Thermocapillarity in a liquid film on an unsteady stretching surface

The influence of thermocapillarity on the flow and heat transfer in a thin liquid film on a horizontal stretching sheet is analysed. The time-dependent governing boundary layer equations for momentum and thermal energy are reduced to a set of coupled ordinary differential equations by means of an exact similarity transformation. The resulting three-parameter problem is solved numerically for some representative values of an unsteadiness parameter S and a thermocapillarity number M for Prandtl numbers from 0.001 to 100. The thermocapillary surface forces drag the liquid film in the same direction as the stretching sheet and a local velocity minimum occurs inside the film. The surface velocity, the film thickness, and the Nusselt number at the sheet increase with M for Pr?10. For higher Prandtl numbers, the thermal boundary layer is confined to the lower part of the liquid film and the temperature at the free surface remains equal to the slit temperature and the thermocapillary forces vanish.     

Unsteady thin-film flow over a heated stretching sheet

The unsteady flow in a thin viscous liquid film over a heated horizontal stretching surface are analyzed considering the stretching velocity and the temperature distribution in their general forms. An evolution equation for the film thickness, that retains the convective heat transport effects, is derived using long-wave theory of thin liquid film and is solved numerically for some representative values of non-dimensional parameters. It is observed that the thermocapillary effects are responsible in shaping the film thickness. Further the thermocapillary effects are more pronounced for lower values of Prandtl number and Biot number.     

Numerical simulation of thermocapillary nonwetting

The nonwetting phenomenon that occurs when a liquid drop is pressed against a solid wall held at a sufficiently lower temperature, is analyzed numerically. An interstitial gas film, induced by thermocapillary convection, separates the drop from the wall, forming a self-lubricating system. The temperature differences and wall distances were probed to evaluate their nonwetting effect. The results indicate that increasing the temperature difference or decreasing the wall distance can enhance the wetting suppression, whether with silicone-oil or water. The thermocapillary nonwetting phenomenon using 5 cSt silicone-oil droplet is more apparent than that obtained with water when the wall distance is small enough, because the capillary number of silicone oil is much larger than that of water. Alternately, when a cold liquid drop is moved towards a hot wall, the thermocapillary flow encourages the occurrence of wetting.     

Study of rising liquid film on surface of horizontal metallic mesh tube

The formation of a rising liquid film on the surface of a horizontal metallic mesh tube in the presence of a temperature field is investigated. A numerical model is established to study the behavior of the rising liquid film. For thermocapillary flow, the velocity distribution of the liquid film is obtained numerically and the influences of wall temperature, geometry of the metallic mesh, and diameter of the tube on the formation of the rising liquid film are also investigated. The results indicate that the velocity of the rising liquid film is influenced by the diameter of the tube and the gap between the tube and the metallic mesh. The velocity of the rising liquid is obviously promoted due to the influence of thermocapillary flow. An experimental system was developed and comparisons between numerical solution and experimental results were made. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20270     

Linear temporal and spatial stability formulations of two‐dimensional surface waves on evaporating,isothermal, or condensing liquid films

When a liquid film is under the evaporating or condensing condition, the flow stability is clearly different from that under an isothermal condition due to the thermal non‐equilibrium effect at the interface, especially under a lower Reynolds number. Based on Prandtl's boundary layer theory and complete boundary conditions, the universal temporal and spatial stability formulations are established using the collocation method for two‐dimensional surface waves of the evaporating or condensing and isothermal liquid films draining down an inclined wall. The evolution equations indicate that the flow stability is closely related to the Reynolds number, thermocapillarity, inclination angle, liquid property, and evaporation, isothermal, or condensation actions. The effects of the above factors are investigated with neutral stability curves at different Reynolds numbers, and stability characteristics are fully indicated in theory for evaporating or condensing films. Results show that the evaporation process destabilizes the film flow and condensation process stabilizes the film flow. Thermocapillarity has a stabilizing effect in an evaporation condition and an adverse effect in the condensation condition. For a lower Reynolds number, the vapor recoil and thermocapillary take dominant effects when compared to the inertia force in determining flow stability. At a higher Reynolds number, the flow stability is controlled by the inertia force. Present study indicates that the disturbance increases with an increase of the Reynolds number and inclination angle, and decreases with increase of Ka numbers. Furthermore, the effects of liquid properties and inclination angle are always significant. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(4): 243–257, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20062     

