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The extended meniscus and the intermolecular and capillary forces that govern its behavior and connection to change-of-phase heat transfer have been the subject of an increasing body of research over the past 50 years. We have been fortunate to be at the forefront of this effort starting from the development of a capillary feeder, in Earth's gravity, to stabilize film boiling to running a series of transparent heat pipe experiments aboard the International space station hoping to better understand the role of intermolecular forces in microgravity. The use of ellipsometry and interferometry to highlight the location and state of the vapor–liquid interface have been key to these studies and have helped to uncover many new, interesting, and sometimes unexpected phenomena associated with fluid flow and change-of-phase heat transfer.

Understanding the fluid dynamics and the phase change heat transfer process within a thin liquid film is important to improve the performance of many industrial processes like coating or distillation. Studies by our group and other research teams showed that thin liquid films begin to oscillate spontaneously as the heat flux increases. We also found that the oscillation amplitude and frequency increase with increasing heat input. This implies that there is a heat transfer advantage to an oscillating thin film. We developed a numerical model to try and understand if there is an advantage to oscillation and under what conditions that advantage occurs. We found that oscillation can enhance net evaporative heat transfer but only if a short period of condensation exists within each oscillation cycle. Such condensation can be driven by intermolecular forces, capillary forces, Marangoni forces, or combinations of all three as we concluded from recent heat pipe experiments. Condensation increases the liquid film thickness at the contact line, and therefore decreases the disjoining pressure impediment to evaporation. These short condensation periods followed by fast evaporation appear as “spikes” in the liquid film thickness over time. These “spikes” were observed experimentally and mimicked by the simulations. Our calculations also show that the heat transfer efficiency increases with increasing oscillation frequency and amplitude in qualitative agreement with experiments.

The Constrained Vapor Bubble (CVB), a simple, wickless, heat pipe design that depends on interfacial forces to drive corner flow in a square cuvette, was studied in the microgravity environment aboard the International Space Station (ISS). In this paper, we consider the effects of different condenser temperatures on the heat transfer and fluid flow behavior using pentane as the working fluid. As the condenser temperature was decreased, the performance of the system decreased. This performance decrease using the pure working fluid was opposite to the behavior observed when using a mixture of 94 vol% pentane and 6 vol% isohexane. The mechanism for the decline in performance as the condenser temperature was lowered was a stronger than expected increase in the apparent strength of Marangoni flows at the heater end of the system. A simple mathematical model was fit to the experimental data and used to extract an evaporator heat transfer coefficient for experiments where we held the condenser temperature constant while increasing the heater power and where we held the heater power constant while decreasing the condenser temperature. All the results could be collapsed onto a single Nusselt number vs. Marangoni number curve. In this formulation, the Nusselt number was found to decrease with increasing Marangoni number to the 1/3 power.

Understanding the dynamics of phase change heat and mass transfer in the three-phase contact line region is a critical step toward improving the efficiency of phase change processes. Phase change becomes especially complicated when a fluid mixture is used. In this paper, a wickless heat pipe was operated on the International Space Station (ISS) to study the contact line dynamics of a pentane/isohexane mixture. Different interfacial regions were identified, compared, and studied. Using high resolution (50×), interference images, we calculated the curvature gradient of the liquid-vapor interface at the contact line region along the edges of the heat pipe. We found that the curvature gradient in the evaporation region increases with increasing heat flux magnitude and decreasing pentane concentration. The curvature gradient for the mixture case is larger than for the pure pentane case. The difference between the two cases increases as pentane concentration decreases. Our data showed that the curvature gradient profile within the evaporation section is separated into two regions with the boundary between the two corresponding to the location of a thick, liquid, “central drop” region at the point of maximum internal local heat flux. We found that the curvature gradients at the central drop and on the flat surfaces where condensation begins are one order of magnitude smaller than the gradients in the corner meniscus indicating the driving forces for fluid flow are much larger in the corners.

