Solomon Adera

Unified Model for Contact Angle Hysteresis on Heterogeneous and Superhydrophobic Surfaces

Understanding the complexities associated with contact line dynamics on chemically heterogeneous and superhydrophobic surfaces is important for a wide variety of engineering problems. Despite significant efforts to capture the behavior of a droplet on these surfaces over the past few decades, modeling of the complex dynamics at the three-phase contact line is needed. In this work, we demonstrate that contact line distortion on heterogeneous and superhydrophobic surfaces is the key aspect that needs to be accounted for in the dynamic droplet models. Contact line distortions were visualized and modeled using a thermodynamic approach to develop a unified model for contact angle hysteresis on chemically heterogeneous and superhydrophobic surfaces. On a surface comprised of discrete wetting defects on an interconnected less wetting area, the advancing contact angle was determined to be independent of the defects, while the relative fraction of the distorted contact line with respect to the baseline surface was shown to govern the receding contact angle. This behavior reversed when the relative wettability of the discrete defects and interconnected area was inverted. The developed model showed good agreement with the experimental advancing and receding contact angles, both at low and high solid fractions. The thermodynamic model was further extended to demonstrate its capability to capture droplet shape evolution during liquid addition and removal in our experiments and those in literature. This study offers new insight extending the fundamental understanding of solid-liquid interactions required for design of advanced functional coatings for microfluidics, biological, manufacturing, and heat transfer applications.

Non-wetting droplets on hot superhydrophilic surfaces

Controlling wettability by varying surface chemistry and roughness or by applying external stimuli is of interest for a wide range of applications including microfluidics, drag reduction, self-cleaning, water harvesting, anti-corrosion, anti-fogging, anti-icing and thermal management. It has been well known that droplets on textured hydrophilic, that is superhydrophilic, surfaces form thin films with near-zero contact angles. Here we report an unexpected behaviour where non-wetting droplets are formed by slightly heating superhydrophilic microstructured surfaces beyond the saturation temperature (>5 °C). Although such behaviour is generally not expected on superhydrophilic surfaces, an evaporation-induced pressure in the structured region prevents wetting. In particular, the increased thermal conductivity and decreased vapour permeability of the structured region allows this behaviour to be observed at such low temperatures. This phenomenon is distinct from the widely researched Leidenfrost and offers an expanded parametric space for fabricating surfaces with desired temperature-dependent wettability.

High-resolution liquid patterns via three-dimensional droplet shape control

Understanding liquid dynamics on surfaces can provide insight into natures design and enable fine manipulation capability in biological, manufacturing, microfluidic and thermal management applications. Of particular interest is the ability to control the shape of the droplet contact area on the surface, which is typically circular on a smooth homogeneous surface. Here, we show the ability to tailor various droplet contact area shapes ranging from squares, rectangles, hexagons, octagons, to dodecagons via the design of the structure or chemical heterogeneity on the surface. We simultaneously obtain the necessary physical insights to develop a universal model for the three-dimensional droplet shape by characterizing the droplet side and top profiles. Furthermore, arrays of droplets with controlled shapes and high spatial resolution can be achieved using this approach. This liquid-based patterning strategy promises low-cost fabrication of integrated circuits, conductive patterns and bio-microarrays for high-density information storage and miniaturized biochips and biosensors, among others.

Dynamic Evolution of the Evaporating Liquid–Vapor Interface in Micropillar Arrays

Capillary assisted passively pumped thermal management devices have gained importance due to their simple design and reduction in energy consumption. The performance of these devices is strongly dependent on the shape of the curved interface between the liquid and vapor phases. We developed a transient laser interferometry technique to investigate the evolution of the shape of the liquid-vapor interface in micropillar arrays during evaporation heat transfer. Controlled cylindrical micropillar arrays were fabricated on the front side of a silicon wafer, while thin-film heaters were deposited on the reverse side to emulate a heat source. The shape of the meniscus was determined using the fringe patterns resulting from interference of a monochromatic beam incident on the thin liquid layer. We studied the evolution of the shape of the meniscus on these surfaces under various operating conditions including varying the micropillar geometry and the applied heating power. By monitoring the transient behavior of the evaporating liquid-vapor interface, we accurately measured the absolute location and shape of the meniscus and calculated the contact angle and the maximum capillary pressure. We demonstrated that the receding contact angle which determines the capillary pumping limit is independent of the microstructure geometry and the rate of evaporation (i.e., the applied heating power). The results of this study provide fundamental insights into the dynamic behavior of the liquid-vapor interface in wick structures during phase-change heat transfer.