Slip and micro flow characteristics near a wall of evaporating thin films in a micro channel

The microscopic liquid flow and heat transfer characteristics near the solid–liquid interface in the evaporating thin film region of a mini channel were investigated based on the augmented Young–Laplace equation and kinetic theory. A physical model using the boundary layer approximation and a constant slip length was developed to obtain the solid–liquid interfacial thermal resistances and interfacial temperatures. The results show that the ordered micro layer and micro flow near the wall reduce the effective liquid superheat and the liquid pressure difference mainly due to the reduced capillary pressure gradient. The solid–liquid interfacial thermal resistances and U‐shaped temperature drops tend to reduce the thin film spreading and heat transfer. The effects of the solid–liquid interfacial thermal resistances on the thin film evaporation outweigh the effects of the thermal conductivity enhancement due to the liquid ordering. The concepts of the micro flow and ordered adsorbed flowing micro layer are clarified to express the Kapitza resistance analytically in terms of the slip length and micro layer thickness. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; 39(7): 460–474, 2010; Published online 3 June 2010 in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20310     

Effects of the liquid polarity and the wall slip on the heat and mass transport characteristics of the micro-scale evaporating transition film

A mathematical model is developed to describe the micro-/nano-scale fluid flow and heat/mass transfer phenomena in an evaporating extended meniscus, focusing on the transition film region under non-isothermal interfacial conditions. The model incorporates polarity contributions to the working fluid field, a slip boundary condition on the solid wall, and thermocapillary stresses at the liquid-vapor interface. Two different disjoining pressure models, one polar and one non-polar, are considered for water as the working fluid so that the effect of polar interactions between the working fluid and solid surface can be exclusively examined on heat and mass transfer from the thin film. The polar effect is examined for the thin film established in a 20-μm diameter capillary pore. The effect of the slip boundary condition is separately examined for the thin film developed in a two-dimensional 20-μm slotted pore. The analytical results show that for a polar liquid, the transition region of the evaporating meniscus is longer than that of a non-polar liquid. In addition, the strong polar attraction with the solid wall acts to lower the evaporative heat transfer flux. The slip boundary condition, on the other hand, increases evaporative heat and mass flux and lowers the liquid pressure gradients and viscous drag at the wall. The slip effect shows a more pronounced enhancement as superheat increases. Another thing to note is that the slip effect of elongating the transition region can counteract the thermocapillary action of reducing the region and a potential delay of thermocapillary driven instability onset may be anticipated.     

Shear-driven flows of locally heated liquid films

This paper considers the flow of a liquid film sheared by gas flow in a channel with a heater placed at the bottom wall. A one-sided 2D model is considered for weakly heated films. The heat and mass transfer problem is also investigated in the framework of a two-sided model. The exact solution to the problem of heat transfer is obtained for a linear velocity profile. The double effect of Marangoni forces is demonstrated by the formation of a liquid bump in the vicinity of the heater’s upper edge and film thinning in the vicinity of the lower edge. The criterion determining the occurrence of “ripples” on the film surface upstream from the bump is found. Numerical analysis reveals that evaporation dramatically changes the temperature distribution, and hence, thermocapillary forces on the gas–liquid interface. All transport phenomena (convection to liquid and gas, evaporation) are found to be important for relatively thin films, and the thermal entry length is a determining factor for heaters of finite length. The thermal entry length depends on film thickness, which can be regulated by gas flow rate or channel height. The influence of the convective heat transfer mechanism is much more prominent for relatively high values of the liquid Reynolds number. The liquid–gas interface Biot number is shown to be a sectional-hyperbolic function of a longitudinal axis variable. Some qualitative and quantitative comparisons with experimental results are presented.     

