Thermocapillary Forces Research Articles

Stability of Viscoelastic Fluid Flowing Through Porous Medium Down Non-uniformly Heated Inclined Plane

The stability of a thin layer of viscoelastic fluid flowing through a porous medium down a non-uniformly heated inclined plane with a constant temperature gradient along the plane is considered. The film flow system is influenced by gravity, mean surface tension, thermocapillary forces, viscoelastic forces, porosity, and permeability of porous medium. We seek a solution of the stability problem in a series in small wave numbers, and the obtained results, when the plane is heated in the downstream direction, show that the Marangoni, Galileo, and Biot numbers, porosity, and permeability of the porous medium have dual roles in the stability of the flow system, while the viscoelastic parameter and angle of inclination have stabilizing effects, and the Prandtl number has a destabilizing effect. The effects of these physical parameters are also discussed in the case when the plane is cooled in the downstream direction, and we found that their effects are opposite to those of the previous case. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21105

Lattice Boltzmann phase-field modeling of thermocapillary flows in a confined microchannel

To understand how thermocapillary forces manipulate the droplet motion in a confined microchannel, a lattice Boltzmann phase-field model is developed to simulate immiscible thermocapillary flows with consideration of fluid–surface interactions. Based on our recent work of Liu et al., 2013 [54], an interfacial force of potential form is proposed to model the interfacial tension force and the Marangoni stress. As only the first-order derivatives are involved, the proposed interfacial force is easily combined with the wetting boundary condition to account for fluid–surface interactions. The hydrodynamic equations are solved using a multiple-relaxation-time algorithm with the interfacial force treated as a forcing term, while an additional convection–diffusion equation is solved by a passive-scalar approach to obtain the temperature field, which is coupled to the interfacial tension by an equation of state. The model is first validated against analytical solutions for the thermocapillary-driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then demonstrated to produce the correct equilibrium contact angle for a binary fluid with different viscosities when a constant interfacial tension is taken into account. Finally, we numerically simulate the thermocapillary flows for a microfluidic droplet adhering on a solid wall and subject to a simple shear flow when a laser is applied to locally heat the fluids, and investigate the influence of contact angle and fluid viscosity ratio on the droplet dynamical behavior. The droplet motion can be completely blocked provided that the contact angle exceeds a threshold value, below which the droplet motion successively undergoes four stages: constant velocity, deceleration, acceleration, and approximately constant velocity. When the droplet motion is completely blocked, three steady vortices are clearly visible, and the droplet is fully filled by two counter-rotating vortices with the smaller one close to the external vortex. The thermocapillary convection is strengthened with decreasing viscosity ratio of the droplet to the carrier fluid. For low viscosity ratios, the droplet motion is completely blocked and exhibits the similar behavior, but the structure of the internal vortices is more complicated at the lowest viscosity ratio. For high viscosity ratios, the droplet motion is partially blocked and undergoes a series of complex transitions, which can be explained as a result of the dynamically varying Marangoni forces.

Role of zinc coating at liquid-vapor interface during laser material processing of zinc coated steel

In laser material processing, one of the major interests is characterizing interfacial phenomena induced by thermal phase changes of materials. The interfacial characteristics in the laser processing of multi-coated materials show different behaviors compared to those of single material processing. The difference in thermo-physical properties of the coated and primary materials induces the contrasting characteristics of multiple interfacial phenomena including temperature, recoil pressure, capillary force, and thermo capillary force. The influence of coating layer to the interfacial physics evolutions is difficult to be modeled mathematically when the laser beam penetrates the multi-coated material layer by layer. This paper addresses the role of the zinc coating at the liquid-vapor interface during the laser processing of zinc coated steel, as a representative case of multi-coated materials. Computational modules incorporating the zinc layers were established and selectively applied at the locations where the zinc coatings exist to investigate the interfacial phenomena. The level set method was integrated with the modules to track the evolution of the liquid-vapor interface in a self-consistent manner. The interfacial phenomena characteristics were estimated by a 3D mathematical simulation study. A reflective topography method was employed to validate the mathematical model and to supplement our understandings of the interfacial evolution.

