The Influence of the Magnitude of Gravitational Acceleration on Marangoni Convection About an Isolated Bubble under a Heated Wall

Thermocapillary or Marangoni convection is the liquid motion caused by surface tension variation in the presence of a temperature gradient along a gas–liquid or vapor–liquid interface. This work numerically investigates the effect of the magnitude of gravitational acceleration on the flow and temperature fields resulting from the presence of a hemispherical air bubble of constant radius of 1.0 mm, situated on a heated wall immersed in a liquid silicone oil layer of constant depth of 5.0 mm. The model is oriented such that the Marangoni and gravitational forces act to oppose one another. To elucidate the effect of gravity on Marangoni flow and heat transfer, the simulations were carried out for a silicone oil of Prandtl number 83, at a Marangoni number of 915. The gravity levels tested were 0g, 0.01g, 0.1g, 0.25g, 0.5g, 0.75g, and 1g, where g represents the earth gravitational acceleration of 9.81 m/s ² . The influence of the magnitude of gravitational acceleration on the velocity profile along the bubble interface and on the location of maximum velocity was analyzed. It was found that the gravity level affects the velocity profile by influencing the interfacial temperature gradient, but that the location of maximum velocity was almost independent of gravity level. The increase in heat flux on the wall to which the bubble is attached was calculated and it has been determined that local heat transfer enhancement of up to nearly 1.7 times that of the conduction only case can be achieved for the parameter range tested. Furthermore, local enhancement was observed to occur up to a distance of seven bubble radii for the zero-gravity case, but increased gravity levels cause a reduction in the effective radius of enhancement. The influence of the Marangoni flow on the heat transfer for the opposite cooled wall has also been analyzed.     

Mixed Convective Heat Transfer Due to Forced and Thermocapillary Flow Around Bubbles in a Miniature Channel: A 2D Numerical Study

Marangoni thermocapillary convection and its contribution to heat transfer during boiling has been the subject of some debate in the literature. Currently, for certain conditions, such as microgravity boiling, it has been shown that Marangoni thermocapillary convection has a significant contribution to heat transfer. Typically, this phenomenon is investigated for the idealized case of an isolated and stationary bubble resting on a heated surface, which is immersed in a semi-infinite quiescent fluid or within a two-dimensional cavity. However, little information is available with regard to Marangoni heat transfer in miniature confined channels in the presence of a cross flow. As a result, this article presents a two-dimensional (2D) numerical study that investigates the influence of steady thermal Marangoni convection on the fluid dynamics and heat transfer around a bubble during laminar flow of water in a miniature channel with the view of developing a refined understanding of boiling heat transfer for such a configuration. This mixed convection problem is investigated under microgravity conditions for channel Reynolds numbers in the range of 0 to 500 at liquid inlet velocities between 0.01 m/s and 0.0 5m/s and Marangoni numbers in the range of 0 to 17,114. It is concluded that thermocapillary flow may have a significant impact on heat transfer enhancement. The simulations predict an average increase of 35% in heat flux at the downstream region of the bubble, while an average 60% increase is obtained at the front region of the bubble where mixed convective heat transfer takes place due to forced and thermocapillary flow.     

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.     

Microlayer thickness under a vapor bubble on a cylindrical probe

The thickness of a liquid microlayer underneath a vapor bubble on a heated, cylindrical probe was determined by simultaneously solving the fourth‐order differential equation for the microlayer thickness that incorporates the momentum and energy equations in the microlayer in conjunction with the pressure distribution in the microlayer and the evaporative heat flux at the interface. The analysis also considers the temperature gradient along the probe due to heat transfer in the probe. The results show that the microlayer on a cylindrical surface is very thin and short except for very low probe surface temperatures, superheated less than 1 K. The microlayer size and the evaporative heat flux both decrease rapidly as the surface temperature increases. The results show that most of the evaporation occurs along the curved portion of the interface. © 2000 Scripta Technica, Heat Trans Asian Res, 29(3): 193–203, 2000     

