Showing papers on "Marangoni effect published in 2003"

Thermophoresis in protein solutions

Abstract: Thermophoresis, unlike thermal diffusion in simple mixtures, consists in particle drift induced by a temperature gradient ∇T. We show that thermophoresis in lysozyme solutions has a very distinctive behavior: particle motion can indeed be tuned from "thermophobic" (towards the cold) to "thermophilic" (along ∇T) by decreasing T. The observed temperature behaviour weakly depends on electrostatic effects, and rather suggests a primary role of hydrophobic interactions, further supported by comparison with the temperature dependence of lysozyme equilibrium solubility. Most of the observed features can be qualitatively understood by envisaging thermophoresis as a "microscopic Marangoni effect", due to thermally induced gradients of the interfacial free energy.

Thermocapillary instability and wave formation on a film falling down a uniformly heated plane

Abstract: We consider a thin layer of a viscous fluid flowing down a uniformly heated planar wall. The heating generates a temperature distribution on the free surface which in turn induces surface tension gradients. We model this thermocapillary flow by using the Shkadov integral-boundary-layer (IBL) approximation of the Navier–Stokes/energy equations and associated free-surface boundary conditions. Our linear stability analysis of the flat-film solution is in good agreement with the Goussis & Kelly (1991) stability results from the Orr–Sommerfeld eigenvalue problem of the full Navier–Stokes/energy equations. We numerically construct nonlinear solutions of the solitary wave type for the IBL approximation and the Benney-type equation developed by Joo et al. (1991) using the usual long-wave approximation. The two approaches give similar solitary wave solutions up to an Reynolds number above which the solitary wave solution branch obtained by the Joo et al. equation is unrealistic, with branch multiplicity and limit points. The IBL approximation on the other hand has no limit points and predicts the existence of solitary waves for all Reynolds numbers. Finally, in the region of small film thicknesses where the Marangoni forces dominate inertia forces, our IBL system reduces to a single equation for the film thickness that contains only one parameter. When this parameter tends to zero, both the solitary wave speed and the maximum amplitude tend to infinity.

On the instability of a falling film due to localized heating

Abstract: We analyse the stability of a thin film falling under the influence of gravity down a locally heated plate. Marangoni flow, due to local temperature changes influencing the surface tension, opposes the gravitationally driven Poiseuille flow and forms a horizontal band at the upper edge of the heater. The thickness of the band increases with the surface tension gradient, until an instability forms a rivulet structure periodic in the transverse direction. We study the dependence of the critical Marangoni number, a non-dimensional measure of the surface tension gradient at the onset of instability, on the associated Bond and Biot numbers, non-dimensional measures of the curvature pressure and heat-conductive properties of the film respectively. We develop a model based on long-wave theory to calculate base-state solutions and their linear stability. We obtain dispersion relations, which give us the wavelength and growth rate of the fastest growing mode. The calculated film profile and wavelength of the most unstable mode at the instability threshold are in quantitative agreement with the experimental results. We show via an energy analysis of the most unstable linear eigenmode that the instability is driven by gravity and an interaction between base-state curvature and the perturbation thickness. In the case of non-zero Biot number transverse variations of the temperature profile also contribute to destabilization.

Oscillatory thermocapillary convection in open cylindrical annuli. Part 1. Experiments under microgravity

Abstract: (Received 9 July 2001 and in revised lorm 23 April 2003) We report results from microgravity experiments on thermocapillary convection in open annuli with outer radius Ro :40 mm and inner radius Ri : 20 mm of various aspect ratios Ar. The measurements are from more than 230 equilibrated states in the Ar Marangoni-number space. We found time-independent and oscillatory states and report some selected oscillation and Fourier spectra from thermocouple measurements. We measured the critical temperature difference AI' for the onset of temperature oscillations in the range 1=<1r(8. We report supercritical oscillation periods and attribute the oscillations in the larger Ar range to hydrothermal waves. This conclusion is supported by the values of the oscillation periods and of the critical Marangoni numbers in that Ar range. The hydrothermal waves exhibit an internal corotating multicellular pattern. For the smaller Ar and near the threshold we report m-fold temperature patterns on the free surface with m decreasing for decreasing Ar. At 4AZ' these patterns become very irregular. Most of the findings are in accordance with the numerical results reported in Part 2 (Sim et al. (2003)). The experimenlal LT' are higher and the experimental periods r' are smaller than the numerical values for Biot number B,:0. However, analysis of the experimental free-surface thermal boundary conditions shows that there was heat input to the free surface. Good agreement with numerical results for AZ' and t'is obtained with Bi+0 (heat input).