Two-Dimensional Numerical Simulation for Flow Pattern Transition of Thermal-Solutal Capillary Convection in an Annular Pool

In order to understand the transition characteristics of the thermal-solutal capillary convection in an annular pool, a series of two-dimensional numerical simulations were conducted. The bottom of the pool is adiabatic rigid wall and the top is adiabatic and non-deformable free surface. The inner and outer cylindrical walls maintain at constant temperature and solute concentration, respectively. The thermo-capillary force is supposed to equal to the solute-capillary force, but their directions are contrary. Results show that the thermal-solutal capillary convection is steady at a small Reylonds number. When the capillary Reynolds number exceeds a critical value, the steady flow transits into unstable thermal-solutal capillary convection. The transition from the steady to oscillatory flow undergoes a Hopf bifurcation. Furthermore, the effects of the liquid layer aspect ratio, the radius ratio, the Prandtl number and the Lewis number on the onset of flow pattern transition are discussed. The physical mechanism of the unstable thermal-solutal capillary convection is also analyzed.

Spreading and bistability of droplets on differentially heated substrates

AbstractAn axisymmetric drop spreads on a radially heated, partially wetting solid substrate in a rotating geometry. The lubrication approximation is applied to the field equations for this thin viscous drop to yield an evolution equation that captures the dependence of viscosity, surface tension, gravity, centrifugal forces and thermocapillarity. We study the quasi-static spreading regime, whereby droplet motion is controlled by a constitutive law that relates the contact angle to the contact-line speed. Non-uniform heating of the substrate can generate both vertical and radial temperature gradients along the drop interface, which produce distinct thermocapillary forces and equivalently flows that affect the spreading process. For the non-rotating system, competition between surface chemistry (wetting) and thermocapillary flows induced by the thermal gradients gives rise to bistability in certain regions of parameter space in which the droplets converge to an equilibrium shape. The centrifugal forces that develop in a rotating geometry enlarge the bistability regions. Parameter regimes in which the droplet spreads indefinitely are identified and spreading laws are computed to compare with experimental results from the literature.

Thermocapillary effects in nonisothermal liquid film at high Reynolds numbers

The temperature and wave characteristics of the water film flowing down a vertical plate with a heater at Re = 300 are studied. The field of film thicknesses at different heat flux values was measured using the fluorescence method. The temperature field on the film surface was measured by an infrared scanner. The experimental data were obtained for variations in temperature over the liquid film surface with time during the propagation of waves. When the falling liquid is heated, the thermocapillary forces lead to formation of rivulets and a thin film between them. Averaging of measurements allowed the value of the transverse film deformation to be determined. Two mechanisms of influence of thermocapillary forces on the motion of the wavy liquid film are marked. For the first time, the exhibition of such a strong thermocapillary effects is revealed in the heated liquid film at high Reynolds numbers.

Experimental investigation of 3-dimensional wavy liquid films under the coupled influence of thermo-capillary and electrostatic forces

Three-dimensional interfacial waves developing on the free surface of falling liquid films are known to intensify heat and mass transfer. In this context, the present paper studies the effect of electrostatic as well as of thermo-capillary forces on a falling film of a dielectric liquid. Therefore, measurements of the local film thickness using a confocal chromatic imaging method were performed under isothermal and heated conditions. The experimental results show that both forces destabilize the flow. It is found, that the application of an additional electric field under heating conditions enhances the generation of rivulets, thereby reducing the overall heat transfer coefficient.

Amplitudes of three-dimensional waves in a nonisothermal falling liquid film

The amplitudes of three-dimensional (3D) waves in a water film flowing down a vertical plate with a local heater have been measured. Thermocapillary forces that arise on heating lead to the formation of rivulets separated by thin-layer troughs, with 3D waves propagating over the crests of rivulets. The film thickness and 3D wave amplitudes on the heater grow with increasing heat flux density and distance downstream the flow, but the relative wave amplitude remains unchanged. In the heated regions between rivulets, the relative amplitude of waves increases with decreasing average thickness (or local Reynolds number). Analysis of results obtained for large Reynolds numbers showed that the relative amplitudes of waves in the regions between rivulets at high heat flux densities are much greater than those for small Reynolds numbers in isothermal falling films.

