Prediction and Characterization of Dry-out Heat Flux in Micropillar Wick Structures

A heat transfer model for liquid film boiling on micro-structured surfaces

High heat transfer coefficient (HTC) and critical heat flux (CHF) are achieved in liquid film boiling by coupling vibrant vapor bubbles with a capillary liquid film, which has thus received increased interest for thermal management of high-power electronics. Although some experimental progress has been made, a high-fidelity heat transfer model for liquid film boiling is lacking. This work develops a thermal-hydrodynamic model by considering both evaporation atop the wick and nucleate boiling inside the wick to simultaneously predict the HTC and CHF. Nucleate boiling is modeled with microlayer evaporation theory, where a unified scaling factor is defined to characterize the change of microlayer area with heat flux. The scaling factor η is found to be independent of wicking structure and can be determined from a few measurements. This makes our model universal to predict the liquid film boiling heat transfer for various micro-structured surfaces including micropillar, micropowder, and micromesh. This work not only sheds light on understanding fundamental mechanisms of phase-change heat transfer, but also provides a tool for designing micro-structured surfaces in thermal management.

Analysis of Drying Front Propagation and Coupled Heat and Mass Transfer During Evaporation From Additively Manufactured Porous Structures Under a Solar Flux

Drying front propagation and coupled heat and mass transfer analysis from porous media is critical for soil-water dynamics, electronics cooling, and evaporative drying. In this study, de-ionized water was evaporated from three 3D printed porous structures (with 0.41 mm, 0.41 mm, and 0.16 mm effective radii, respectively) created out of acrylonitrile butadiene styrene (ABS) plastic using stereolithography technology. The structures were immersed in water until all the pores were invaded and then placed on the top of a sensitive scale to record evaporative mass loss. A 1000 W/m2 heat flux was applied with a solar simulator to the top of each structure to accelerate evaporation. The evaporative mass losses were recorded at 15 min time intervals and plotted against time to compare evaporation rates from the three structures. The evaporation phenomena were captured with a high-speed camera from the side of the structures to observe the drying front propagation during evaporation, and a high-resolution thermal camera was used to capture images to visualize the thermal gradients during evaporation. The 3D-structure with the smallest effective pore radius (i.e., 0.16 mm) experienced the sharpest decrease in the mass loss as the water evaporated from 0.8 g to 0.1 g within 180 min. The designed pore structures influenced hydraulic linkages, and therefore, evaporation processes. A coupled heat-and-mass-transfer model modeled constant rate evaporation, and the falling rate period was modeled through the normalized evaporation rate.

Grain Crystallinity, Anisotropy, and Boundaries Govern Microscale Hydrodynamic Transport in Semicrystalline Porous Media

Polycrystallinity is often an unintended consequence of real manufacturing processes used to produce designer porous media with deterministic and periodic architectures. Porous media are widely employed as high-surface conduits for fluid transport; unfortunately, even small concentrations of defects in the long-range order become the dominant impediment to hydrodynamic transport. In this study, we isolate the effects of these defects using a microfluidic analogy to energy transport in atomic polycrystals by directly tracking capillary transport through polycrystalline inverse opals. We reveal─using high-fidelity florescent microscopy─the boundary-limited nature of flow motions, along with nonlinear impedance elements introduced by the presence of "grain boundaries" that are separating the well-ordered "crystalline grains". Coupled crystallinity, anisotropy, and linear defect density contribute to direction-dominated flow characteristics in a discretized manner rather than traditional diffusive-like flow patterns. Separating individual crystal grains' transport properties from polycrystals along with new probabilistic data sets enables demonstrating statistical predictive models. These results provide fundamental insight into transport phenomena in (poly)crystalline porous media beyond the deterministic properties of an idealized unit cell and bridge the gap between engineering models and the ubiquitous imperfections found in manufactured porous materials.

