) slow electron transport across the oil–aqueous electrolyte interface and the electrochemical process commencing solely from the triple interface. Numerical simulation procedures for these three models, which allow for interaction of redox centers via a regular solution theory approach, are compared with experimental data. A positive interaction parameter, Z=1.4, consistent with a dominant ionic liquid–ionic liquid and neutral oil–neutral oil type interaction is determined from experimental data recorded at sufficiently slow scan rates. The overall mechanism, which governs the voltammetric characteristics at higher scan rates, is shown to be apparently consistent with the triple interface model C). However, the rate of diffusional transport determined by comparison of experimental with simulation data is orders of magnitudes too high. Additional convection processes, possibly of the Marangoni type, appear to be responsible for the fast rate observed for the redox process. The significance of the models presented in the context of microdroplet deposits for other related electrochemical systems is discussed.

Behavior of nonmetallic inclusions in front of the solid-liquid interface in low-carbon steels

Abstract: The present study is concerned with the interaction phenomena of nonmetallic inclusions in front of a moving solid-liquid interface. The in situ observation was done in a high-temperature experiment by using a laser microscope. Alumina inclusions in an aluminum-killed steel with low oxygen content exhibited the well-known clustering behavior. The velocity of the advancing interface first increased while approaching the particle, but became stagnant during engulfment and increased again after that. Alumina-magnesia complex inclusions in a magnesium-added steel with high oxygen content were very finely dispersed in the molten pool. These inclusions escaped from the advancing interface during solidification, but gathered again at the retreating interface during remelting. The tiny inclusions were thought to behave just as tracer particles of a local flow. The velocity of particles was measured on a video image, and the significant acceleration or deceleration was found near the interface. It was concluded that the flow was induced by the Marangoni effect due to the local difference in temperature and oxygen content in front of the interface, particularly in the case of a higher oxygen content. However, the flow was weak in the case of a low oxygen content.

Theory of Heat/Mass Transfer Additives in Absorption Chillers

Abstract: A new theory is presented, termed the vapor surfactant theory, which explains the heat and mass transfer enhancement mechanism of additives in absorption chillers. The theory holds that the enhancement additives are surfactants delivered to the surface of the solution film from the vapor, and that they produce enhancement by generating intense secondary flows on the film. The secondary flows, driven by surface tension gradients (Marangoni convection), augment the transfer process by providing mixing of the film. The primary variable in the enhancement is the surface concentration distribution of the surfactant additive because the surface tension gradients arise due to non-uniformities in the surface concentration. The vapor surfactant theory is found to explain all observations from several types of experiments. The new theory is a significant departure from past theories in its emphasis on the primary role of the vapor in the process.

Rates of Mass Transfer and Adsorption of Hexadecyltrimethylammonium Bromide at an Expanding Air-Water Interface.

Abstract: An overflowing cylinder (OFC) provides a convenient method for studying nonequilibrium liquid interfaces under steady-state conditions In the presence of surfactants in solution, large accelerations in the surface velocity are observed as a result of Marangoni effects The surface expansion rate is approximately uniform over the surface of the OFC and falls in the range of 1-10 s(-1) In this paper, a quantitative model is presented for the mass transport to the expanding surface of the OFC The model is then used to analyze experimental measurements of surface expansion rates and surface excess for solutions of a cationic surfactant, hexadecyltrimethylammonium bromide (CTAB), obtained by laser Doppler scattering and neutron reflection, respectively The experimental results are in satisfactory agreement with the predictions of diffusion-controlled adsorption close to the critical micelle concentration (cmc) At concentrations well above and well below the cmc, kinetic barriers to adsorption appear to exist The data at low concentrations are discussed in terms of a model for mass transport through the electrical double layer At high concentrations, double-layer effects are negligible and steric barriers to adsorption are postulated Copyright 2000 Academic Press