Destabilization of a creeping flow by interfacial surfactant: linear theory extended to all wavenumbers

Abstract: Creeping flow of a two-layer system with a monolayer of an insoluble surfactant on the interface is considered. The linear-stability theory of plane Couette-Poiseuille flow is developed in the Stokes approximation. To isolate the Marangoni effect, gravity is excluded. The shear-flow instability due to the interfacial surfactant, uncovered earlier for long waves only (Frenkel & Halpern), is studied with inclusion of all wavelengths, and over the entire parameter space of the Marangoni number M, the viscosity ratio m, the interfacial velocity shear s, and the thickness ratio n (≥ 1). The complex wave speed of normal modes solves a quadratic equation, and the growth rate function is continuous at all wavenumbers and all parameter values. If M > 0, s ¬= 0, m 1, the small disturbances grow provided they are sufficiently long wave. However, the instability is not long wave in the following sense: the unstable waves are not necessarily much longer than the smaller of the two layer thicknesses. On the other hand, there are parametric regimes for which the instability has a mid-wave character, the flow being stable at both sufficiently large and small wavelengths and unstable in between

The influence of non-equilibrium surfactant dynamics on the flow of a semi-infinite bubble in a rigid cylindrical capillary tube

Abstract: We have utilized a computational model of semi-infinite air bubble progression in a surfactant-doped, fluid-filled rigid capillary to investigate the continual interfacial expansion dynamics that occur during the opening of collapsed pulmonary airways. This model simulates mixed-kinetic conditions with nonlinear surfactant equations of state similar to those of pulmonary surfactant. Several dimensionless parameters govern the system responses: the capillary number (Ca) that relates viscous to surface tension forces; the elasticity number (El), a measure of the ability of surfactant to modify the surface tension; the bulk Peclet number (Pe), relating bulk convection rates to diffusion rates; the adsorption and desorption Stanton numbers (Sta and Std) that relate the adsorption/desorption rates to surface convective rates; and finally the adsorption depth (λ), a dimensionless bulk surfactant concentration parameter. We investigated this model by performing detailed parameter variation studies at fixed and variable equilibrium concentrations. We find that the surfactant properties can strongly influence the interfacial pressure drop through modification of the surface tension and the creation of Marangoni stresses that influence the viscous stresses along the interface. In addition, these studies demonstrate that, depending upon the range of parameters, either film thickening or film thinning responses are possible. In particular, we find that when Pe[Gt ]1 (as with pulmonary surfactant) or when sorption rates are low, concentration profiles can substantially differ from near-equilibrium approximations and can result in film thinning. These responses may influence stresses on epithelial cells that line pulmonary airways and the stability of these airways, and may be important to the delivery of exogenous surfactant to deep regions of the lung.

3D Large scale Marangoni convection in liquid films

Abstract: We study large scale surface deformations of a liquid film unstable due to the Marangoni effect caused by external heating on a smooth and solid substrate. The work is based on the thin film equation which can be derived from the basic hydrodynamic equations. To prevent rupture, a repelling disjoining pressure is included which accounts for the stabilization of a thin precursor film and so prevents the occurrence of completely dry regions. Linear stability analysis, nonlinear stationary solutions, as well as three-dimensional time dependent numerical solutions for horizontal and inclined substrates reveal a rich scenario of possible structures for several realistic fluid parameters.

Theoretical Model for Nucleate Boiling Heat and Mass Transfer of Binary Mixtures

Abstract: A model is presented to calculate nucleate boiling heat transfer coefficients of binary mixtures. The model includes the governing physical phenomena, such as the variation of the phase interface curvature, the adhesion pressure between wall and liquid, the interfacial thermal resistance as well as the local variation of composition and liquid-vapor equilibrium. Marangoni convection is considered, too. The theoretical background of these phenomena is described and their implementation is explained. The model is verified by comparing calculated heat transfer coefficients of hydrocarbon mixtures with experimental data