The effect of cooling temperature on heat pipe performance has generally received little consideration. In this paper, we studied the performance of a Constrained Vapor Bubble (CVB) heat pipe using a liquid mixture of 94 vol%-pentane and 6 vol%-isohexane at different cooling temperatures in the microgravity environment of the International Space Station (ISS). Using a one-dimensional (1-D) heat transfer model developed in our laboratory, the heat transfer coefficient of the evaporator section was calculated and shown to decrease with increasing cooler temperature. Interestingly, the decreasing trend was not the same across the cooler settings studied in the paper. This trend corresponded with the change in the temperature profile along the cuvette. When the cooling temperature went from 0 to 20 °C, the temperature of the cuvette decreased monotonically from the heater end to the cooler end and the heat transfer coefficient decreased slowly from 456 to 401 (W m −2 K −1 ) (at a rate of 2.75 W m −2 K −2 ). However, when the cooling temperature increased from 25 to 35 °C, a minimum point formed in the temperature profile, and the heat transfer coefficient dramatically decreased from 355 to 236 (W m −2 K −1 ) (at a rate of 11.9 W m −2 K −2 ). A similar change in decreasing trend was observed in the pressure gradient and liquid velocity profile. The reduced heat pipe performance at high cooling temperatures was consistent with the reduced evaporation which was indicated by the decreasing internal heat transfer and the increasing liquid film thickness along the cuvette as seen in the surveillance images. The result obtained is important for future heat pipe design because we now have a better understanding of the working temperature ranges of these devices.

The Constrained Vapor Bubble (CVB) is a transparent, wickless heat pipe experiment carried out in the US Labs of the International Space Station (ISS). Experiments were carried out using the 40 mm CVB, 3 mm× 3 mm in cross-section, pentane as the working fluid, with the power inputs of up to 3 W. Due to the low Bond number (Bo) in microgravity and materials of construction, the CVB system was ideally suited to determine the contribution of the Marangoni forces toward the limiting heat pipe performance, and the transparent quartz shows exactly how that limitation occurs. Previous literature models and experimental temperature and pressure measurements suggested that at high enough temperature gradients, the working fluid should be subjected to enough Marangoni force to force it away from the heater and ultimately, dry out the hot end. The CVB experiment shows that high temperature gradients lead to a totally opposite behavior, i.e., ‘flooding’ of the heated end. Flooding of the heater end is attributed to a competition between Marangoni-induced flow due to high temperature gradients at the heater end and capillary return flow from the cooler. This creates a thick liquid layer in the corner of the cuvette at the heater end. At the point of flow balance, a thick layer of liquid is observed on the flat surface of the quartz cuvette. This is defined as the central drop. The region from the top of the heater end to the central drop is referred to as the interfacial flow region. The interfacial flow region develops at a power input of around 0.7 W, and increases in length to the power input of 2 W. At 2 W, the strength of the Marangoni forces saturate. As a result, the forces in the flooded interfacial region are not able to push the liquid further into the capillary region and a further penetration of liquid down the axis of the heat pipe is arrested. As the power input is increased to nearly 3 W, an increase in the vapor space is observed near the heater end at 3 W. This behavior suggests that the flooding might just be an intermediate stage in reaching the dry-out limitation. The flat quartz surface at the hot end is covered by a wavy thin liquid film due to the interfacial forces. The hot end region closest to the heater is a superheated vapor region that leads to the condensation. This additional observation is discussed in Appendix.

Previous studies on wickless heat pipes showed that a temperature induced “Marangoni flow” prevents liquid from recirculating to the heater end, and therefore reduces the effectiveness of the heat pipe. Recently, several research groups used a water and alcohol mixture, with a low concentration of alcohol, resulting in better performance of the heat pipe. The alcohol/water combinations were peculiar in that for a certain composition range, the surface tension increases with increasing temperature thereby driving liquid toward the hotter end. It was believed that changing the direction of the Marangoni stress or reducing its magnitude by differential evaporation of an ideal binary mixture would also improve the performance of the heat pipe. For the first time, an ideal fluid mixture of 94 vol%-pentane and 6 vol%-isohexane was used as the working fluid in the Constrained Vapor Bubble (CVB) heat pipe experiment on the International Space Station (ISS). Using a simple heat transfer model developed in our laboratory, an internal heat transfer coefficient in the evaporator section was determined and shown to be almost twice that of the case where pure pentane was used under the same conditions. The Marangoni stress in the mixture was five times lower. Interestingly, reducing the Marangoni stress led to less liquid accumulation near the heater end and surveillance images of the device, taken at the steady state, showed that the bubble gets much closer to the heater end in the mixture case instead of being isolated from the heater by a thick liquid pool as in the pure pentane case. The proximity of the bubble to the heater wall led to more evaporation at the heater end in the mixture case, and therefore a higher heat transfer coefficient. The pressure profile calculated from the Young–Laplace equation supports the observations made from the surveillance images.