Biomimetic Micropillar Wick for Enhanced Thin-Film Evaporation

Sustainable liquid cooling solutions are recognized as the future of thermal management in the chip industry. Among them, phase change heat transfer devices such as heat pipes and vapor chambers have shown tremendous potential. These devices rely on the physics of capillary-driven thin-film evaporation, which is inherently coupled with the design and optimization of the evaporator wicks used in these devices. Here, we introduce a biomimetic evaporator wick design inspired by the peristome of the Nepenthes alata that can achieve significantly enhanced evaporative cooling. It consists of an array of micropillars with multiple wedges along the sidewall of each micropillar. The efficacy of the wedged micropillar is evaluated based on a validated numerical model on the metrics of dryout heat flux and effective heat transfer coefficient. The wedge angle is chosen such that wedged micropillars cause liquid filaments to rise along the micropillar vertical walls. This results in a significant increase in thin-film area for evaporation. Additionally, the large mean curvature of the liquid meniscus produces strong capillary pumping pressure and simultaneously, the wedges increase the overall permeability of the wick. Consequently, our model predicts that the wedged micropillar wick can attain ∼234% enhancement of dryout heat flux compared to a conventional cylindrical micropillar wick of similar geometrical dimensions. Moreover, the wedged micropillars can also attain a higher effective heat transfer coefficient under dryout conditions, thus outperforming the cylindrical micropillar in terms of heat transfer efficiency. Our study provides insight into the design and capability of the biomimetic wedged micropillars as an efficient evaporator wick for various thin-film evaporation applications.

Electro-osmosis Aided Thin-Film Evaporation from a Micropillar Wick Structure

The heat-dissipating capacity of a surface having micropillar wick structures, which resembles the evaporator section of a vapor chamber, is mainly limited by the liquid flow rate through the porous structure (permeability) and the capillary pressure gradient. The efficacy of a regular vapor chamber is determined from two parameters, namely, the dry-out heat flux and temperature of the evaporator surface. These two parameters possess a counter relation to each other. The work described herein introduces and evaluates the performance of a novel idea of electro-osmosis-aided thin-film evaporation from a micropillar array structure. This study is conducted using a discretized approach that is validated against the thin-film evaporation model and additionally the electro-osmotic flow model with pre-existing pressure gradient conditions. The unique feature of this approach is that it results in an increment in the magnitude of dry-out heat flux without significantly changing the surface temperature, wherein the increase in permeability is due to the addition of electro-osmotic flow. This comprehensive model considers various geometries, zeta potentials, and extremal electric fields and establishes the beneficial effects of the application of an external electric field. The results are used to predict the sensitivity and the dependence of the dry-out heat flux and the evaporator surface temperature on these parameters. For a host of electro-osmotic parameters considered herein, a maximum increment of up to 320% in the dry-out heat flux is observed for an external electric field of 10⁵ V/m. The study, therefore, conclusively demonstrates the beneficial impact of electro-osmosis in enhancing the dry-out heat flux without any significant Joule heating.

Turning traditionally nonwetting surfaces wetting for even ultra-high surface energy liquids

Control over the interaction between liquids and surfaces is used in numerous thermofluidic systems, with behaviors ranging from highly repellent to highly wetting. In this work, we demonstrate that surface engineering enables highly wetting behavior from liquid/surface combinations that are typically nonwetting, broadening the design space for thermofluidic systems.

We present a surface-engineering approach that turns all liquids highly wetting, including ultra-high surface tension fluids such as mercury. Previously, highly wetting behavior was only possible for intrinsically wetting liquid/material combinations through surface roughening to enable the so-called Wenzel and hemiwicking states, in which liquid fills the surface structures and causes a droplet to exhibit a low contact angle when contacting the surface. Here, we show that roughness made of reentrant structures allows for a metastable hemiwicking state even for nonwetting liquids. Our surface energy model reveals that with liquid filled in the structure, the reentrant feature creates a local energy barrier, which prevents liquid depletion from surface structures regardless of the intrinsic wettability. We experimentally demonstrated this concept with microfabricated reentrant channels. Notably, we show an apparent contact angle as low as 35° for mercury on structured silicon surfaces with fluorinated coatings, on which the intrinsic contact angle of mercury is 143°, turning a highly nonwetting liquid/material combination highly wetting through surface engineering. Our work enables highly wetting behavior for previously inaccessible material/liquid combinations and thus expands the design space for various thermofluidic applications.

