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Prediction of hemiwicking dynamics in micropillar arrays
Physics of Fluids
Abstract
Dynamic hemiwicking behavior is observable in both nature and a wide range of industrial applications ranging from biomedical devices to thermal management. We present a semi-analytical modeling framework (without empirical fitting coefficients) to predict transient capillary-driven hemiwicking behavior of a liquid through a nano/microstructured surface, specifically a micropillar array. In our model framework, the liquid domain is discretized into micropillar unit cells to enable the time marching of the hemiwicking front. A simplified linear pressure drop is assumed along the hemiwicking length such that the local meniscus curvature, contact angle, and effective liquid height are determined at each time step in our transient model. This semi-analytical model is validated with experimental data from our own experiments and from published literature for different fluids. Our model predicts hemiwicking dynamics with <20% error over a broad range of micropillar geometries with height-to-pitch ratio ranging between ≈0.34 and 6.7 and diameter-to-pitch ratio in the range of ≈0.25–0.7 and without any fitting parameters. For lower diameter-to-pitch ratio data points related to sparse micropillar array arrangements, we suggest modifications to the semi-analytical model. This work sheds light on complex and dynamic solid–liquid–vapor interfacial interactions which could serve as a guide for the design of textured surfaces for wicking enhancement in multi-phase thermal and mass transport technologies and applications.
... The typical length scales of interest go from a few nm to a few cm. These phenomena play an important role in a broad spectrum of relevant scientific and technological applications, such as microfluidics [1][2][3][4][5][6] and open microfluidics [7][8][9][10]; functional surface design for self-cleaning, anti-fogging, printing, water and thermal management technologies, etc. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]; bio-inspired surfaces for atmospheric water extraction from condensation, superwetting, superhydrophobicity, etc. [27][28][29][30][31][32][33]; bio-microarray fabrication [34,35]; meniscus-guided coating for organic field-effect transistors [36]; biomolecular condensates [37]; generation of monodisperse microdroplets [38,39]; optofluidics [40]; micro-robotics [41]; aerospace applications such as propellant-management devices [42][43][44][45], fluid management in low-gravity environments [46][47][48], and brazing for repairs in space [49]; molten metal shape geometry for soldering in chip-manufacture applications such as surface-mount devices, solder bump technology, reflow soldering, etc. [50][51][52][53][54][55]; petroleum engineering [56] and enhanced oil recovery [57][58][59][60][61]; coal dust suppression [62][63][64][65][66]; fluid displacement and retention in porous media [67][68][69][70][71][72][73]; shape of capillary bridges for mechanical behavior of powders, restructuring soot aggregates, water retention in granular soil, etc. [74][75][76][77]; de-foaming for industrial processes [78]; foams [79][80][81]; particle-stabilized emulsions, bubbles and foams [82][83][84][85][86][87][88][89][90][91][92][93][94]; thin liquid films [95]; bijels [96,97]; colloidal gels [98]; food powder reconstitution [99]; froth flotation for mineral industry, micro-plastic removal from water, etc. [100][101][102][103][104]; synthesis of (anisotropic) colloidal particles [105][106][107][108][109][110][111][112][113][114][115] and formation 1 to time, then IE cannot predict how the FF interface's shape evolves in time (i.e. while this parameter varies). However, if this time-dependent parameter varies slowly, such that the fluid-fluid-solid system can be considered in quasi-equilibrium (i.e., fluid dynamics effects are negligible on the FF interface's current shape), then IE can be used to predict how the shape of the FF interface evolves in such a time-dependent fluid-fluid-solid system by executing multiple (separate) equilibrations, each to compute the FF interface's mesh equilibrium shape in the same fluid-fluidsolid system, except for the parameter of interest, that is tuned according to the experiments. ...