The liquid-vapor distribution and its effects on the fluid dynamics and heat transfer occurring within a wickless heat pipe are little understood, especially in a microgravity environment. Such information is vital to the design of thermal management systems for deep space robotic and manned exploration missions, especially if unexpected behaviors arise. We observed an unusual analog of a terrestrial rip current during the operation of a wickless heat pipe on the International Space Station. The current arose spontaneously as the heat input increased, flowing along the flat surfaces of the device toward the heater end, and was driven by a pair of counterrotating vortices that formed from the interaction of opposing surface tension and capillary driven corner flows. The current served as a natural way of increasing the total contact line length within the device and this enabled higher evaporation rates than would have been possible based on the engineered geometry of the device alone.

Wickless heat pipes are being studied for use in cooling critical components of spacecraft. The wickless design is thought to produce a simpler and lighter heat transfer system than heat pipes containing wicks or mechanically driven systems. The constrained vapor bubble experiment (CVB) is one such system tested on the International Space Station where the Bond Number (ratio of gravitational force to surface force) is small maximizing the affects of capillarity. The CVB is essentially a square, fused silica spectrophotometer cuvette evacuated and then partially filled with pentane as the working fluid. Along with temperature and pressure measurements, the two-dimensional thickness profile of the menisci formed at the corners of the quartz cuvette was determined using an interferometry based system contained with the station’s Light Microscopy Module (LMM). The CVB can be viewed as a hollow fin and its behavior analyzed using a simple, one-dimensional heat transfer model. That model, coupled with the visual observation of the vapor–liquid distribution inside the fin, provides an enhanced understanding of what the measured temperature and pressure profiles represent and the heat transfer mechanisms controlling the operation of the device. The internal heat transfer processes were found to be very complicated, multi-dimensional, and greatly dependent on internal and external radiative heat transfer. Internal radiative exchange was found to be more significant than originally anticipated as was the effect Marangoni forces on internal convective heat transfer. An analysis of the temperature profiles in conjunction with vapor–liquid interface mapping showed that the system could be separated into a number of discrete operation zones depending on the dominant mode of heat transfer.

Nucleate boiling was observed in the microgravity environment on International Space Station during operation of the Constrained Vapor Bubble (CVB) heat pipe experiment. Surveillance images of the boiling dynamics within this constant volume system were correlated with transient liquid pressures and transient temperature profiles. Nucleation events occurred in a non-periodic but non-random way and individual events were recorded over a twenty (20) hour time period. Each nucleation event originated at the heater surface and new bubble growth was accompanied by a shock wave that passed through the heat pipe and partially collapsed the original vapor bubble. The critical size of the equilibrium homogeneous nucleating bubble radius was determined using the experimental data and standard thermodynamic descriptions of boiling to be on the order of 140 nm for a superheat of 42 K. Maximum heat input to the heat pipe closely followed the timing of the nucleation event. Maximum heat loss, via thermal radiation from the walls of the device, followed the timing of bubble motion and bubble coalescence in the device. The whole process resulted in about a 10% increase in the overall heat transfer rate. Using literature data for an evaporating droplet on a surface, a Kelvin–Clapeyron model for incipient boiling was used to compare the CVB and droplet experimental results. A simple model for the effect of location on the nucleation probability in the CVB was developed.

The Constrained Vapor Bubble (CVB) is a wickless, grooved heat pipe and is the first, full-scale fluids experiment flown on the U.S. module of the International Space Station. The CVB promises to provide new insight into the operation of a heat pipe in space. It is a relatively simple device constructed from a spectrophotometer cuvette and uses pentane as the working fluid. The pentane flows within the corners of the cuvette due to a curvature gradient in the liquid menisci associated with the cuvette corners. The curvature of the liquid interface can be determined by viewing the meniscus through the transparent quartz walls. Extremely accurate temperature and pressure measurements were obtained in addition to the images. In the article, the results from the first two CVB modules—a dry calibration module and a wet heat pipe module—are presented. We show that the axial temperature profiles are significantly different in space. The heat pipes were seen to operate at a higher pressure and higher temperature ...

The constrained vapor bubble experiment scheduled to fly aboard the International Space Station in the near future promises to give us new insight into the fundamental science of interfacial thermophysics. The evaporating meniscus formed at the corner of the vapor bubble is expected to behave in a significantly different manner in the microgravity environment as compared with the Earth's gravity environment. Since the constrained vapor bubble can also behave as a micro heat pipe, it will additionally help in gaining a technical understanding of the performance of a micro heat pipe in a space environment. Earth-based experiments have been conducted for the past two decades to gain a better knowledge of the rich phenomenon observed in the relatively simple constrained vapor bubble setup. Here, some recent Earth's-gravity-environment-based data obtained on a 30-mm-long constrained vapor bubble have been presented. The data were fitted to a model, and a self-consistent value of the inside heat transfer coefficient was obtained. The external convective and radiative heat transfer coefficients were also determined. These ground-based experiments form a calibration against which the future data from space-based experiments will be compared.