Models for enhanced boiling heat transfer by unusual Marangoni effects under microgravity conditions

A new approach is suggested to enhance boiling heat transfer through introduction of unusual surface tension effects. The surface tension of aqueous solutions of alcohols with a chain length longer than four carbon atoms offers a positive gradient with temperature when the temperature exceeds a certain value. Moreover, the positive gradient near the boiling point has a very large value. This will generate a considerable driving force for bubble departure. As a result, in the nucleate boiling of these solutions, the Marangoni effect around the bubble surface will not impede the bubble detachment from the heater surface but rather will provide an additional driving force for the bubble departure. This effect combines with the buoyancy under normal gravity and acts as a main driving force of bubble departure in microgravity. Models for predictions of the bubble detachment diameters, the nucleate boiling heat transfer coefficient, and the critical heat flux are developed.     

Numerical analysis of the dynamics of moving vapor bubbles

Bubbles have been observed rapidly sweeping along very fine heated wires during subcooled nucleate boiling with jet flows emanating from the tops of the vapor bubbles. This paper analyzes the physical mechanisms driving the bubble and the jet flows from the tops of these moving bubbles. The flows are analyzed by numerically solving the governing equations for the velocity and temperature distributions around the bubble and the heated wire as the bubble moves along the wire. The bubble motion is due to the non-uniform temperature distribution in the liquid and in the wire caused by the bubble as it moves along the wire. The flow is driven by the horizontal Marangoni flow induced by the temperature difference across the bubble which thrusts the bubble forward. Comparisons with experimental observations suggest that the condensation heat transfer at the bubble interface is restricted by non-condensable gases that increases the surface temperature gradient and the resulting Marangoni flow.     

MARANGONI EFFECT IN MICROBUBBLE SYSTEMS

This work explores the application of the Marangoni effect in micro systems involving small gas or vapor bubbles in a liquid environment subjected to a temperature gradient. The Marangoni effect characterizes the variation of surface tension along the bubble surface resulting from the temperature gradient around the bubble, thus driving the bubble toward the higher temperature region. This phenomenon is more pronounced as the bubble becomes smaller and the temperature gradient becomes steeper, both of which can be achieved in microbubble systems. Potential applications based on the Marangoni effect include linear bubble actuators, dynamic microvalves, and hot-spot locators. The optimum bubble size for these applications is expected to be of the order of 10 mu m. A smaller bubble may be difficult to introduce into the working system and maintain its size. Presented for illustration is a feasibility analysis for both a noncondensable gas bubble and a vapor bubble situated above a microheater. The analysis yields results for the temperature field around the bubble surface and the Marangoni driving pressure, which is a key element of the performance evaluation for all Marangoni-effect-based applications. The findings demonstrate clearly that the Marangoni effect on microbubbles is very significant and shows great promise for applications in microelectromechanical systems (MEMS).     

Heat transfer for Marangoni‐driven boundary layer flow

Marangoni convection induced by variation of the surface tension with temperature along a surface influences crystal growth melts and other processes with liquid–vapor interfaces, such as boiling in both microgravity and normal gravity in some cases. This paper presents the Nusselt number for Marangoni flow over a flat surface calculated using a similarity solution for both the momentum equations and the energy equation assuming developing boundary layer flow along a surface. Solutions are presented for the surface velocity, the total flow rate, and the Nusselt number for various temperature profiles, Marangoni numbers, and Prandtl numbers. For large bubbles, the predicted boundary layer thickness would be less than the bubble diameter, so the curvature effects could be neglected and this analysis could be used as a first estimate of the effect of Marangoni flow around a vapor bubble. © 2002 Scripta Technica, Heat Trans Asian Res, 31(2): 105–116, 2002; DOI 10.1002/htj.10019     

Interface Shape and Marangoni Effect Around aBubble Within the Thermal Boundary Layer