Thermal entry length in falling liquid films at high Reynolds numbers

A behavior of the length of thermal entry was studied experimentally in the vertically falling wavy liquid film at high Reynolds numbers with application of the field methods for thickness and temperature measurements. According to data, obtained by a high-speed IR camera, the zones, whose temperatures exceed the inlet temperature of the film, are formed at 7–10mm from upper edge of the heater in the interrivulet area between the crests of developed 3D synchronous waves even at low heat fluxes. It was determined that in the area of rivulets, formed on the crests of 3D synchronous waves, the length of thermal entry is higher, but it decreases drastically with a rise of heat flux. Analysis of data on the film thickness, obtained by the fluorescent method, has shown that between the synchronous 3D waves in spanwise direction the average film thickness is lower. Respectively, the values of local Reynolds numbers of the film and distances before the appearance of temperature nonuniformity decrease. In these regions the effect of thermocapillary forces is obvious even at relatively low heat fluxes, what finally leads to a considerable decrease in the length of thermal entry.

Thermocapillary effects on steadily evaporating contact line: A perturbative local analysis

The evaporation process taking place close to the three-phase contact line is considered and studied theoretically using a linear stability analysis approach. A domain perturbation method, taking into consideration thermocapillary effects and surface forces, is used to develop the higher-order solution in terms of series expansion about lubrication condition. A closed-form solution is found for the film thickness, the pressure jump across the liquid-vapor interface and the evaporative flux in the vicinity of the contact line. The key novelty in this work is considering thermocapillary instability for very thin films (∼10 nm) accounting for surface forces. For (quasi-) flat-very-thin films, the analysis shows no instability, which is consistent with general knowledge in this field. However, for films extending from a meniscus, as encountered in wetting configurations, it is found that the competition between London–van der Waals, capillary, and thermocapillary forces leads to contact line instability and behavior revealed for the first time. According to the sign of the Marangoni number, the instability can enhance (if positive) or reduce (if negative) the evaporation rate by widening out or narrowing, respectively, the contact region and, in both cases, significantly modifies the vortical structure of the flow. If the Marangoni number is positive, the film interface close to the contact line can exhibit corrugations. The occurrence of these latter is discriminated, in addition to the Marangoni number, by the value of three operating parameters, namely the film aspect ratio, the ratio of the film diffusive thermal resistance to evaporative heat transfer resistance, and the ratio of capillary pressure to disjoining pressure. By modifying the physical and operating parameters, it is also shown that the system can be optimized in order to suppress these corrugations.

Numerical simulation of natural convection in a sessile liquid droplet

Heat transfer in a sessile liquid droplet was studied with numerical methods. A computer code was developed for solving the problem of convection in an axisymmetric hemispherical droplet and in a spherical layer as well. The problem of establishing an equilibrium state in a droplet was solved using several variables: temperature, stream function, and vorticity. Simulation was performed for droplets of water, ethyl alcohol, and model liquids. Variable parameters: intensity of heat transfer from droplet surface, Rayleigh and Marangoni dimensionless criteria, and the characteristic temperature difference. It was revealed that the curve of convective flow intensity versus heat transfer intensity at droplet surface has a maximum. A dual-vortex structure was obtained in a stationary hemispherical profile of liquid droplet for the case of close values for thermocapillary and thermogravitational forces. Either thermocapillary or thermogravitational vortex might be dominating phenomena in the flow structure.

Mixed Thermocapillary and Forced Convection Heat Transfer Around a Hemispherical Bubble in a Miniature Channel—A 3D Numerical Study

It has been established that for certain conditions, such as microgravity boiling, thermocapillary Marangoni flow has associated with it a significant enhancement of heat transfer. Typically, this phenomenon was investigated for the idealized case of an isolated and stationary bubble resting atop a heated solid that is immersed in a semi-infinite quiescent fluid or within a two-dimensional cavity. This article presents a three-dimensional numerical study that investigates the influence of thermal Marangoni convection on the fluid dynamics and heat transfer around a bubble during laminar flow of water in a minichannel. This mixed thermocapillary and forced convection problem is investigated for channel liquid inlet velocity of 0.01 m/s to 0.03 m/s and Marangoni numbers in the range of 10 to 300 under microgravity conditions. Three-dimensional effects become particularly important on the side and rear regions of the bubble. The thermocapillary forces accelerate the flow along almost the entire bubble interface. The hot core fluid from the heated bottom wall region is forced inward and propelled upward into the thermocapillary jet above the bubble. It can be quantified that the influence of thermocapillary flow on heat transfer enhancement shows an average increase by 40% at the downstream of the bubble and by 60% at the front and rear regions. This heat transfer enhancement depends mainly on the temperature differential as the driving potential for thermocapillary flow and bulk liquid velocity.