Unsteady marangoni flow in a molten pool when welding dissimilar metals

Abstract: The unsteady variations of transport processes in molten pools when welding dissimilar metals are systematically investigated. Convection is driven by Marangoni forces with different directions and magnitudes on a flat free surface. For a clear description without loss of generality, three-dimensional quasi-steady welding is stimulated by an unsteady two-dimensional process. Applying the volume of fluid (VOF) and enthalpy methods to determine the interfaces between the immiscible dissimilar metals and between solid and liquid, the computed results show in detail the unsteady variations in the velocity and temperature fields, the solute concentration on the free surface, and the shapes of the molten regions affected by varying the signs and magnitudes of the surface-tension coefficients. The predicted shapes of the fusion-zone and solute distributions agree with the available experimental results in welding iron to aluminum, copper and iron, and copper to nickle.

Surface contouring by controlled application of processing fluid using Marangoni effect

Abstract: An apparatus and method for modifying the surface of an object by contacting said surface with a liquid processing solution using the liquid applicator geometry and Marangoni effect (surface tension gradient-driven flow) to define and confine the dimensions of the wetted zone on said object surface. In particular, the method and apparatus involve contouring or figuring the surface of an object using an etchant solution as the wetting fluid and using realtime metrology (e.g. interferometry) to control the placement and dwell time of this wetted zone locally on the surface of said object, thereby removing material from the surface of the object in a controlled manner. One demonstrated manifestation is in the deterministic optical figuring of thin glasses by wet chemical etching using a buffered hydrofluoric acid solution and Marangoni effect.

A note on the effect of surface contamination in water wave damping

Abstract: Asymptotic formulas are derived for the effect of contamination on surface wave damping in a brimful circular cylinder; viscosity is assumed to be small and contamination is modelled through Marangoni elasticity with insoluble surfactant. It is seen that an appropriately chosen finite Marangoni elasticity provides an explanation for a significant amount of the unexplained additional damping rate in a well-known experiment by Henderson & Miles (1994); discrepancies are within 15%, significantly lower than those encountered by Henderson & Miles (1994) under the assumption of inextensible film.

Marangoni convection. Part 1. A cavity with differentially heated sidewalls

Abstract: Marangoni convection in a cavity with differentially heated sidewalls has been investigated. The analysis includes the complete effects of interface deformation. The results determined for large Biot and zero Marangoni (zero Prandtl) numbers show that steady convection may exist for Reynolds numbers Re larger than, and for capillary numbers Ca and cavity lengths L smaller than, certain critical values. The main factor limiting the existence of steady convection involves the interface becoming tangential to the hot wall at the contact point (tangency condition). Unsteady analysis shows that the tangency condition defines the limit point for the system; its violation is most likely to lead to the formation of a dry spot at the hot wall. The critical values of Re, Ca, and L are mutually dependent and change with the heating rate (they reach a minimum for instantaneous heating). For a certain range of parameters, multiple (i.e. steady and oscillatory) states are possible. The oscillatory state has a form consisting of the steady mode with a simple harmonic sloshing motion superposed on it. A reduction in the heating rate permits heating of the liquid without triggering the oscillatory state. Transition between the steady and the oscillatory states involves a nonlinear instability process.

Onset of solutal Marangoni convection in a suddenly desorbing liquid layer

Abstract: The onset of surface-tension-driven convection in an initially quiescent liquid layer experiencing sudden desorption from a free surface is analyzed using the linear stability theory. The propagation theory was developed for the basic time-dependent concentration profile, which is strongly nonlinear. Based on this theory, a new set of stability equations is derived in considering the effect of Gibbs adsorption and by neglecting the surface diffusion. It is found that the liquid layer becomes more stable by decreasing the Schmidt and Biot numbers. It is interesting that, during an initial period, the system is stable, depending on the Gibbs effect. The predictions agree favorably with the existing experimental results of triethylamine desorption in water in a wetted-wall and a liquid-jet column.