Multiobjective Optimization of Graded, Hybrid Micropillar Wicks for Capillary-Fed Evaporation

As electronic device power densities continue to increase, vapor chambers and heat pipes have emerged as effective thermal management solutions for hotspot mitigation. A crucial aspect of vapor chamber functionality depends on the properties of the microporous wick that drives heat and mass transport within the device. While many prior studies have focused on the optimization of these porous structures to increase the maximum capillary-limited dryout heat flux, an equally important aspect of porous wick design is the minimization of the thermal resistance above heated areas. Segmented wicks with geometries that vary along the length of the wick are attractive candidates that can potentially be used to fulfill these simultaneous design goals. Previous studies on bisegmented wicks with only two distinct adiabatic and heated region geometries, however, have shown mixed results regarding the degree of performance benefit over homogeneous wicks. In this work, we present a systematic modeling approach to investigate the optimal composition of segmented micropillar wicks comprising multiple, discrete regions of graded geometry. Using a genetic algorithm, we generate Pareto fronts of optimal segmented wick distributions that maximize the dryout heat flux and minimize the thermal resistance for a given heating configuration. We find that optimal, graded segmented wicks are capable of dissipating dryout heat fluxes more than 200% higher than baseline homogeneous wicks with significantly lower thermal resistance. The sensitivity of the wick performance to the total number of geometry segments is found to vary depending on the desired heat flux and thermal resistance operating regimes.

Spreading and Drying Dynamics of Water Drop on Hot Surface of Superwicking Ti-6Al-4V Alloy Material Fabricated by Femtosecond Laser

A superwicking Ti-6Al-4V alloy material with a hierarchical capillary surface structure was fabricated using femtosecond laser. The basic capillary surface structure is an array of micropillars/microholes. For enhancing its capillary action, the surface of the micropillars/microholes is additionally structured by regular fine microgrooves using a technique of laser-induced periodic surface structures (LIPSS), providing an extremely strong capillary action in a temperature range between 23 °C and 80 °C. Due to strong capillary action, a water drop quickly spreads in the wicking surface structure and forms a thin film over a large surface area, resulting in fast evaporation. The maximum water flow velocity after the acceleration stage is found to be 225–250 mm/s. In contrast to other metallic materials with surface capillarity produced by laser processing, the wicking performance of which quickly degrades with time, the wicking functionality of the material created here is long-lasting. Strong and long-lasting wicking properties make the created material suitable for a large variety of practical applications based on liquid-vapor phase change. Potential significant energy savings in air-conditioning and cooling data centers due to application of the material created here can contribute to mitigation of global warming.

Stable and Efficient Nanofilm Pure Evaporation on Nanopillar Surfaces

Molecular dynamics simulations were conducted to systematically investigate how to maintain and enhance nanofilm pure evaporation on nanopillar surfaces. First, the dynamics of the evaporation meniscus and the onset and evolution of nanobubbles on nanopillar surfaces were characterized. The meniscus can be pinned at the top surface of the nanopillars during evaporation for perfectly wetting fluid. The curvature of the meniscus close to nanopillars varies dramatically. Nanobubbles do not originate from the solid surface, where there is an ultrathin nonevaporation film due to strong solid-fluid interaction, but originate and evolve from the corner of nanopillars, where there is a quick increase in potential energy of the fluid. Second, according to a parametric study, the smaller pitch between nanopillars (P) and larger diameter of nanopillars (D) are found to enhance evaporation but also raise the possibility of boiling, whereas the smaller height of nanopillars (H) is found to enhance evaporation and suppress boiling. Finally, it is revealed that the nanofilm thickness should be maintained beyond a threshold, which is 20 Å in this work, to avoid the suppression effect of disjoining pressure on evaporation. Moreover, it is revealed that whether the evaporative heat transfer is enhanced on the nanopillar surface compared with the smooth surface is also affected by the nanofilm thickness. The value of nanofilm thickness should be determined by the competition between the suppression effect on evaporation due to the decrease in the volume of supplied fluid and the existence of capillary pressure and the enhancement effect on evaporation due to the increase in the heating area. Our work serves as the guidelines to achieve stable and efficient nanofilm pure evaporative heat transfer on nanopillar surfaces.