Experiment and modeling of microstructured capillary wicks for thermal management of electronics

Novel thermal management approaches are desired due to the ever-increasing power densities in high-performance microelectronics. The rising power density along with the shrinking real estate in these devices results in a substantial increase in device temperature beyond the typical operating temperatures required for a reliable performance. For the typical silicon based technology, efficient thermal management schemes with high heat transfer coefficients such that heat fluxes in excess of ≈ 100 W / cm2 can be dissipated without severely exceeding normal operating temperatures of ≈ 80°C are desired. State-of-the-art single phase cooling technologies that rely on sensible heat are bulky and insufficient under these conditions. As a result, liquid-vapor phase change based novel thermal management solutions which utilize latent heat of vaporization of a fluid for high heat transfer with little temperature increase are needed. In this work, we present a multiphase thermal management scheme where we use arrays of cylindrical micropillars of silicon for thin-film evaporation. The microstructures maintain a continuous liquid supply via capillary pressure while controlling the liquid film thickness and the associated thermal resistance. A variety of silicon samples with various wick geometries were fabricated using standard contact photolithography and deep reactive ion etching. Effects of micropillar diameter, pitch, height and the array length on the maximum heat dissipation capability before dry-out were investigated. An analytical model was developed to predict the experimentally observed values of the evaporative heat flux. While the parametric effects of micropillar geometry were qualitatively captured by the model predictions, quantitative predictions could not be achieved due to the limitations in the experimental setup. These preliminary results suggest the potential of thin-film evaporation on microstructured surfaces for advanced thermal management applications.

Capillary-Limited Evaporation From Well-Defined Microstructured Surfaces

Thermal management is increasingly becoming a bottleneck for a variety of high power density applications such as integrated circuits, solar cells, microprocessors, and energy conversion devices. The performance and reliability of these devices are usually limited by the rate at which heat can be removed from the device footprint, which averages well above 100 W/cm2 (locally this heat flux can exceed 1000 W/cm2). State-of-the-art air cooling strategies which utilize the sensible heat are insufficient at these large heat fluxes. As a result, novel thermal management solutions such as via thin-film evaporation that utilize the latent heat of vaporization of a fluid are needed. The high latent heat of vaporization associated with typical liquid-vapor phase change phenomena allows significant heat transfer with small temperature rise.In this work, we demonstrate a promising thermal management approach where square arrays of cylindrical micropillar arrays are used for thin-film evaporation. The microstructures control the liquid film thickness and the associated thermal resistance in addition to maintaining a continuous liquid supply via the capillary pumping mechanism. When the capillary-induced liquid supply mechanism cannot deliver sufficient liquid for phase change heat transfer, the critical heat flux is reached and dryout occurs. This capillary limitation on thin-film evaporation was experimentally investigated by fabricating well-defined silicon micropillar arrays using standard contact photolithography and deep reactive ion etching. A thin film resistive heater and thermal sensors were integrated on the back side of the test sample using e-beam evaporation and acetone lift-off. The experiments were carried out in a controlled environmental chamber maintained at the water saturation pressure of ≈3.5 kPa and ≈25 °C. We demonstrated significantly higher heat dissipation capability in excess of 100 W/cm2. These preliminary results suggest the potential of thin-film evaporation from microstructured surfaces for advanced thermal management applications.© 2013 ASME

Detailed thermal resistance model for characterization of the overall effective thermal conductivity of a flat heat pipe

The present work describes the method by which the thermal resistance of a flat heat pipe spreader can be more accurately computed. The total effectiveness of the heat spreader is dependent on the one-dimensional (R1D) thermal resistance and the thermal spreading resistance (Rs). Recently developed more accurate methods from the literature were used to calculate the spreading resistance by taking into account all the multiple layers of the heat pipe. Both R1D and Rs depend to a large extent on the effective thermal conductivity of the wick. The calculation of effective thermal conductivity of wick is demonstrated using well-defined silicon micropillars. The effect of interfacial heat transfer resistance, which is usually neglected on the wicks thermal resistance is also discussed. Finally, the effective thermal conductivity of a flat heat pipe as a function of vapor chamber size and effective wick thermal conductivity is calculated. As the overall device performance strongly depends on the estimation of wick thermal resistance, the results of this study show that an effective thermal conductivity that is equal to or better than diamond can be attained with proper design. Furthermore, this work provides design tools that can be used to optimize the overall device level thermal performance.