This paper introduces Interface Equilibrator (IE), a new graphical-user-interface software for simulating the equilibrium shape of fluid–fluid interfaces in a wide range of wetting and capillarity problems. IE provides an easy-to-use three-dimensional computer-aided-design environment to define the problem's geometry (i.e., the solid surfaces and the fluids' volumes), by simply loading opportune triangular meshes, and chemistry, by selecting the value of the relevant experimental parameters (e.g., Young's contact angle). No other input is required. Then, IE calculates the fluid–fluid interface's equilibrium shape using a novel numerical methodology, presented in this paper, that consists in an energy-minimization Monte Carlo simulation alongside other built-in automated methods to, e.g., refine the fluid–fluid interface mesh according to its local curvature and polish it. The energy-minimization algorithm is based on a numerical approach introduced a few years ago [Soligno et al., “The equilibrium shape of fluid-fluid interfaces: Derivation and a new numerical method for Young's and Young–Laplace equations,” J. Chem. Phys. 141, 244702 (2014)] that is generalized here to handle unconstructed meshes with any topology and to include also new types of forces (e.g., due to a rotating system or to a line tension). In addition, several illustrative and scientifically interesting novel results are presented in this paper to demonstrate IE's versatility and capability of addressing a broad spectrum of research problems, relevant for many technological applications, such as microfluidics, fluid management at various length scales, printing, colloids, soldering for chip manufacture, etc. Finally, the paper reports numerous validation tests, where known analytic or numerical solutions are compared with IE's results to verify the correctness and accuracy of IE's calculations.
Surfaces with micron-scale pillars have shown great potential in delaying the boiling crisis and enhancing the critical heat flux (CHF). However, the physical mechanisms enabling this enhancement remains unclear. This knowledge gap is due to a lack of diagnostics that allow elucidating how micro-pillars affect thermal transport phenomena on the engineered surface. In this study, for the first time, we are able to measure time-dependent temperature and heat flux distributions on a boiling surface with engineered micro pillars using infrared thermometry. Using these data, we reveal the presence of an intra-pillar liquid layer, created by the nucleation of bubbles, and partially refilled by capillary effects. However, contrarily to conventional wisdom, the energy removed by the evaporation of this liquid cannot explain the observed CHF enhancement. Yet, predicting its dry out is the key to delaying the boiling crisis. We achieve this goal using simple analytic models and demonstrate that this process is driven by conduction effects in the boiling substrates and, importantly, in the intra-pillar liquid layer itself. Importantly, these effects also control the wicking flow rate and its penetration length. The boiling crisis occurs when, by coalescing, the size of the intra-pillar liquid layer becomes too large for the wicking flow to reach its innermost region. Our study reveals and quantifies unidentified physical aspects, key to the performance optimization of boiling surfaces for cooling applications.
Hemiwicking is the phenomena where a liquid wets a textured surface beyond its intrinsic wetting length due to capillary action and imbibition. In this work, we derive a simple analytical model for hemiwicking in micropillar arrays. The model is based on the combined effects of capillary action dictated by interfacial and intermolecular pressures gradients within the curved liquid meniscus and fluid drag from the pillars at ultra-low Reynolds numbers (10−7≲Re≲10−3). Fluid drag is conceptualized via a critical Reynolds number: Re=v0x0ν, where v0 corresponds to the maximum wetting speed on a flat, dry surface and x0 is the extension length of the liquid meniscus that drives the bulk fluid toward the adsorbed thin-film region. The model is validated with wicking experiments on different hemiwicking surfaces in conjunction with v0 and x0 measurements using Water (v0≈2m/s,25µm≲x0≲28µm), viscous FC-70 (v0≈0.3m/s,18.6µm≲x0≲38.6µm) and lower viscosity Ethanol (v0≈1.2m/s,11.8µm≲x0≲33.3µm).
We investigated the role of surface microstructures in two-phase microchannels on suppressing flow instabilities and enhancing heat transfer. We designed and fabricated microchannels with well-defined silicon micropillar arrays on the bottom heated microchannel wall to promote capillary flow for thin film evaporation while facilitating nucleation only from the sidewalls. Our experimental results show significantly reduced temperature and pressure drop fluctuation especially at high heat fluxes. A critical heat flux (CHF) of 969 W/cm2 was achieved with a structured surface, a 57% enhancement compared to a smooth surface. We explain the experimental trends for the CHF enhancement with a liquid wicking model. The results suggest that capillary flow can be maximized to enhance heat transfer via optimizing the microstructure geometry for the development of high performance two-phase microchannel heat sinks.