Formation and Stability of Thin Condensing Films on Structured Amphiphilic Surfaces

We present a microamphiphilic surface to promote the formation of a thin, stable liquid film during condensation. The surface consists of a hydrophilic micropillar array with hydrophobic pillar tips and was made using photolithography, deep reactive ion etching, and liftoff. The hydrophobic tips prevent the liquid film from growing thick, thereby keeping the thermal resistance low without the cyclical growth and shedding process of dropwise condensation. The wetting behavior was modeled analytically, and the parameters required for film formation were determined and verified with ESEM experiments. When a surface filled with condensate and lacked a low-pressure zone for the water to leave, a rupture event occurred, and a large Wenzel droplet emerged to flood the surface irreversibly. A number of strategies were found to combat rupture events. Tilting the surface vertically and dipping in a liquid pool gave the condensate a low-pressure region and prevented rupture. Irreversible flooding can also be avoided by ensuring that the emerged droplet was a nonwetting, highly mobile Cassie droplet. Parameters for Cassie-stable amphiphilic surfaces were determined analytically, but the high aspect ratios required prevented the manufacture of these surfaces for this study. Instead a hierarchical design was presented that demonstrated emerged Cassie droplets without challenging the manufacturing limits of the microfabrication procedure. This design avoided Wenzel droplet flooding without the need for a designated low-pressure zone. Additionally, sites for Cassie emergence could be engineered by removing a single pillar from the array at a designated location.

Local Meniscus Curvature During Steady-State Evaporation from Micropillar Arrays

Micropillar arrays are an ideal model system for capillary-aided thin film evaporation that can be fabricated with precise geometric control using microfabrication methods. The capillary limit leading to dryout is a critical performance metric for capillary-aided thin film evaporation and is proportional to the product of the permeability and capillary pressure. Capillary flow models for steady-state thin-film evaporation typically employ capillary pressure and permeability as separate parameters; however, it is difficult to separate the two from experimental hemiwicking characterizations or dryout observations. Furthermore, for micropillar arrays, local permeability depends on meniscus curvature varying spatially and with the evaporation rate. In this work, we use thin-film interference microscopy to profile local meniscus curvature during steady-state evaporation of water in a pure vapor environment. Local capillary pressure is calculated from curvature without requiring knowledge of contact angle or permeability. Results are compared against a Darcian semianalytical model for flow through micropillar wicks incorporating local permeability due to meniscus curvature. Although traditionally a slip boundary condition has been assumed at the liquid-vapor interface, we find much better agreement using a no-slip condition. The consequence of no-slip behavior is larger pressure gradients for a given evaporation flux and a lower dryout heat flux relative to a full slip condition. Heat transfer coefficient data are also presented and discussed in terms of curvature and sample geometry.

Unified Modeling Framework for Thin-Film Evaporation from Micropillar Arrays Capturing Local Interfacial Effects

Thin-film evaporation from micropillar array porous media has gained attention in a number of fields including energy conversion and thermal management of electronics. Performance in these applications is enhanced by leveraging the geometries of the micropillar arrays to both optimize flow through these arrays via capillary pumping and increase the curved liquid-vapor interface (meniscus) area for active phase-change heat transfer. In this work, we present a unified semianalytical modeling framework to predict the dry-out heat flux accurately for thin-film evaporation from micropillar arrays with the precise prediction of (i) the pressure profile along the wick achieved by discretizing the porous media domain and (ii) the local permeability that depends on the local meniscus shape. We validate the permeability model with 3D numerical simulations and verify the accuracy of the thin-film evaporation modeling framework with available experimental data from the literature. We emphasize the importance of predicting an accurate liquid-vapor interface shape for the prediction accuracy of both the permeability and the associated governing equations for liquid propagation and phase-change heat transfer through porous materials. This modeling framework is an accurate non-CFD-based methodology for predicting the dry-out heat flux during thin-film evaporation from micropillar arrays and will serve as a general framework for modeling steady liquid-vapor phase-change processes (evaporation and condensation) in porous media.