We compared the phase change behavior of a partially wetting fluid, nonane, on various SiO2 surfaces that had been modified to alter their roughness at the nanoscale. We compared a total of four surfaces: an as-received, smooth surface; a surface roughened by plasma-enhanced chemical vapor deposition (PECVD) of SiO2; and two surfaces where SiO2 nanorods had been deposited using glancing angle deposition (GLAD). Scanning electron microscopy (SEM) and atomic force microscopy (AFM) were used to characterize the surfaces. The topography of the rough surface controlled the wetting characteristics of the fluid that in turn, controlled the change-of-phase heat transfer rate. The measured apparent contact angle characterized the wetting property during the phase change process. Surface roughness promoted wetting in this system, but the direction of heat transfer controlled the topographic design required for enhanced performance. A comparison between two nanorod coatings of differing heights shows that the longer nanorod coating (30 nm high) acted somewhat like a porous surface promoting condensation heat transfer while the shorter nanorod coating (10 nm high) was much more effective at promoting evaporative heat transfer. Surface alteration at the scale over which intermolecular forces dominates the fluid-solid interaction provides a convenient means for probing those interactions.

Liquid-vapor phase-change processes are becoming increasingly important in a wide variety of fields ranging from energy conversion, to microelectronics cooling, MEMs devices, and self-assembly. The phase change in these systems is governed by processes that occur at the contact line, where three phases meet. Evidence suggests that alterations of the surface chemistry and surface topography on the nanoscale can be used to dramatically enhance the phase-change process. This article reviews the current state of the art in nanoscale surface modification as applied to the enhancement of evaporative processes.

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.

Boiling, a dynamic and multiscale process, has been studied for several decades; however, a comprehensive understanding of the process is still lacking. The bubble ebullition cycle, which occurs over millisecond time-span, makes it extremely challenging to study near-surface interfacial characteristics of a single bubble. Here, we create a steady-state vapor bubble that can remain stable for hours in a pool of sub-cooled water using a femtosecond laser source. The stability of the bubble allows us to measure the contact-angle and perform in-situ imaging of the contact-line region and the microlayer, on hydrophilic and hydrophobic surfaces and in both degassed and regular (with dissolved air) water. The early growth stage of vapor bubble in degassed water shows a completely wetted bubble base with the microlayer and the bubble does not depart from the surface due to reduced liquid pressure in the microlayer. Using experimental data and numerical simulations, we obtain permissible range of maximum heat transfer coefficient possible in nucleate boiling and the width of the evaporating layer in the contact-line region. This technique of creating and measuring fundamental characteristics of a stable vapor bubble will facilitate rational design of nanostructures for boiling enhancement and advance thermal management in electronics.

Image analyzing interferometry was used to study the spreading characteristics of an evaporating octane meniscus (purity: 99+%) on a quartz surface. The thickness, slope, and curvature profiles in the contact line region of the meniscus were obtained using a microscopic data analysis procedure. The results obtained for the octane were compared to that of pure pentane (purity: >99.8%) under similar operating conditions. Isothermal experimental conditions of the menisci were used for the in situ estimation of the retarded dispersion constant. The experimental results for the pure pentane demonstrate that the disjoining pressure (the intermolecular interactions) in the thin-film region controls the fluid flow. Also, an imbalance between the disjoining pressure in the thin-film region and the capillary pressure in the thicker meniscus region resulted in a creeping evaporating pentane meniscus, which spreads over the solid (quartz) surface. On the contrary, for less pure octane, the intermolecular interactions between octane and quartz had a significantly different contribution for fluid flow, and hence, the octane meniscus of lower purity did not creep over the quartz surface. As a result, we had a stationary, evaporating octane meniscus. Using the experimental data and a simple model for the velocity distribution, we evaluated the Marangoni shear in a portion of the stationary, evaporating octane meniscus. An extremely small change in the concentration due to distillation had a significant effect on fluid flow and microscale heat transfer. Also, it was found that nonidealities in small interfacial systems, i.e., the presence of impurities in the working fluid, can have a significant effect on the thickness of the adsorbed film, the heat flux, the spreading characteristics of an almost pure fluid, and, therefore, the assumptions in modeling.