Hotspot thermal management via thin-film evaporation

The emerging three-dimensional vertical chip stacking architecture is expected to reduce form factor and improve performance by providing energy efficient chip design. However, increased power density and non-uniform heat generation in stacked dies offset its advantages and pose a significant thermal management challenge by creating hotspots where heat loads in excess of 1 kW/cm2 are generated from sub-millimeter areas. Furthermore, the localized heating in hotspots creates high junction temperature which can degrade the performance, reliability, and life time of electronic chips. Such ultra-high heat fluxes are challenging to remove using state-of-the-art single-phase cooling technology. Consequently, chip-level phase-change based hotspot thermal management is increasingly becoming pivotal for cooling next-generation of microelectronic devices and power amplifiers. This work experimentally characterizes capillary-limited thin-film evaporation from well-defined silicon micropillar wicks to demonstrate its potential as a thermal solution for ultra-high heat fluxes. We used contact photolithography and deep-reactive-ion-etching to create a 1×1 cm2 microstructured area. The microstructured area was surrounded by a water reservoir. Various sized thin-film heaters which were created using electron-beam evaporation and acetone lift-off were integrated on the backside of the test sample. Hotspots were emulated by locally heating a 640×620 μm2 area while background heating was emulated by heating the entire 1×1 cm2 microstructured area. The background and hotspot heaters were calibrated prior to experiment to measure temperature. All experiments were conducted in an environmental chamber which was maintained near saturated condition, i.e., saturation temperature and corresponding pressure. The working fluid, degassed de-ionized water, was transported from the surrounding water reservoir to the microstructured area passively via capillary-wicking. We dissipated ≈5.8 kW/cm2 from a 620×640 μm2 footprint when the hotspot temperature was ≈260 °C. Most importantly, when the surface dried out at ≈5.8 kW/cm2, the background temperature as well as the local temperatures 3 mm away from the hotspot were less than 50 °C. Increasing the heat flux beyond ≈5.8 kW/cm2 resulted in the formation of a dry island at the center of the hotspot which grew radially outwards. Dryout and thermal runaway occurred when viscous losses exceed the capillary pressure. Furthermore, the maximum dryout heat flux from a single hotspot decreased from ≈5.8 kW/cm2 to ≈2.9 kW/cm2 when the hotspot was assisted by a 20 W/cm2 background heating. Lastly, the dryout heat flux decreased from ≈5.8 kW/cm2 to ≈2.9 kW/cm2 per heater when three spatially distributed hotspots were created concurrently. Unlike the dryout heat flux, the total heating power increased by assisting hotspot with background heating as well as by creating spatially distributed concurrent hotspots over the microstructured area.

Experimental Characterization and Modeling of Capillary-Pumped Thin-Film Evaporation From Micropillar Wicks

Generation of concentrated heat load in confined spaces in integrated circuits and advanced microprocessors has presented a thermal management challenge for the semiconductor industry. Compared to state-of-the-art single phase cooling strategies, phase-change based approaches are promising for cooling the next generation microelectronic devices. In particular, thin-film evaporation from engineered surfaces has received significant attention in the last few decades as a potential candidate since it enables passive transport of the working fluid via capillarity in addition to increasing the evaporation area via extending the liquid meniscus and three-phase contact line. Thin-film evaporation, however, is coupled with nucleate boiling making experimental characterization as well as modeling of the fluidic and thermal transport a challenging task for thermal engineers. Furthermore, quantifying the relative contributions of nucleate boiling and thin-film evaporation from the experimentally reported heat fluxes has been difficult. Unlike previous studies, our work experimentally characterizes thin-film evaporation in the absence of nucleate boiling from arrays of silicon micropillars. In particular, we characterize the capillary-limit where the microstructured surface dries out due to liquid starvation when the capillary pressure that is generated due to the meniscus shape cannot overcome the viscous losses within the micropillar wick. We modeled the fluidic and thermal transport of the evaporating meniscus by solving the coupled heat and mass transfer equations. Compared to experiments, our model predicts the dryout heat flux with ±20% accuracy. The insights gained from this study provide a suitable platform to design and optimize micropillar wicks for phase-change based thermal management devices such as heat pipes and vapor chambers.

Thin-film evaporation from micropillar wicks in ambient environment

We characterize thin-film evaporation of water from well-defined silicon micropillar arrays under ambient conditions (≈24 °C and ≈100 kPa). We compare the dryout heat fluxes from these experiments with the corresponding heat fluxes for experiments conducted at saturated conditions for water (≈24 °C and ≈3 kPa). Dryout heat fluxes for the experiments at 100 kPa were higher (τ2×) when compared to the corresponding values at 3 kPa. The dryout heat fluxes were found to be in good agreement with a semi-analytical thermal-fluidic model which accounts for the favorable change in the figure of merit of water when the vapor pressure changes from ≈3 kPa to ≈100 kPa. The experimental results show that self-regulated capillary-fed fluidic transport is vital for delaying nucleate boiling and achieving higher heat fluxes.