Since Moore’s prediction in 1965, transistor count density on computer chips has grown exponentially and roadmaps for future industry growth still project exponential development for the next decade. With higher transistor densities, greater heat flux dissipation is required in order for performance to keep par with chip development. However, it is theorized that current cooling systems would not be able to cope with heat fluxes of future computer chips. Microchip heat management systems can be either active or passive. Active systems require an external driving component that increases the system’s complexity and ultimately power consumption. Heat pipes are passive fluidic systems, which are more robust and easier to implement than their active counterparts. Recirculation of the coolant in a heat pipe is done passively by means of a wicking structure that induces capillary flow from the condenser to the evaporator. However, there are many limiting factors associated with heat pipes based on the wick dimensions, fluid selection and orientation. At CPU chip operating temperatures the most significant limitation is the capillary limit. This limitation must be addressed in order to meet future computer chip heat dissipation requirements. In order to find an optimal geometry that would maximize the capillary flow, a theoretical model was developed using a rectangular pillar array. Surface tension forces induce a capillary flow that is opposed by viscous stresses from the pillars. Due to the regular and well-defined geometry of the pillar array, an ab initio approach can be used to model this flow, rather than resorting to Darcy’s flow and empirical permeability correlations. Predicted values of maximum flow rate were obtained from this theoretical model. This model and its results are directly applicable to carbon nanotube (CNT) and nanowire (NW) based wick structures. To validate the merit of nanostructure wicks for use in heat pipes, experimental data was collected to show the capillary limits of various nanowicks. The capillary limit of a wick was associated with the heat flux at which the wick cannot sustain the fluid flow necessary for heat removal and burnout occurs. When a baseline wick was experimentally compared to a nanowick, it was found that due to the difference in thickness of the wicks, the baseline wick provided higher flow rates. However, when the data were normalized to produce velocity values, the nanowick was found to have a higher velocity than the baseline wicks.
This paper presents the fabrication and application of a micro-scale hybrid wicking structure in a flat polymer-based heat pipe heat spreader, which improves the heat transfer performance under high adverse acceleration. The hybrid wicking structure which enhances evaporation and condensation heat transfer under adverse acceleration consists of 100 µm high, 200 µm wide square electroplated copper micro-pillars with 31 µm wide grooves for liquid flow and a woven copper mesh with 51 µm diameter wires and 76 µm spacing. The interior vapor chamber of the heat pipe heat spreader was 30×30×1.0 mm³. The casing of the heat spreader is a 100 µm thick liquid crystal polymer which contains a two-dimensional array of copper-filled vias to reduce the overall thermal resistance. The device performance was assessed under 0–10 g acceleration with 20, 30 and 40 W power input on an evaporator area of 8×8 mm². The effective thermal conductivity of the device was determined to range from 1653 W (m K)⁻¹ at 0 g to 541 W (m K)⁻¹ at 10 g using finite element analysis in conjunction with a copper reference sample. In all cases, the effective thermal conductivity remained higher than that of the copper reference sample. This work illustrates the possibility of fabricating flexible, polymer-based heat pipe heat spreaders compatible with standardized printed circuit board technologies that are capable of efficiently extracting heat at relatively high dynamic acceleration levels.
We describe how a wetting liquid brought into contact with a forest of micropillars impregnates this forest. Both the driving and the viscous forces depend on the parameters of the texture (radius b and height h of the pillars, pitch p of the network) and it is found that two different limits characterize the dynamics of wicking. For small posts (h<p), the film progresses all the faster since the posts are high, allowing a simple control of this dynamics. For tall pillars (h>p), the speed of impregnation becomes independent of the pillar height, and becomes mainly fixed by the radius of the posts.
We report the fabrication of dense arrays of super-hydrophilic Cu microposts at solid fractions as high as 58% and aspect ratios as high as four using electrochemical deposition and chemical oxidation techniques. Oxygen surface plasma treatments of photoresist molds and a precise control of the initial electrodeposition current are found to be critical in creating arrays of nearly defect-free Cu posts. The capillary performance of the micropost arrays is characterized using capillary rate of rise experiments and numerical simulations that account for the finite curvatures of liquid menisci. For the given wick morphology, the capillary performance generally decreases with increasing solid fraction and is enhanced by almost an order of magnitude when thin nanostructured copper oxide layers are formed on the post surface. The present work provides a useful starting point to achieve optimal balance between the capillary performance and the effective thermal conductivity of advanced wicks for micro heat pipes.