The Constrained Vapor Bubble (CVB) experiment concerns a transparent, simple, "wickless" heat pipe operated in the microgravity environment of the International Space Station (ISS). In a microgravity environment, the relative effect of Marangoni flow is amplified because of highly reduced buoyancy driven flows as demonstrated herein. In this work, experimental results obtained using a transparent 30 mm long CVB module, 3 mm × 3 mm in square cross-section, with power inputs of up to 3.125 W are presented and discussed. Due to the extremely low Bond number and the dielectric materials of construction, the CVB system was ideally suited to determining if dry-out as a result of Marangoni forces might contribute to limiting heat pipe performance and exactly how that limitation occurs. Using a combination of visual observations and thermal measurements, we find a more complicated phenomenon in which opposing Marangoni and capillary forces lead to flooding of the device. A simple one-dimensional, thermal-fluid flow model describes the essence of the relative importance of the two stresses. Moreover, even though the heater end of the device is flooded and the liquid is highly superheated, boiling does not occur due to high evaporation rates.

The evaporative heat flux distribution in the leading edge region of a moving evaporating thin liquid film of pentane on quartz was obtained by analyzing the measured thickness profile for thicknesses, δ < 2 μm. The profiles in a constrained vapor bubble were obtained using image analyzing interferometry. Although the evaporating meniscus appeared to be benign (i.e., without additional observed motion beyond creeping), high heat fluxes were obtained. Significantly higher heat fluxes are possible. The interfacial slope, curvature, interfacial shear stress, and liquid pressure profiles were also obtained. Results obtained using a continuum model were consistent with those obtained using a control volume model. The measured pressure field profile of the isothermal extended meniscus agreed with the constant pressure field predicted by the augmented Young-Laplace model. For the non-isothermal case, measured thickness gradients lead to disjoining pressure and curvature gradients for fluid flow and evaporation. The experimental results demonstrate that disjoining pressure at the contact line controls fluid flow within an evaporating completely wetting thin curved film and is, therefore, a useful boundary condition. However, in small interfacial systems, non-idealities can have a dramatic effect.

Using image-analyzing interferometry, the thickness profile, in the range of δ0 (adsorbed thickness)

A Constrained Vapor Bubble Loop Thermosyphon, CVBLT, made of quartz was used to study the stability and oscillations of an evaporating curved wetting film of pentane in a corner. The film thickness profile was measured as a function of heat input, time, and axial position using image analyzing interferometry. The curvatures and apparent contact angles for the evaporating film under various operating conditions were obtained from the measured film thickness profiles. Instability (oscillation) of the liquid film was observed at relatively higher values of the heat input. The behavior of the curvature and the apparent contact angle of an oscillating film with changes in heat input was evaluated. Moving velocities of the oscillating film were calculated from the measured values of the liquid-wall wetted lengths and were found to be directly proportional to the difference between the instantaneous force acting on the curved film and the reference force. Using an augmented Young-Laplace pressure jump model, the effect of the excess free energy at the contact line on the oscillations was demonstrated.

A vertical constrained vapor bubble, VCVB, made of fused silica was used to study the stability and oscillations of an evaporating wetting film of HFE- 7000® in a corner. The film thickness profile was measured as a function of time and axial position using an advanced form of image analyzing interferometry. The curvature, apparent contact angle, and pressure profiles for the evaporating film were calculated from the measured film thickness profiles. Oscillation of the liquid film was observed and profiles for both the advancing and receding films were obtained. These are the first such detailed profiles obtained for an oscillating meniscus below a thickness of 0.1 μm. The film thickness profiles demonstrated the spreading of the meniscus during advance as well as the presence of a curvature gradient near the contact line region. The maximum curvature decreased for the advancing menisci and increased with time for the receding menisci. An increase in the adsorbed film thickness was associated with the advancing stage and a decrease with the receding stage. Pressure profiles were measured as a function of position indicating the potential for driving the flow of the fluid toward or away from the contact line. As the film advances or recedes, the pressure gradients change as a function of position fueling the next oscillation cycle.

Image-analyzing interferometry was used to investigate the dynamics of the dewetting meniscus of a partially wetting fluid on a modified quartz surface during dropwise condensation. The vivid difference in the behavior of the retracting meniscus with respect to its variation in apparent contact angle and curvature after the merger of the drop with the meniscus was found to depend on the wettability of the surface. On the hydroxylated quartz surface, the meniscus shed mass during retraction. The dewetting velocity decreased with time. On a slightly hydrophobic quartz surface, the meniscus showed a curvature gradient in the axial direction during drop merger and that gradient decreased as the meniscus moved towards the corner. The dewetting of the meniscus is discussed using the interfacial concepts of spreading and the Kelvin–Clapeyron phase change model.