Marangoni flotation of liquid droplets

Abstract: Flotation of liquid droplets on pool surfaces, in the presence of temperature differences, is studied experimentally and numerically. Coalescence or sinking of the droplet is prevented by the thermal Marangoni motion, owing to the surface tension imbalance at the pool surface. The mechanism is the same as that investigated in previous works on coalescence and wetting prevention in the presence of temperature differences. If the droplet is colder than the liquid surface, the flow is directed radially towards the drop; this radial flow field drags the ambient air under the drop, thus creating an air film and avoiding a direct contact between the droplet and the pool molecules.The surface velocities are measured visually with a CCD camera to image the motion of tracers floating on the pool surface; the surface temperature distributions along the pool and the droplet surfaces are measured by an infrared thermocamera. The experimental results are correlated by numerical results obtained under the assumption of spherical drop and axisymmetric flow regime. Different liquids are considered and the influence of evaporation is discussed, showing a good agreement between the experiments and the numerical simulations.

Oscillatory thermocapillary convection in open cylindrical annuli. Part 2. Simulations

Abstract: Oscillatory thermocapillary convection in open cylindrical annuli heated from the outer wall is investigated numerically. Results at fixed inner/outer radius ratio of 0.5, aspect ratios (.

Effect of surfactants on film flow down a periodic wall

Abstract: The effect of an insoluble surfactant on the gravity-driven flow of a liquid film down an inclined wall with periodic undulations or indentations is investigated in the limit of vanishing Reynolds number. A perturbation analysis for walls with small-amplitude sinusoidal corrugations reveals that the surfactant amplifies the deformation of the film surface, though it also renders the film thickness more uniform over the inclined surface. The effect of the surfactant is most significant when the film thickness is less than half the wall period. To explain the deforming influence of the surfactant, a linear stability analysis of film flow down an inclined plane is undertaken for two-dimensional perturbations. The results reveal the occurrence of a Marangoni normal mode whose rate of decay is lower than that of the single mode occurring in the absence of surfactants. Numerical methods based on a combined boundary-element/finite-volume method are implemented to compute flow down a periodic wall with large-amplitude corrugations or semi-circular depressions. In the case of a wavy wall, it is found that the shape of the film surface is described well by the linear perturbation expansion for small and moderate wave amplitudes. Streamline patterns reveal that, although the effect of the surfactant on the shape of the film surface is generally small, Marangoni tractions may have a profound influence on the kinematics by causing the onset of regions of recirculating flow.

Interfacial Phenomena and the Marangoni Effect

Abstract: Preface.- Static and Dynamic Three-Phase Contact Lines (L. M. Pismen).- Hydrodynamics of Surface Tension Dominated Flows (D. T. Papageorgiu).- Benard Layers with Heat or Mass Transfer (M. G. Velarde).- Theoretical Aspects of Interfacial Phenomena and Marangoni Effect: Modelling and Stability (R. Kh. Zeytounian).- Hydrodynamics of Slopped Falling Films (V. Ya. Shkadov).- The Effect of Interfacial Phenomena on Materials Processing (K. C. Mills)

Marangoni effect in nanosphere-enhanced laser nanopatterning of silicon

Abstract: We report a Marangoni effect in nanosphere-enhanced laser direct nanopatterning of silicon surface. A monolayer of nanosphere array was formed on the silicon substrate by self-assembly. A 248-nm excimer laser was used to irradiate the sample surface. Due to optical field enhancement between the nanosphere and the substrate, the silicon surface was locally melted. The molten material was redistributed due to surface tension forces, resulting in the formation of a nanodent array. The morphology of the nanodents changed from bowl-type to “Sombrero” with increase of laser intensity as a result of a Marangoni effect that arises due to the competition between a thermocapillary force and a chemicapillary force acting on the molten material.

Estimating surfactant surface coverage and decomposing its effect on drop deformation.

Abstract: A novel method is introduced to estimate surface coverage and the equation of state of insoluble surfactant on droplets, involving measurement of interfacial tension on a single parent drop and progressively subdivided generations of daughter drops. This has enabled quantitative decomposition of the dilution, tip-stretching, and Marangoni effects of surfactants on drop deformation. For a small viscosity ratio of 0.09, the Marangoni effect dominates, increasing first and then decreasing with surface coverage, the dilution effect is significant at high, and tip-stretching only at low surface coverage. For a viscosity ratio of 2.3, the dilution effect dominates, and neither Marangoni nor tip-stretching effects play an important role.