Thermal entry length in a falling liquid film at high reynolds numbers

Using the fluorescence and the infrared technique of thickness and temperature measuring, experimental study is performed on variation of the thermal entry length in a falling water film at high Reynolds numbers. The data obtained by means of a high-speed infrared camera show that, in the interrivulet area occurring between the crests of the developed synchronous 3D waves, even at low heat fluxes, at distances of 7–10 mm from the upper heater edge, zones are formed with the temperature above the initial film temperature. The thermal entry length is shown to be larger within the area of the rivulets forming over the synchronous 3D wave crests, but it decreases rapidly with the heat flux density increase. Analysis of the film thickness data obtained by the fluorescent technique shows that, within the areas between the synchronous 3D waves, the averaged film thickness is less. Respectively, the values of the local film Reynolds number decrease, as do the distances to the localities of the temperature non-uniformities. In those places, even at relatively low heat fluxes, the influence of the thermo-capillary force takes place thus causing a significant decrease in the thermal entry length.

Bubble jet flow interaction during pool boiling of subcooled water on horizontal thin wires

Both visual experiments and numerical analyses were conducted to investigate the interaction between bubble jet flows during pool boiling of subcooled water on horizontal thin wires. The bubble jet flows nearby attracted each other, and they can combine into one jet flow under strong interaction. As the adjacent bubble departs, the bubble jet flow would experience an unsteady evolution process with the jet flow interaction weakening. Since the unsymmetrical thermocapillary force at the bubble interface was induced by the adjacent bubble as a cold source, the bubble jet flow would trend to the adjacent bubble, and the mechanism based on thermocapillary force and cold source can explain the bubble jet flow interaction very well. The steady bubble jet flow interaction phenomena were further simulated by laminar model, and the calculated jet flow interaction phenomena were in a good agreement with the experimental results.

Modeling and simulation of thermocapillary flows using lattice Boltzmann method

To understand how thermocapillary forces manipulate droplet motion in microfluidic channels, we develop a lattice Boltzmann (LB) multiphase model to simulate thermocapillary flows. The complex hydrodynamic interactions are described by an improved color-fluid LB model, in which the interfacial tension forces and the Marangoni stresses are modeled in a consistent manner using the concept of a continuum surface force. An additional convection–diffusion equation is solved in the LB framework to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. A stress-free boundary condition is also introduced to treat outflow boundary, which can conserve the total mass of an incompressible system, thus improving the numerical stability for creeping flows.The model is firstly validated against the analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of three-dimensional deformable droplet at various Marangoni numbers, and its accuracy is once again verified against the theoretical prediction in the limit of zero Marangoni number. Finally, we numerically investigate how the localized heating from a laser can block the microfluidic droplet motion through the induced thermocapillary forces. The droplet motion can be completely blocked provided that the intensity of laser exceeds a threshold value, below which the droplet motion successively undergoes four stages: constant velocity, deceleration, acceleration, and constant velocity. When the droplet motion is completely blocked, four steady vortices are clearly visible, and the droplet is fully filled by two internal vortices. The external vortices diminish when the intensity of laser increases.

Scaling weld or melt pool shape induced by thermocapillary convection

The molten pool shape and transport variables induced by thermocapillary force during welding (or melting) of workpieces, such as pure iron, titanium, high speed steel and stainless steel alloys, can be self-consistently predicted from scale analysis. Determination of the molten pool shape and transport variables is crucial due to their close relationship with the microstructures, strength and properties of the fusion zone. In this study, the pool excludes a strongly wavy bottom and the surface velocity profile has two peaks valid for Prandtl numbers lying between 0.3 and unity. The surface tension coefficient is negative and suitable for all pure liquid metals and alloys containing minor surface active solutes, giving rise to an outward surface flow. In view of high Marangoni number, the domain of scaling is divided into the hot and cold corner regions, boundary layers on the solid–liquid interface and ahead of the melting front. The results find that the width and depth of the pool, peak and secondary peak surface velocities, and maximum temperatures in the hot and cold corner regions can be explicitly and separately determined as functions of working variables, or Marangoni, Prandtl, Peclet, Stefan, and beam power numbers and solid-to-liquid thermal conductivity ratio. The scaled results agree with numerical data and available experimental data. This work has academic and practical importance. Successful scaling not only reveals physical mechanisms, but also provides quantitative predictions of the fusion zone shapes and transport variables prior to melting or welding.