Microgravity experiments on a constrained vapor bubble heat exchanger (CVB) are being developed for the space station. Results are presented of precursory experiments and modeling on microscale transport processes in the evaporator of the vertical constrained vapor bubble in the Earth's environment. A nonisothermal experimental setup was designed and built to study heat transfer and fluid flow in an ethanol/quartz vertical CVB system. Temperature profiles were measured using an in situ Labview® data acquisition system via thermocouples. Film thickness profiles were measured using image analyzing interferometry. A mathematical model was developed to yield the liquid film curvature profile in the evaporator. Experimentally measured curvature profiles were in good agreement with modeling results. A theoretical relation between the curvature and temperature profiles in the Earth's environment was developed. Under microgravity conditions, an analytical expression that reveals an inherent relation between temperature and liquid film curvature profiles was derived for the first time.

Image-analyzing interferometry is used to measure the apparent contact angle and the curvature of a drop and a meniscus during condensation and evaporation processes in a constrained vapor bubble (CVB) cell. The apparent contact angle is found to be a function of the interfacial mass flux. The interfacial velocity for the drop during condensation and evaporation is a function of the apparent contact angle and the rate of change of radius of curvature. The dependence of velocity on the apparent contact angle is consistent with Tanner's scaling equation. The results support the hypothesis that evaporation/condensation is an important factor in contact line motion. The main purpose of this article is to present the experimental technique and the data. The equilibrium contact angle for the drop is found experimentally to be higher than that for the corner meniscus. The contact angle is a function of the stress field in the fluid. The equilibrium contact angle is related to the thickness of the thin adsorbed film in the microscopic region and depends on the characteristics of the microscopic region. The excess interfacial free energy and temperature jump were used to calculate the equilibrium thickness of the thin adsorbed film in the microscopic region.

The near-equilibrium microscale transport processes in a system composed of a small condensing sessile drop subsequently removed by capillarity into a corner meniscus were studied. Experimental results on the following three stages for ethanol with a small contact angle on heat-treated fused quartz were analyzed: droplet nucleation, droplet growth and the transfer of the liquid from the drop to the corner meniscus. The dynamic character of the experiment allowed the heterogeneous condensation/removal cycle to be related to the chemical potential gradient, which is a function of the excess free energy (due to the liquid shape) and an excess temperature. The liquid thickness profile and contact angle were obtained using image analyzing interferometry in which the interference fringes were recorded using a video camera attached to a microscope. The capillary pressure, the polar and apolar components of the spreading coefficient, and the excess free energy were obtained from the equilibrium thickness profile data and the extended Young–Laplace equation. Using the derivative of the excess free energy per unit volume, flat film thicknesses in the film thickness range 0.6

The slow growth characteristics of a condensing ethanol sessile drop on a quartz substrate were studied experimentally. Using interference microscopy measurements of the transient liquid film profile (curvature) to obtain the pressure field and a Kelvin−Clapeyron model of interfacial mass flux to obtain the interfacial temperature difference, changes in the apparent contact angle were related to interfacial subcooling and, therefore, adsorption. We found that while the radius of curvature of the growing drop increased linearly with time, the apparent contact angle remained the same during slow growth at a constant condensation heat flux. The radii of curvature and the apparent contact angles at different axial locations were measured and compared. The results demonstrated that the curvature, the contact angle, the interfacial subcooling, the interfacial mass flux, the spreading velocity, and adsorption are coupled at the moving contact line. Motion and the apparent contact angle are governed by the conden...

Improved experimental and analytical techniques were developed to measure the liquid pressure field in a meniscus formed in the right angled corner of a Constrained Vapor Bubble (CVB) heat exchanger. Based on the definition of the curvature, an analytical expression for the curvature as a function of the film thickness profile and the apparent contact angle was obtained. The error associated with the resolution of the image processing system was defined and several imaging factors affecting the error are discussed. The error associated with the system resolution, Er, increases as the curvature increases; the apparent contact angle increases; the wavelength decreases; and the number of dark fringes used for the data fitting decreases. The accuracy of the data fitting can be used to also determine the region where the disjoining pressure and viscous stresses affect the results. Examples using pentane data are presented. The relatively large experimental cell size with regions of low capillary pressure was dictated by future use in microgravity. � 2002 Elsevier Science Ltd. All rights reserved.