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.     

A consideration on the relation between the oscillatory thermocapillary flow in a liquid bridge and the hydrothermal wave in a thin liquid layer

The present study aims to establish relation between the hydrothermal wave (HW) in a thin liquid layer and the oscillatory flow in a half-zone liquid bridge with a small height to radius ratio. Numerical and experimental studies are performed on the HW in a liquid layer. Near the hot wall, the propagation direction of the HW is similar to that of the temperature traveling wave in the short liquid bridge. Thus, the oscillatory thermocapillary flow in the short liquid bridge should be interpreted to be closely similar to the HW appearing in the vicinity of the hot wall of the liquid layer.     

Investigation on heat transfer characteristics of aircraft icing including runback water

The heat transfer characteristics of aircraft icing process were investigated based on the theories of liquid–solid phase change and film flow. The heat transfer model which couples runback water flow with liquid–solid phase change was established and the influence of airflow parameters on the characteristics of icing growth was analyzed. The results indicate that the runback water on the icing surface will accelerate the liquid–solid phase change and the icing process. The shear stress caused by the airflow is the key factor to the runback water flow. The higher the airflow velocity, the greater the shear stress and stronger the runback water flow. Under the condition of runback water flow, the velocity and temperature of the airflow are the main causes effecting on the icing accretion. The higher the airflow velocity or the lower the temperature is, the greater the icing rate will be. The liquid water content (LWC) and the collection efficiency have weak effect on the icing rate comparatively.     

Thermocapillary instabilities in liquid columns under co – and counter-current gas flows

The thermocapillary flows in an infinite liquid column surrounded by an annular channel of gas with the axial temperature gradient are investigated. The gas is pumped through the channel parallel to the interface with a given flow rate. The solution for stationary motion is derived and possible flow regimes are analyzed depending on the Marangoni number and dimensionless gas flow rate. Linear stability analysis of these regimes is performed. It is shown that gas pumping in the same direction with respect to the thermocapillary motion on the interface has a destabilizing effect on the system. Gas pumping in the opposite direction can be stabilizing or destabilizing depending on the gas flow rate. It is shown that the motion of liquid can be completely vanished by the gas flow with a specified flow rate. The obtained results demonstrate the possibility of controlling thermocapillary flows and their stability in liquid columns (liquid bridges) by gas flows.     

A Numerical Method for Multiphase Incompressible Thermal Flows with Solid–Liquid and Liquid–Vapor Phase Transformations

ABSTRACT

A numerical method for multiphase incompressible thermal flows with solid–liquid and liquid–vapor phase transformations is presented. The flow is mainly driven by thermocapillary force and vaporization. Based on the level set method and mixture continuum model, a set of governing equations valid for solid, liquid, and vapor phases is derived, considering phase boundary conditions as source terms in the transport equations. The vaporization process is treated as a source term in the continuity equation. The model developed is applied to the laser welding process, where the flow is coupled with optical phenomena. Formation and collapse of a laser-created hole is simulated.     

A study of retardation of the thermocapillary flow caused by surfactant addition

Surfactant effect on thermocapillary flow that artificially provoked by a steady point heat source at an air/liquid interface was studied. The experimentally measured surface velocity and temperature profiles reveal that small amounts of SDS in ethylene glycol retard significantly the thermocapillary flow. A dimensionless elasticity number E, which is a ratio of the surfactant-induced restoring force to the thermocapillary force that triggers the flow, is proposed to express the interplay of concentration and temperature effects on interfacial turbulence. The data of this highly viscous liquid together with those of water in a previous work were examined and shown to be satisfactorily correlated by an equation developed in terms of the elasticity number.     