Weakly nonlinear analysis of Benard-Marangoni instability in viscoelastic fluids

Abstract: The coupled thermogravitational and thermocapillary instability in a thin fluid layer of a viscoelastic medium heated from below is investigated. A linear and a weakly nonlinear analysis are successively presented. The viscoelastic medium is modelled by means of a general rheological model including the lower convected, the upper convected, and the co-rotational Jeffreys models as particular cases. in comparison with previous analyses, two new dimensionless numbers are introduced, namely the so-called gravitational and rate of heating numbers instead of the classical Rayleigh and Marangoni numbers. The critical values for the temperature gradient, wave number and oscillation frequencies corresponding to the onset of convection are determined from a linear approach. After motion has set in, particular patterns are predicted taking the form of either rolls, or hexagon, or squares. By means of a nonlinear technique, restricted to steady situations, it is determined under which specific conditions one pattern is preferred. The influence of the constitutive equation, the Prandtl and the Blot numbers is examined and discussed in details. (C) 2000 Elsevier Science B.V. All rights reserved.

Experimental analysis of the heat transfer induced by thermocapillary convection around a bubble

Abstract: The surface tension driven flow in the liquid vicinity of gas bubbles on a heated wall and its contribution to the heat transfer are investigated experimentally in a configuration where surface tension force and buoyancy forces oppose one another. This liquid flow caused by the temperature gradient along the interface is called thermocapillary or thermal Marangoni convection. The studies were made with silicone oils of different viscosities so that a wide range of dimensionless numbers were encountered. The velocity fields are determined from the motion of carbon particles in the meridian plane of the bubble. The influence of the temperature gradient, the oil viscosity, and the bubble shape on the profiles along the interface and in the direction normal to the interface is analyzed. The temperature field is determined by holographic interferometry. For the axisymmetric problem, the interferograms are evaluated by solving the Abel-integral equation. From the isotherms, the temperature distribution along the bubble surface and in the liquid beneath the bubble is measured. To quantify the contribution of thermocapillarity to the heat transfer, the heat flux transferred by thermocapillarity is measured. A heat exchange law giving the increase in heat flux due to Marangoni convection in comparison to themore » conductive regime is proposed.« less

Influence of buoyancy forces on Marangoni flow instabilities in liquid bridges

Abstract: The influence of buoyancy forces on oscillatory Marangoni flow in liquid bridges of different aspect ratio is investigated by three‐dimensional, time‐dependent numerical solutions and by laboratory experiments using a microscale apparatus and a thermographic visualisation system. Liquid bridges heated from above and from below are investigated. The numerical and experimental results show that for each aspect ratio and for both the heating conditions the onset of the Marangoni oscillatory flow is characterized by the appearance of a standing wave regime; after a certain time, a second transition to a travelling wave regime occurs. The three‐dimensional flow organization at the onset of instability is different according to whether the bridge is heated from above or from below. When the liquid bridge is heated from below, the critical Marangoni number is larger, the critical wave number (m) is smaller and the standing wave regime is more stable, compared with the case of the bridge heated from above. For the critical azimuthal wave number, two correlation laws are found as a function of the geometrical aspect ratio A.

Steady thermocapillary-buoyant flow in an unbounded liquid layer heated nonuniformly from above

Abstract: Thermocapillary and buoyant flows induced by nonuniform heating of the free surface of a horizontally unbounded liquid layer over a cold solid bottom are studied numerically and by order of magnitude analyses for large Marangoni and Rayleigh numbers. The Prandtl number of the liquid is assumed to be of order unity or large, which are the cases of most interest in combustion. The asymptotic structures of plane and axisymmetric stationary flows are described qualitatively, showing that they consist of several horizontally spaced regions. Heat conduction and viscous forces are confined to thin boundary layers in a region around the heat source, while viscous forces extend to the whole liquid layer in a longer region where the flow is driven by the momentum imparted to the liquid by thermocapillary stresses around the source, in the case of plane thermocapillary flow; by this momentum and remaining thermocapillary stresses, in the case of axisymmetric thermocapillary flow; and by the horizontal gradient of a hydrostatic pressure distribution, in the case of buoyant flows. For large values of the Prandtl number, this region is followed by a region of viscosity-dominated flow which may be responsible for a large fraction of the heat loss to the bottom. A linear stability analysis of the surface boundary layer in the vicinity of the heat source gives values of the critical Marangoni number for the transition to oscillatory flow that are comparable to known experimental results.