The optimum use of interfacial free-energy gradients to control fluid flow in small regions naturally leads to simpler passive heat transfer systems. In this context, passive refers to the natural pressure field for fluid flow due to changes in the intermolecular force field resulting from an imposed nonisothermal temperature field. Although the particular constrained vapor bubble (CVB) discussed can be viewed as a large version of a wickless heat pipe, it is a much more general heat transfer concept. Herein, it is an ideal system for the optical study of microscale transport processes in droplet condensation due to interfacial phenomena. This article concerns the movement of a single condensed ethanol sessile drop into a concave liquid film. The intermolecular force is found to be much larger than the gravitational force and dominates condensate removal. A dimensionless force balance for viscous shear stress demonstrates the effect of changes in the contact angle and curvature. A dimensionless difference in free energy is identified as the cause of spontaneous condensate removal

The etching of various xerogel films has been studied in high-density fluorocarbon plasmas. The xerogel etch rate is in part enhanced by the porosity. In discharges resulting in low surface polymerization, such as CF4 or oxygen-rich fluorocarbon plasmas, an additional enhancement up to 60% is observed. When the polymerization of the discharge is increased, this additional enhancement disappears and the xerogel etch rate becomes more suppressed. The suppression is more pronounced for xerogel films with a higher porosity and a larger pore size. X-ray photoelectron spectroscopy analysis on partially etched samples shows that the suppression in etch rate is accompanied by an increasing amount of fluorocarbon material at the xerogel surface, especially in the pores of the xerogel structure. Finally, a 30% porous xerogel film was patterned using CHF3 as an etching gas. Slight bowing of the sidewalls was observed.

A Constrained Vapor Bubble (CVB) with a relatively large Bond number formed by partially underfilling liquid in an evacuated cavity is capable of high thermal conductance. Il operates on the principle of closed loop phase-change along with capillarity to circulate the working fluid. Analytical investigations were conducted to compare with existing experimental data. A steady-state fluid flow model combined with a two-dimensional heat transfer model was developed and solved to yield key operating parameters ( i.e., temperature and liquid meniscus curvature) of the CVB. The modeling results of the outside wall temperature in the evaporator were found to agree well with the measured experimental data. An area average heat transfer coefficient was used to characterize the heat transfer on the inside wall of the evaporator. The value of this heat transfer coefficient was found to increase with the heat flow rate. The fluid flow model with the heat transfer model in the evaporator to provide the energy balance ...

Spin-on xerogels, which are promising candidates for use as interlayer dielectric materials in future microelectronic devices, change from a Newtonian liquid to a solid gel during processing. Since the rheology of the sol may affect the uniformity of the xerogel films produced, here we relate the rheology of a two-step, acid-base catalyzed, sol-gel system to the thickness and porosity profiles across xerogel films of importance to the microelectronics industry. We also analyze the effect of spin speed on the thickness and porosity of the films. Our rheological studies of the xerogel sol demonstrated that the sol changes from Newtonian far from the gel point, to shear thinning close to the gel point. On films spin coated with shear-thinning sols there is a region of uniformity extending for a distance of about 5 mm from the center. The film thickness and porosity are highest in this region and both quantities decrease towards the edge. If the sol is spun in its Newtonian regime, the resulting films are uni...

The variation of long-range intermolecular forces near interfaces profoundly affects the performance of change-of-phase heat exchangers. Starting with the fundamental electromagnetic force between molecules (dielectric properties), the effects of shape (Kelvin effect), temperature (Clapeyron effect) and concentration on the heat-transfer characteristics of thin films and larger systems are reviewed and connected. A judicious selection of literature gives a consistent set of models of particular use in heat transfer. Examples of experimental verification of these interfacial models in this rapidly developing field are also presented.

Using an image analyzing interferometer, IAI, the interfacial characteristics of an isothermal constrained vapor bubble, CVB, in a quartz cuvette were studied as a precursor to heat transfer research. The effects of pH and electrolyte concentration on the meniscus properties (curvature and adsorbed film thickness) and the stability of the aqueous wetting films were evaluated. The surface potential in the electric double layer was a function of the cleaning and hydroxylation of the quartz surface. The disjoining pressure isotherm for pure water was very close to that predicted by the Langmuir equation. For aqueous solutions of moderate electrolyte concentration, the Gouy-Chapman theory provided a good representation of the electrostatic effects in the film. The effect of temperature on the film properties of aqueous solutions and pure water was also evaluated: The meniscus curvature decreased with increasing temperature, while Marangoni effects, intermolecular forces, and local evaporation and condensation enhanced waves on the adsorbed film layer. Pure water wetting films were mechanically metastable, breaking into droplets and very thin films (less than 10 nm) after a few hours. Aqueous wetting films with pH 12.4 proved to be stable during a test of several months, even when subjected to temperature and mechanical perturbations. The mechanical stability of wetting films can explain the reported differences between the critical heat fluxes of pure water and aqueous solutions. The IAI-CVB technique is a simple and versatile experimental technique for studying the characteristics of interfacial systems. Copyright 1999 Academic Press.