Fabrication of Micro-Patterned Surface for Pool-boiling Enhancement by Using Powder Injection Molding Process

In this study, two kinds of copper micro-patterned surfaces with different heights were fabricated by using a powder injection molding (PIM) process. The micro-pattern's size was 100 μm, and the gap size was 50 μm. The short micro-pattern's height was 100 μm, and the height of the tall one was 380 μm. A copper powder and wax-polymer-based binder system was used to fabricate the micro-patterned surfaces. The critical heat flux (CHF) and heat transfer coefficient (HTC) during pool-boiling tests were measured with the micro-patterned surfaces and a reference plain copper surface. The CHF of short and tall micro-patterned surfaces were 1434 and 1444 kW/m², respectively, and the plain copper surface's CHF was 1191 kW/m². The HTC of the plain copper surface and the PIM surface with short and tall micro-patterned surfaces were similar in value up to a heat flux 1000 kW/m². Beyond that value, the plain surface quickly reached its CHF, while the HTC of the short micro-patterned surface achieved higher values than that of the tall micro-patterned surface. At CHF, the maximum values of HTC for the short micro-pattern, tall micro-pattern, and the plain copper surface were 68, 58, and 57 kW/m² K.

Capillary-Enhanced Filmwise Condensation in Porous Media

Condensation is prevalent in various industrial and heat/mass transfer applications, and improving condensation heat transfer has a direct effect on process efficiency. Enhancing condensation performance has historically been achieved via the use of low surface energy coatings to promote the efficient dropwise mode over the typical filmwise mode of condensation. However, low surface tension fluids condense on these coatings in the filmwise mode, and low surface energy coatings are generally not robust at thicknesses required to enhance condensation heat transfer. We present a robust and scalable condensation enhancement method where a high heat transfer coefficient is achieved by leveraging capillary forces within a high thermal conductivity porous wick to promote condensate removal. The capillary pressure is supported by a pump to sustain steady condensate removal, and the high thermal conductivity of the wick decreases the overall thermal resistance. This technique has the potential to enhance condensation for a variety of fluids including low surface tension fluids and is capable of operating in both a gravity and a micro- (or zero-) gravity environment. We highlight key characteristics and enhancements achieved through this capillary-enhanced filmwise condensation technique using a porous media flow model. The model results indicate that increased wick thickness and permeability increase the operational envelope and delay the failure that occurs when the condensate floods the wick. However, increasing the permeability is more favorable as both the heat transfer coefficient and the flooding threshold are increased. The working fluid thermophysical properties determine both the degree of enhancement possible and the relative contributions from gravitational and capillary pressure forces when condensation occurs in the presence of gravity. This study provides fundamental insight into an enhanced filmwise condensation technique and an improved framework for modeling porous media flows with mass addition via condensation.

Heat Transfer Enhancement During Water and Hydrocarbon Condensation on Lubricant Infused Surfaces

Vapor condensation is routinely used as an effective means of transferring heat or separating fluids. Dropwise condensation, where discrete droplets form on the condenser surface, offers a potential improvement in heat transfer of up to an order of magnitude compared to filmwise condensation, where a liquid film covers the surface. Low surface tension fluid condensates such as hydrocarbons pose a unique challenge since typical hydrophobic condenser coatings used to promote dropwise condensation of water often do not repel fluids with lower surface tensions. Recent work has shown that lubricant infused surfaces (LIS) can promote droplet formation of hydrocarbons. In this work, we confirm the effectiveness of LIS in promoting dropwise condensation by providing experimental measurements of heat transfer performance during hydrocarbon condensation on a LIS, which enhances heat transfer by ≈450% compared to an uncoated surface. We also explored improvement through removal of noncondensable gases and highlighted a failure mechanism whereby shedding droplets depleted the lubricant over time. Enhanced condensation heat transfer for low surface tension fluids on LIS presents the opportunity for significant energy savings in natural gas processing as well as improvements in thermal management, heating and cooling, and power generation.