Benard-Marangoni convection in two-layered liquids

Abstract: We describe experiments on B\'enard-Marangoni convection in horizontal layers of two immiscible liquids. Unlike previous experiments, which used gases as the upper fluid, we find a square planform close to onset which undergoes a secondary bifurcation to rolls at higher temperature differences. The scale of the convection pattern is that of the thinner lower fluid layer for which buoyancy and surface tension forces are comparable. The wave number of the pattern near onset agrees with the linear stability prediction for the full two-layer problem. The square planform is in qualitative agreement with recent two-layer weakly nonlinear theories, which fail however to predict the transition to rolls.

Visualization of Marangoni convection in simulated weld pools containing a surface-active agent

Abstract: The theory that a surface-active agent can cause weld pool Marangoni convection to reverse itself -to go inward along the pool surface and downward toward the pool bottom and result in deeper weld penetration - was proposed by Heiple and Roper in 1982 and studied worldwide since then. To actually observe such a flow pattern, a simulated transparent weld pool of NaNO 3 (10 mm in diameter) was heated with a defocused CO 2 laser beam to induce Marangoni convection, and C 2 H 5 COOK was used as a surface-active agent to cause flow reversal. A laser light-cut technique was used to reveal convection in the pool. With pure NaNO 3 , convection was outward along the free surface and downward along the pool wall. However, when C 2 H 5 COOK was present (e.g., at 0.5 and 1 mole-%), convection slowed down. When more C 2 H 5 COOK was present (e.g., at 1.5 and 2 mole-%), convection was reversed to go inward along the pool surface and downward along the pool axis. Since this is in the opposite direction of gravity-induced buoyancy convection, Marangoni convection clearly dominated in the pools. In stationary laser beam welding, NaNO, containing 1 mole-% C 2 H 5 COOK showed deeper weld pools and inward surface flow, while pure NaNO, showed shallower weld pools and outward surface flow. This is consistent with the reversal of Marangoni convection caused by C 2 H 5 COOK observed in the flow visualization.

Limiting cases of gravitational drainage of a vertical free film for evaluating surfactants

Abstract: The evolution of the deforming free surface of a vertically oriented thin film draining under gravity is examined for the case when there is an insoluble surfactant monolayer on a viscous, incompressible, and free liquid film with finite surface viscosity. Three coupled nonlinear partial differential equations describing the free surface shape, the surface velocity, and surfactant transport are obtained. These equations are derived at leading order and do not have inertial effects. We examine the case where the film is nearly flat so that mean surface tension is negligible; this will be in good agreement with experimental data with respect to long-time behavior of film thickness. This will be shown both analytically and computationally.We will show that in the limit of large surface viscosity, the evolution of the free surface is that obtained for the tangentially immobile case. It is verified that increasing surface viscosity slows down film drainage, thereby enhancing film stability. The Marangoni effec...

Shock transitions in Marangoni gravity-driven thin-film flow

Abstract: Thin films of silicon oil driven up an inclined silicon wafer by a thermally induced Marangoni force develop unusual shock profiles involving a non-classical undercompressive shock, if the counteracting parallel component of gravity is sufficiently large (Bertozzi et al 1998 Phys. Rev. Lett. 81 5169-72). They arise as a result of the interaction of a non-convex flux with the fourth-order diffusion generated by surface tension. In this work, we investigate how the dynamical behaviour of the solution is affected by including second-order diffusion resulting from the normal component of gravity; this component was neglected in the previous study. Then the governing equation for the film profile h (x , t ) becomes ht + ( h 2 - h 3 )x = - ( h 3 hxxx )x + D ( h 3 hx )x D 0. The numerical simulations in this paper confirm that neglecting second-order diffusion is justified for small D , but find that for larger D , the structure of the solution changes dramatically. We give a detailed account of the transitions that occur while increasing D and make predictions for future experiments carried out at small inclination angles, corresponding to moderately large D .