The effect of compatibilizer on the coalescence of two drops in flow

Abstract: This paper reports results from an experimental study of the effects of copolymer/compatibilizer on the coalescence of two equal size drops in the flow field produced by a four-roll mill. The data encompass two different fluid systems, both with PDMS as the suspending fluid and PBd as the drops, and an acid-base complex of PDMS–NH3+ −OOC–PBd adsorbed at the interface that we shall refer to as a copolymer. The two systems differ in the ratio of viscosities (λ) of the drop to the suspending fluid, one having λ=0.19 and the other λ=1.3. For the lower viscosity ratio system, as the amount of adsorbed copolymer is increased, the drainage time for coalescence in a head-on collision is increased monotonically and the critical capillary number for coalescence in a glancing collision is also reduced monotonically in a manner that appears qualitatively consistent with a slowing of the film drainage process due to Marangoni stresses. Detailed trajectory measurements for drops with copolymer show agreement with predi...

Marangoni flow at the gas/melt interface of steel

Abstract: Direct observation with a scanning laser microscope was made to determine the direction and velocity of surface flow of steel melt in the vicinity of the solid/melt (S/M) interface. During solidification, a fast solutal Marangoni flow moving away from the S/M interface was confirmed to exist on steel melts containing oxygen and sulfur of 10 to 105 ppm. Even in such a low range of oxygen and sulfur content, the solutal Marangoni flow can be very fast, carrying inclusion particles up to the free surface along the S/M interface. During heating and holding, however, a thermal Marangoni flow combined with convective flow generated a reverse flow directed toward the S/M interface. These features have important relevance to inclusion entrainment and solute segregation during the solidification of steel.

Phase-field model for Marangoni convection in liquid-gas systems with a deformable interface

Abstract: We developed a phase-field model for Marangoni convection in a liquid-gas system with a deformable interface, heated from below. In order to describe both Marangoni instabilities (with short and long wavelengths), an additional force component must be considered in the Navier-Stokes equation. This term describes the coupling of the temperature to the velocity field via the phase-field function. It results by minimizing the free-energy functional of the system. For a bidimensional problem in linear approximation we performed a numerical code that successfully computes both Marangoni instabilities. In the limit of sharp and rigid interfaces, our results are compared with the literature.

Marangoni instability of a thin liquid film resting on a locally heated horizontal wall

Abstract: Long-wave Marangoni instabilities can be induced thermally on a thin liquid layer overlying a horizontal solid substrate with either a uniform or a nonuniform base temperature. For a nonuniform base temperature, the film height thickens near the region where temperature gradients are negligible and severely thins upstream; ``fingering'' patterns are observed in this region. These states are related to the patterns observed in the isothermal case, which are reasonably well understood. The stability of these spatiotemporally evolving states to transverse disturbances is investigated using a transient growth-type analysis. It is found that the band of unstable wave numbers exhibiting growth is strongly dependent on the lateral extent of the heating source. Inspection of surface reconstructions of the film thickness profiles reveals the existence of three-dimensional patterns in the thinning region behind the thickened front.

Effect of rotation on surface tension driven flow during protein crystallization

Abstract: The effect of rotation on surface tension gradient driven flow, also known as Marangoni convective flow, during protein crystallization is modeled and studied computationally under microgravity conditions, where the surface tension gradient force is the main significant driving force. The main parameters are the solutal Marangoni number Mc, representing the surface tension gradient force and the Taylor number Ta representing the rotational effect. The numerical computations for various values of the parameters and low gravity levels indicated nontrivial competing effects, due to surface tension gradient, centrifugal and Coriolis forces on the flow adjacent to the protein crystal interface and the associated solute flux. In particular, for given values of Mc, certain values of Ta were detected where the Sherwood number (Sh), representing the convective solute flux, and the convective flow effects are noticeably reduced. These results can provide conditions under which convective flow transport during the protein crystallization approaches the diffusion limited transport, which is desirable for the production of higher quality protein crystals.

Modeling of marangoni-induced droplet motion and melt convection during solidification of hypermonotectic alloys

Abstract: A two-phase volume averaging approach to model Marangoni-induced droplet motion of the minority liquid phase and the convection in the parent melt during solidification of the hypermonotectic alloys is presented. The minority liquid phase decomposed from the parent melt as droplets in the miscibility gap was treated as the second-phase L2. The parent melt including the solidified monotectic matrix was treated as the first phase L1. Both phases were considered as different and spatially interpenetrating continua. The conservation equations of mass, momentum, solute, and enthalpy for both phases, and an additional transport equation for the droplet density, were solved. Nucleation of the L2 droplets, diffusion-controlled growth, interphase interactions such as Marangoni force at the L1-L2 interface, Stokes force, solute partitioning, and heat release of decomposition were taken into account by corresponding source and exchange terms in the conservation equations. The monotectic reaction was modeled by adding the latent heat on the L1 phase during monotectic reaction, and applying an enlarged viscosity to the solidified monotectic matrix. A two-dimensional (2-D) square casting with hypermonotectic composition (Al-10 wt pct Bi) was simulated. This paper focused on Marangoni motion, hence gravity was not included. Results with nucleation, droplet evolution, Marangoni-induced droplet motion, solute transport, and macrosegregation formation were obtained and discussed.