The generic nonisothermal constrained vapor bubble (CVB) is a miniature, closed heat transfer device capable of high thermal conductance that uses interfacial forces to recirculate the condensate on the solid surface constraining the vapor bubble. Herein, for the specific case of a large length-to-width ratio it is equivalent to a wickless heat pipe. Experiments were conducted at various heat loads on a pentane/quartz CVB to measure the fundamental governing parameter fields: temperature, pressure, and liquid film curvature. An “intermediate” section with a large effective axial thermal conductivity was identified wherein the temperature remains nearly constant. A one-dimensional steady-state model of this intermediate section was developed and solved numerically to yield pressure, velocity, and liquid film curvature profiles. The experimentally obtained curvature profiles agree very well with those predicted by the Young-Laplace model. The operating temperature of the CVB was found to be a function of the operating pressure and not a function of the heat load. Due to experimental design limitations, the fundamental operating limits of the CVB were not reached.

The equilibrium and nonequilibrium phenomena associated with a very thin liquid film formed between a vapor bubble and a container are discussed. Numerical examples of the effects of temperature and intermolecular forces on the film thickness and transport processes are presented. For relatively thick films, the sensitivity of experimental measurements to extremely small temperature gradients is found to be large. For extremely thin films, the sensitivity is small. Large superheats and heat fluxes are possible near the contact line. A small amount of adsorbed contamination has a large effect on the film profile. The constrained vapor bubble has both basic uses in the study of thermophysical properties and transport processes, and has applied uses as a heat exchanger.

A new adsorption model for the spreading dynamics of completely wetting fluids on a heated solid substrate that emphasizes interfacial phenomena is developed and evaluated. The model is based on the premise that both interfacial intermolecular forces and temperature affect the vapor pressure in change-of-phase heat transfer and (therefore) the spreading velocity. Classical change-of-phase kinetics, and interfacial concepts like the Clapeyron, Kelvin, and the augmented Young–Laplace equations are used to evaluate the effects of stress (change in apparent dynamic contact angle), temperature, and superheat on the rewetting velocity. Explicit equations are obtained for the velocity, heat flux, and superheat in the contact line region as a function of the initial plate temperature. Comparisons with experimental data for substrate superheats below a critical value demonstrate that the resulting interfacial model of evaporation/condensation in the contact line region can describe the effect of the saturation temperature and superheat on the rewetting velocity.

The microscopic details of fluid flow and heat transfer in the contact line region of an evaporating curved liquid film were experimentally and theoretically evaluated. The evaporating film thickness profiles were measured optically using null ellipsometry and image analyzing interferometry. These thickness profiles were analyzed using the augmented Young-Laplace equation to obtain the pressure field. Using the liquid pressure field, the evaporative mass flux profile was obtained from a Kelvin -Clapeyron model for the local vapor pressure. A correlation for the local slope (apparent contact angle) at a film thickness of 6 = 20 nm as a function of a dimensionless contact line heat sink was thereby obtained for a group of completely wetting fluids. This change in local slope leads to a decrease in the maximum value of the possible capillary suction at the base of the meniscus. A complementary macroscopic interfacial force balance was also used to describe the effects of viscous losses and interfacial forces on the local values of the apparent contact angle and curvature that are functions of the film thickness and heat flux. These two perspectives give a complete description of an evaporating, nonpolar, completely wetting curved film in the contact line region.

Isothermal profiles of the extended meniscus in a quartz cuvette were measured in the earth's gravitational field using an image-analyzing interferometer that is based on computer-enhanced video microscopy of the naturally occurring interference fringes. These profiles are a function of the stress field. Experimentally, the augmented Young-Laplace equation is an excellent model for the force field at the solid-liquid-vapor interfaces for heptane and pentane menisci on quartz and tetradecane on SFL6. The effects of refractive indices of the solid and liquid on the measurement techniques were demonstrated. Experimentally obtained values of the disjoining pressure and dispersion constants were compared to those predicted from the Dzyaloshinskii - Lifshitz - Pilaevskii theory for an ideal surface and reasonable agreements were obtained. A parameter introduced gives a quantitative measurement of the closeness of the system to equilibrium. The nonequilibrium behavior of this parameter is also presented