INTRoDUCTIoNDuetohighheattransferperformancecharacter-izedbysmalltemPeraturedifferencesandhighheatfluxes,transportprocesseswithphasechange,espe-ciallyboilingandcondensationprocessesarewidelyemployedinnumerousenergyconversionandtrans-portsystems,heatingand/orcoolingdevices,andaerospaceaPplications.Priortotheutilizationofboil-ingprocessesinspaceapplications,suchasspacecraftthermalcontrol,additionalunderstandingofboilingheattransferbehaviorisneeded.Becauselargedmer-encesekistinthefiuiddensiti…     

Investigation of heat transfer and bubble dynamics in a boiling thin liquid film flowing over a rotating disk

Nucleate boiling heat transfer and bubble dynamics in a thin liquid film on a horizontal rotating disk were studied. A series of experiments were conducted to determine the heat transfer coefficient on the disk. At low rotation and flow rates, vigorous boiling increased the heat transfer coefficients above those without boiling. Higher rotational speeds and higher flow rates increased the heat transfer coefficient and suppressed boiling by decreasing the superheat in the liquid film. The flow field on the disk, which included supercritical (thin film) flow upstream of a hydraulic jump, and subcritical (thick film) flow downstream of a hydraulic jump, affected the type of bubble growth. Three types of bubble growth were identified. Vigorous boiling with large, stationary bubbles were observed in the subcritical flow. Supercritical flow produced small bubbles that remained attached to the disk and acted as local obstacles to the flow. At low rotational rates, the hydraulic jump that separated the supercritical and subcritical regions produced hemispherical bubbles that protruded out of the water film surface and detached from the disk, allowing them to slide radially outward. A model of the velocity and temperature of the microlayer of water underneath these sliding bubbles indicated that the microlayer thickness was approximately 1/25th of that of the surrounding water film. This microlayer is believed to greatly enhance the heat transfer rate underneath the sliding bubbles.     

Condensate drop movement in Marangoni condensation by applying bulk temperature gradient on heat transfer surface

The spontaneous movement of condensate drops by application of a bulk temperature gradient on the heat transfer surface in Marangoni condensation was investigated, with consideration for applications to heat transfer devices. In the Marangoni condensation process, the removal of condensate on the heat transfer surface is important to maintain good heat transfer. A heat transfer device, in which the liquid movement occurs without external forces such as gravity and vapor shear force, may be useful in various applications. As a result of experiments using a water–ethanol vapor mixture, the movement of droplets from the low‐temperature side to high‐temperature side could be observed on a horizontally arranged heat transfer surface. The relation between the velocity of drop movement and the gradient of surface tension was studied for different concentrations. Furthermore, the effect of inclination of the condensing surface was examined. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(7): 387–397, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20218     

A sharp-interface level-set method for analysis of Marangoni effect on microdroplet evaporation

A level-set method is presented for computation of microdroplet evaporation including not only the effects of heat and mass transfer, phase change and contact line dynamics but also the Marangoni effect, which is a key parameter affecting the internal flow of the droplet and the particle deposition pattern. A sharp-interface formulation of the Marangoni force is derived and tested for two-phase Marangoni convection in a cavity. The computed results show good convergence in both the liquid and gas regions and are in excellent agreement with the analytical solutions. The level-set formulation is applied to microdroplet evaporation on a solid surface to investigate the Marangoni effect.     

Comprehensive experimental and theoretical study of fluid flow and heat transfer in a microscopic evaporating meniscus in a miniature heat exchanger