Water Wicking and Droplet Spreading on Randomly Structured Thin Nanoporous Layers

Growing thin, nanostructured layers on metallic surfaces is an attractive, new approach to create superhydrophilic coatings on heat exchangers that enhance spray cooling heat transfer. This paper presents results of an experimental study of enhanced droplet spreading on zinc oxide, nanostructured surfaces of this type that were thermally grown on copper substrates. The spreading rate data obtained from experimental high speed videos was used to develop a model specifically for this type of ultrathin, nanoporous layer. This investigation differs from previous related studies of droplet spreading on porous surfaces, which have generally considered either ordered, thin, moderately permeable layers, or thicker, microporous layers. Our layers are both very thin and have nanoscale porosity, making them low-permeability layers that exhibit strong wicking. An added benefit is that the thermally grown, stochastic nature of our surfaces make manufacturing easily scalable and particularly attractive for spray-cooled heat exchanger applications. The model presented here can predict the spreading rate for the wetted footprint of a deposited water droplet over two spreading stages: an early synchronous spreading stage, followed by hemispreading. The comparison of experimental data and model predictions confirms the presence of these two specific spreading stages. The model defines the transition conditions between synchronous and hemispreading regimes based on the change in spreading mechanisms, and we demonstrate that the model predictions of spreading rate are in good agreement with the experimental determinations of droplet footprint variation with time. The results indicate that the early synchronous spreading regime is characterized by flow in the porous layer that is primarily localized near the upper droplet contact line. The potential use of these experimental findings and model for optimizing superhydrophilic, nanostructured surface coatings is also discussed, as it pertains to the surface's ability to enhance water vaporization processes.

Coexistence of Pinning and Moving on a Contact Line

Textured surfaces are instrumental in water repellency or fluid wicking applications, where the pinning and depinning of the liquid-gas interface plays an important role. Previous work showed that a contact line can exhibit nonuniform behavior due to heterogeneities in surface chemistry or roughness. We demonstrate that such nonuniformities can be achieved even without varying the local energy barrier. Around a cylindrical pillar, an interface can reside in an intermediate state where segments of the contact line are pinned to the pillar top while the rest of the contact line moves along the sidewall. This partially pinned mode is due to the global nonaxisymmetric pattern of the surface features and exists for all textured surfaces, especially when superhydrophobic surfaces are about to be flooded or when capillary wicks are close to dryout.

Dynamics of Microscale Liquid Propagation in Micropillar Arrays

Understanding the dynamics of microscale liquid propagation in micropillar arrays can lead to significant enhancement in macroscopic propagation modeling. Such a phenomenon is fairly complicated, and a fundamental understanding is lacking. The aim here is to estimate three main parameters in liquid propagation, capillary pressure, average liquid height, and contact angle on the pillar side, through modeling and experimental validation. We show that the capillary pressure is not constant during liquid propagation, and the average capillary pressure is evaluated using its maximum and minimum values. The average liquid height influences the permeability of such a structure, which is challenging to determine as a result of the complicated three-dimensional (3D) meniscus shape. A simple physical model is provided in this paper to predict the average liquid height with less than 7% error. The contact angle on the micropillar side, which has considerable impact on the capillary pressure and the average liquid height, has been debated for a long time. We propose a model to predict this contact angle and validate it against experimental values in the literature. Our findings also indicate that the microscopic motion of the liquid front is significantly affected by the ratio of the pillar height to edge-to-edge spacing, and a correlation is provided for quantification. The proposed models are able to predict the droplet spreading dynamics and estimate spreading distance and time reasonably.

Detection of Liquid Penetration of a Micropillar Surface Using the Quartz Crystal Microbalance

A quantitative characterization of the wetting states of droplets on hydrophobic textured surfaces requires direct measurement of the liquid penetration into surface cavities, which is challenging. Here, the use of quartz crystal microbalance (QCM) technology is reported for the characterization of the liquid penetration depth on a micropillar-patterned surface. The actual liquid-air interface of the droplet was established by freezing the droplet and characterizing it using a cryogenically focused ion beam/scanning electron microscope (cryo FIB-SEM) technique. It was found that a direct correlation exists between the liquid penetration depth and the responses of the QCM. A very small frequency shift of the QCM (1.5%) was recorded when the droplet was in the Cassie state, whereas a significant frequency shift was observed when the wetting state changed to the Wenzel state (where full liquid penetration occurs). Furthermore, a transition from the Cassie to the Wenzel state can be captured by the QCM technique. An acoustic-structure-interaction based numerical model was developed to further understand the effect of penetration. The numerical model was validated by experimentally measured responses of micropillar-patterned QCMs. The results also show a nonlinear response of the QCM to the increasing liquid penetration depth. This research provides a solid foundation for utilizing QCM sensors for liquid penetration and surface wettability characterization.