Three-dimensional numerical simulation of Marangoni flow instabilities in floating zones laterally heated by an equatorial ring

Abstract: Instability of Marangoni convection in floating zones (full zone configuration) of a low Prandtl number fluid under microgravity conditions is investigated by parallel supercalculus and direct three-dimensional and time-dependent simulation of the problem. A parametric analysis (still absent in literature) of the influence of the aspect ratio of the liquid column on the features of the three-dimensional bifurcation of Marangoni flow is carried out. A novel distribution is introduced for the surface heat flux corresponding to the radiative flux generated by a ring heater positioned around the equatorial plane of the full zone at a distance h from the free interface. Axisymmetric computations are used to obtain the steady basic state, then the three-dimensional Navier–Stokes equations are solved to investigate the evolution of azimuthal disturbances. These disturbances always exhibit antisymmetric behavior with respect to the equatorial plane. The mirror symmetry with respect to this plane is broken. Strong interaction occurs in fact between the toroidal convection rolls located in the upper part and lower part of the liquid column. This leads for some values of the aspect ratio to a heretofore unseen “apparent” doubling or quadrupling of the azimuthal wave number of the azimuthal velocity distribution in the midplane. The present analysis points out that the instability of the half zone flow is not relevant for the full zone configuration.

Thin film traveling waves and the navier slip condition

Abstract: We consider the lubrication model for a thin film driven by competing gravitational forces and thermal gradients on an inclined plane. We are interested in the general traveling wave problem when the Navier slip boundary condition is used. We contrast (1) gravity dominated flow, (2) Marangoni dominated flow, and (3) flow in which the two driving effects balance. For a "singular slip" model we show that when Marangoni forces are present the resulting traveling wave ODE reduces locally near the contact line to a case not considered previously in the literature. We compute an asymptotic expansion of the solution near the contact line and compare with numerical simulations of the full problem. Using numerical simulations and phase space analysis involving Poincare sections, we show that for all three problems there is a finite range of admissible contact angles for which traveling wave solutions exist. Even in the well-studied case (1), this is a new observation that has ramifications for the use of constitut...

Simulation of Time-Dependent Pool Shape during Laser Spot Welding: Transient Effects

Abstract: The shape and depth of the area molten during a welding process is of immense technical importance. This study investigates how the melt pool shape during laser welding is influenced by Marangoni convection and tries to establish general qualitative rules of melt pool dynamics. A parameter study shows how different welding powers lead to extremely different pool shapes. Special attention is paid to transient effects that occur during the melting process as well as after switching off the laser source. It is shown that the final pool shape can depend strongly on the welding duration. The authors use an axisymmetric two-dimensional (2-D) control-volume-method (CVM) code based on the volume-averaged two-phase model of alloy solidification by Ni and Beckermann[1] and the SIMPLER algorithm by Patankar.[2] They calculate the transient distribution of temperatures, phase fractions, flow velocities, pressures, and concentrations of alloying elements in the melt and two solid phases (peritectic solidification) for a stationary laser welding process. Marangoni flow is described using a semiempirical model for the temperature-dependent surface tension gradient. The software was parallelized using the shared memory standard OpenMP.

Fluidic Ratchet Based on Marangoni−Bénard Convection

Abstract: A mean flow is observed experimentally in a layer of fluid undergoing Marangoni-Benard convection over a heated substrate that presents a pattern of asymmetrical grooves. The direction of the mean flow is a function of the temperature difference across the layer and of the thickness of the layer; the direction can be controlled by changing these parameters. This system acts as a fluidic ratchet: the local structure of the thermally driven convection interacts with the asymmetry of the local topographical pattern and causes a net, global flow in the fluid. This fluidic ratchet may be useful in handling fluids on macroscopic and microscopic scales.