The complex physicochemical phenomena occurring in the contact line region of an evaporating meniscus are described using a unique combination of high-resolution experimental data and three complementary models. The following were used: (1) high-resolution experimental liquid profile data (thickness, slope, curvature and curvature gradient) to obtain the pressure gradient in the evaporating pentane meniscus in a vertical constrained vapor bubble (VCVB); (2) macroscopic outside surface temperature profile data; (3) a finite element model to obtain the two-dimensional heat conduction profile in the solid substrate wall (macro-model) and the solid–liquid interfacial temperature profile in the evaporating meniscus region; (4) a continuum fluid-dynamics model (micro-model) to obtain the liquid–vapor interfacial temperature, mass flow rate, Marangoni stresses, and evaporative heat flux profiles along the length of the evaporating meniscus; and (5) the Kelvin–Clapeyron model to obtain the vapor temperature profile (liquid–vapor interfacial temperature jump) in the evaporating meniscus region.The retarded dispersion constant and high-resolution thickness, slope, curvature and curvature gradient profiles were obtained from the experimental reflectivity profiles. There was a substantial increase in the measured curvature in the transition region, where the evaporation rate and flux are a maximum. To obtain numerical closure between the three complementary models, the continuum fluid dynamics model (micro-model) required slip at the solid–liquid interface to support the observed high mass flow rates in the evaporating pentane meniscus. Mass flow rates due to Marangoni stresses, capillary pressure and disjoining pressure are compared. Depending on the liquid thickness, Marangoni stresses can either enhance or hinder fluid flow towards the contact line for the evaporating pure pentane meniscus. Due to the high heat removal rate by the evaporating pentane meniscus in the transition region, dips in the vapor, liquid–vapor and solid–liquid interface temperature were obtained. The results demonstrate and describe the sensitivity and complexity of the phase change process in micro-regions.     

Heat transfer during pool boiling based on evaporation from micro and macrolayer

An analytical model of heat transfer based on evaporation from the micro and macrolayers to the vapor bubble during pool boiling is developed. Evaporation of microlayer and macrolayer during the growth of individual bubbles is taken care of by using temporal and spatial variation of temperature in the liquid layer. Change of bubble shape during the entire cycle of bubble growth and departure is meticulously considered to find out the rate of heat transfer from the solid surface to the boiling liquid. Continuous boiling curve is developed by considering the bubble dynamics and decreasing thickness of liquid layer along with the increase of dry spot radius. Transient variation of macrolayer and microlayer thickness is predicted along with their effect on CHF. Present model exhibits a good agreement with reported experimental data as well as theories.     

Boiling heat transfer in a narrow space controlled by punched interference plate

An experiment on pool boiling in methanol was performed for a case in which the boiling space was controlled by an interference plate with many holes. The narrow space, 0.12 mm in thickness, between the heat transfer surface and the interference plate was hermetically sealed at the perimeter. Therefore, the vapor and liquid were only exchanged through the holes in the interference plate. The degree of superheat at the onset of boiling was 0.7 K without overshoot at 10‐mm plate thickness, 1‐mm hole diameter, and 3.85‐mm hole pitch. The critical heat flux obtained was the same value without the interference plate mentioned above. The interference plate disturbed free convection and a superheat layer was provided under small heat flux on the heat transfer surface. The critical bubble diameter for the onset of boiling was decreased as the temperature of the superheat layer was increased. Thus, the degree of superheat at the onset of boiling was decreased. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(7): 462–471, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20028     

Numerical study of bubble growth and boiling heat transfer on a microfinned surface

The bubble growth and boiling heat transfer on a microfinned surface are studied numerically by solving the conservation equations of mass, momentum and energy. The bubble shape is tracked by a sharp-interface level-set method, which is modified to include the effect of phase change and to treat the contact angle and microlayer heat flux on an immersed solid surface. The present computation demonstrates that the microfinned surface enhances boiling heat transfer significantly compared to a plain surface. The effects of fin spacing and height on the bubble growth and heat transfer are investigated to find the optimal conditions for boiling enhancement.     