Internal flow in evaporating droplet on heated solid surface

This work numerically studies the evaporation process of a liquid droplet on a heated solid surface using a comprehensive model. The internal flow within the evaporating liquid droplet is elucidated, while considering the effects of buoyancy force, thermocapillary force, and viscous resistance. The evaporation process is modeled by simultaneously solving the Navier–Stokes equations and energy equation for the liquid domain and the heat conduction equation for the solid domain, while assuming the liquid–vapor interface is a free surface. Three dimensionless parameters are utilized to describe the contribution of individual driving forces to internal flow. Evolutions of the thermal and internal flows during evaporation are discussed. The volume evolution and experimental data are in good agreement.     

开口圆形浅池内低Pr流体的热毛细对流

为了了解开口圆形浅池内低Pr流体的热毛细对流基本规律,利用有限差分法进行了三维直接数值模拟。结果表明,当侧壁温度不均匀性较小时,流动为稳定的三维流动。当温度不均匀性超过某一临界值后,流动将转化为振荡的三维流动,为此,确定了流动转化的临界条件,分析了三维振荡热毛细对流的基本特性。发现在自由表面Marangoni效应作用下,冷壁附近温度和速度波动的滞后是引起三维振荡流动的主要原因。     

Molecular Dynamics Simulation on Rapid Boiling of Thin Water Films on Cone-Shaped Nanostructure Surfaces

Molecular dynamics simulations (MDS) are employed to investigate the effects of the size of a nanocone on rapid boiling of an ultrathin liquid water film that is suddenly heated by a hot aluminum plate. A physically sound thermostat is applied to control the temperature of the aluminum plate and then to heat the water molecules that are placed on the solid surface. The results show that the cone nanostructures drastically enhance heat transfer from the solid aluminum plate to liquid water and the phase change process from liquid water to vapor. They also have significant effects on temperature histories and the density distributions in the system. In all cases studied, the water molecules above the solid surface rapidly boil after contact with an extremely hot aluminum plate and consequently a cluster of liquid water is observed to move upward during the phase change. It is also observed that the separation temperature associated with separation of liquid water film from the solid surface and its final temperature when the system is at equilibrium strongly depend on the height of the nanocone. Furthermore, in all cases, at a specific time after beginning of boiling, a nonvaporized water molecular layer is formed above the surface of the aluminum plate.     

液层厚度比对环形腔内双层液体的热毛细对流稳定性的影响

为了了解微重力条件下、水平温度梯度作用时,上部为固壁的环形腔内双层流体系统中液层厚度比对流动稳定性的影响,采用隐式重启Arnoldi方法(IRAM)对环形池内5cSt硅油/HT-70双层流体的热对流过程进行了线性稳定性分析,获得了不同液层厚度比下的临界Marangoni数、临界波数、临界相速度,并通过计算特征向量,得到了临界Marangoni数附近液-液界面的热流体波形态。     

Experimental study on combined buoyant-thermocapillary flow along with rising liquid film on the surface of a horizontal metallic mesh tube

Temperature distribution and variation with time has been considered in the analysis of the influences of the initial level of immersion of a horizontal metallic mesh tube in the liquid on combined buoyant and thermo-capillary flow. The combined flow occurs along with the rising liquid film flow on the surface of a horizontal metallic mesh tube. Three different levels of immersion of the metallic mesh tube in the liquid have been tested. Experiments of 60 min in duration have been performed using a heating metallic tube with a diameter of 25 mm and a length of 110 mm, sealed outside with a metallic mesh of 178 mm by 178 mm, and distilled water. These reveal two distinct flow patterns. Thermocouples and infrared thermal imager are utilized to measure the temperature. The level of the liquid free surface relative to the lower edge of the tube is measured as angle q. The results show that for a smaller q angle, or a low level of immersion, with a relatively low heating power, it is possible to near fully combine the upwards buoyant flow with the rising liquid film flow. In this case, the liquid is heated only in the vicinity of the tube, while the liquid away from the flow region experiences small changes in temperature and the system approaches steady conditions. For larger q angles, or higher levels of immersion, a different flow pattern is noticed on the liquid free surface and identified as the thermo-capillary (Marangoni) flow. The rising liquid film is also present. The higher levels of immersion cause a high temperature gradient in the liquid free surface region and promote thermal stratification; therefore the system could not approach steady conditions.