Thermocapillary migration in small-scale temperature gradients: Application to optofluidic drop dispensing

We experimentally investigate the thermocapillary migration induced by local laser heating of the advancing front of a growing droplet confined in a microfluidic channel. When heating implies an effective increase in interfacial tension, the laser behaves as a "soft door" whose stiffness can be tuned via the optical parameters (beam power and waist). The light-driven thermocapillary velocity of a growing droplet, which opposes the basic flow, is characterized for different types of fluid injection, either pressure or flow rate driven, and various channel aspect ratios. Measurements are interpreted using a simplified model for the temperature gradient at the interface, based on a purely diffusive, three-layer system. Considering the mean temperature gradient, we demonstrate that the classical large-scale temperature gradient behavior is retrieved in the opposite case when the thermal gradient length scale is smaller than the droplet size. We also demonstrate that the thermocapillary velocity is proportional to the smallest droplet curvature imposed by the channel confinement. This suggests that the thermocapillary velocity is in fact proportional to the mean temperature gradient and to the largest interface curvature radius, which both coincide with the imposed one and the spherical droplet radius in large-scale and unconfined situations. Furthermore, as used surfactant concentrations are largely above the critical micelle concentration, we propose a possible explanation, relying on state-of-the-art considerations on high-concentration surfactant-covered interfaces for the observed effective increase in interfacial tension with temperature. We also propose a mechanism for explaining the blocking effect at the scaling-law level. This mechanism involves the temporal evolution of hydrodynamic and thermocapillary forces, based on experimental observations. We finally show that this optocapillary interaction with a microfluidic droplet generator allows for controlling either the flow rate (valve) or the droplet size (sampler), depending on the imposed fluid injection conditions.

Noncontact Bubble Manipulation in Microchannel by Using Photothermal Marangoni Effect

A noncontact bubble manipulation by an optically induced local surface tension gradient is described in this paper. In microfluidic devices, the effects of interfacial phenomena become dominant with decreasing of the length scale. An appropriate control of the local gradient of the interfacial properties can provide a powerful method for bubble handling in the microfluidic system. Here, the photothermal technique is used to induce the gradient in surface tension around a microbubble. The thermocapillary force around the bubble is induced and controlled by local laser focusing. The bubble in a microchannel filled with silicone oil with varied viscosity was examined to verify experimentally the optical manipulation method of bubbles based on the photothermal Marangoni effect. As a result, three applications of bubble manipulation by using photothermal Marangoni effect are obtained: detachment from channel wall, trapping in liquid phase, and transportation in the channel. Additionally, minimum optical power for the manipulation was evaluated. The effects of bubble size, liquid viscosity, and irradiated optical power on the manipulation characteristics can be summarized by a dimensionless number that is a ratio of the thermocapillary force to viscous drag force for the bubble.

Evolution of the temperature field at the three-dimensional wave front in a heated liquid film

An experimental study of the transformation of three-dimensional waves into thermocapillarywave structures in the flow of water film on a vertical plate with a heater was carried out using the fluorescent thickness measurement technique and a high-speed infrared recording technique in order to measure the temperature field on the liquid film surface. It was shown that the temperature disturbances occur in the residual layer of the wave film. Then, as the film flows along the heater, temperature inhomogeneities appear transverse to the flow at the three-dimensional wave front; and these inhomogeneities cause deformation of the liquid film and formation of rivulet due to the action of thermocapillary forces.

Controlling Nanoparticles Formation in Molten Metallic Bilayers by Pulsed-Laser Interference Heating

The impacts of the two-beam interference heating on the number of core-shell and embedded nanoparticles and on nanostructure coarsening are studied numerically based on the non-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20 nm) metallic bilayers. The model incorporates thermocapillary forces and disjoining pressures, and assumes dewetting from the optically transparent substrate atop of the reflective support layer, which results in the complicated dependence of light reflectivity and absorption on the thicknesses of the layers. Stabilizing thermocapillary effect is due to the local thickness-dependent, steady- state temperature profile in the liquid, which is derived based on the mean substrate temperature estimated from the elaborate thermal model of transient heating and melting/freezing. Linear stability analysis of the model equations set for Ag/Co bilayer predicts the dewetting length scales in the qualitative agreement with experiment.