环形池内具有自由表面的双层流体热毛细对流

采用数值模拟方法研究微重力条件下环形双层液体内存在水平温度梯度时的热毛细对流及其稳定性。流体为5cSt硅油/HT-70,外壁被加热、内壁被冷却,下固壁和上自由表面均绝热。结果表明:当Ma较小时,流动为稳定的轴对称流动;随着Ma和深宽比的增大,流动加强,等温线发生强烈的非线性变形;当Ma超过临界值后,流动转化为非稳定的多胞流动;随着Ma和深宽比的增大,速度振荡增大并向热壁方向运动,多胞流动结构占据区域拓展;流动转变的临界Ma随着深宽比的增大而减小。     

Three-dimensional modeling of heat transfer and fluid flow in laminar-plasma material re-melting processing

Modeling study is performed concerning the heat transfer and fluid flow for a laminar argon plasma jet impinging normally upon a flat workpiece exposed to the ambient air. The diffusion of the air into the plasma jet is handled by using the combined-diffusion-coefficient approach. The heat flux density and jet shear stress distributions at the workpiece surface obtained from the plasma jet modeling are then used to study the re-melting process of a carbon steel workpiece. Besides the heat conduction within the workpiece, the effects of the plasma-jet inlet parameters (temperature and velocity), workpiece moving speed, Marangoni convection, natural convection etc. on the re-melting process are considered. The modeling results demonstrate that the shapes and sizes of the molten pool in the workpiece are influenced appreciably by the plasma-jet inlet parameters, workpiece moving speed and Marangoni convection. The jet shear stress manifests its effect at higher plasma-jet inlet velocities, while the natural convection effect can be ignored. The modeling results of the molten pool sizes agree reasonably with available experimental data.     

Microscale heterogeneous boiling on smooth surfaces—from bubble nucleation to bubble dynamics

In this investigation, boiling incipience and bubble dynamics on a microheater with a geometry of 100 μm × 100 μm fabricated with MEMS technology are evaluated using a high-speed digital camera. For the purpose of comparison with conventional boiling heat transfer, boiling incipience and bubble dynamics are also studied on a carefully selected microheater with a fabricated defect (i.e., a microcavity on the heater surface). Of industrial interest are the effects of dissolved gases on boiling incipience and bubble dynamics, which are also discussed in detail. The possible nucleation temperature (or incipience temperature) is analyzed and discussed from the perspective of the measured bulk temperature of the microheater and a 3D heat conduction numerical model. The time-resolved bubble dynamics (i.e., the bubble size evolution, interface velocity and interface acceleration) are all presented along with high-speed digital images. Based upon this investigation, it is clear that explosive boiling can take place on a smooth surface no matter how slow the heating rate, and dissolved gases have a significant influence on the incipience temperature and bubble behavior. Furthermore, this study illustrates that the classical kinetics of boiling can explain the explosive boiling occurring on a smooth surface in principle and can provide a useful guide for the design of microscale heat transfer and/or MEMS devices. Although unexpected, due to the gravitational effects, Marangoni flow on the vapor–liquid interface induced by the temperature gradient was also observed.     

Oscillatory thermocapillary flow in liquid bridges of high Prandtl number fluid with free surface heat gain

Oscillatory thermocapillary flow in liquid bridges of high Prandtl number fluid is studied. The effect of free surface heat transfer, especially heat gain, on the oscillation phenomenon is investigated experimentally and numerically. It is shown that the critical temperature difference (ΔT_cr) changes substantially when the free surface heat transfer changes from loss to gain in the case of nearly straight liquid bridges. In contrast, ΔT_cr is not affected by the free surface heat transfer with concave liquid bridges. The free surface heat transfer rate is computed numerically by simulating the interaction of the liquid and the surrounding air. The oscillatory flow is also investigated numerically by analyzing the liquid flow in three-dimensions for straight bridges. The computed results agree well with the experimental data. The simulation shows that the free surface heat gain enhances the surface flow and that the oscillatory flow is a result of interactions between the convection effect and buoyancy. The flow does not become oscillatory if there is no net heat gain at the free surface in the range of Marangoni number of the present work (⩽1.8 × 10⁴), so the present cause of oscillations is different from that in the free surface heat loss case we investigated in the past.