A scaling model is presented for low Reynolds number viscous flow within an array of microfabricated posts. Such posts are widely used in several lab-on-a-chip applications such as heat pipes, antibody arrays and biomolecule separation columns. Finite element simulations are used to develop a predictive model for pressure driven viscous flow through posts. The results indicate that the flow rate per unit width scales as approximately h1.17g1.33/d0.5 where h is the post height, d post diameter and g is the spacing between the posts. These results compare favorably to theoretical limits. The scaling is extended to capillary pressure driven viscous flows. This unified model is the first report of a scaling that incorporates both viscous and capillary forces in the microfabricated post geometry. The model is consistent with Washburn dynamics and was experimentally validated to within 8% using wetting on microfabricated silicon posts.
Using high-intensity femtosecond laser pulses, we create a novel surface pattern that transforms regular silicon to superwicking. Due to the created surface structure, water sprints vertically uphill in a gravity defying way. Our study of the liquid motion shows that the fast self-propelling motion of water is due to a supercapillary effect from the surface structures we created. The wicking dynamics in the produced surface structure is found to follow the classical square root of time dependence.
Roughness on hydrophilic surfaces allows for fast propagation of liquids. In this paper, the hypothesis is tested which theorizes that pillar array structures with nonuniform pillar height levels can enhance wicking rates. In this work, within a unit cell, nonuniform micropillars were arranged with one pillar at constant height, while other shorter pillars were varied in height to study these nonuniform effects. Subsequently, a new microfabrication technique was developed to fabricate a nonuniform pillar array surface. Capillary rising-rate experiments were conducted with water, decane, and ethylene glycol as working liquids to determine the behavior of propagation coefficients that were dependent on pillar morphology. It is found that a nonuniform pillar height structure leads to a separation of layers in the liquid spreading process and the propagation coefficient increases with declining micropillar height for all liquids tested. This indicated a significant enhancement of wicking rates compared to uniform pillar arrays. A theoretical model was subsequently developed to explain and predict the enhancement effect by considering capillary force and viscous resistance of nonuniform pillar structures. The insights and implications from this model thus advance our understanding of the physics of the wicking process and can inform the design of pillar structures with an enhanced wicking propagation coefficient.
In this study, an experimental investigation was conducted on the rising height and contact angle of fluid in an annular wick-type heat pipe. The annular wick-type heat pipe was characterized by a small gap between the wick structure and tube wall, which compensated for the pressure drop along with the porous media and created additional capillary force. To describe and model the advantage of this gap, the rising of a wetting liquid in the gap between a vertical solid plate and a mesh (with a small angle between them) was experimentally measured and analyzed. An additional experiment was performed to investigate the effect of curvature on the capillary rise using tubes and meshes of varying radii. Resultantly, we confirmed that the linear combination of the contact angles of the solid plate and mesh could be applied to calculate the rising height from the Laplace-Young equation. Furthermore, the effect of curvature on the rising height of the liquid was negligible. These results were extended to the investigation of finding the optimal gap distance for the annular wick-type heat pipe by referring to previous studies. We observed that a gap distance of 1.27 mm provided the largest permeability over the effective pore radius value for a heat pipe with ethanol, which in turn resulted in the highest capillary limitation. For a sodium heat pipe, a gap distance of 0.84 mm resulted in the highest capillary limitation.
Boiling heat transfer is dictated by interfacial phenomena at the three-phase contact line where vapor bubbles form on the surface. Structured surfaces have shown significant enhancement in critical heat flux (CHF) during pool boiling by tailoring interfacial phenomena. This CHF enhancement has been primarily explained by two structural effects: roughness, which extends the contact line length at the bubble base, and wickability, the ability to imbibe liquid through surface structures by capillary pumping. In this work, we show that CHF enhancement on structured surfaces cannot be described by roughness or wickability alone. This result was confirmed using systematically designed micropillar surfaces with controlled roughness and wickability. Further, we performed a scaling analysis and derived a unified descriptor, which represents the combined effects of thin film density and volumetric wicking rate. This unified descriptor shows a reasonable correlation with CHF values with our experiments and literature data. This work provides important insights in understanding the role of surface structures on CHF enhancement, thereby providing guidelines for the systematic design of surface structures for enhanced pool boiling heat transfer.
The ability to predict liquid transport rates on textured surfaces is key to the design and optimization of devices and processes such as oil recovery, coatings, reaction-separation, high-throughput screening, and thermal management. In this work we develop a fully analytical model to predict the propagation coefficients for liquids hemiwicking through micropillar arrays. This is carried out by balancing the capillary driving force and a viscous resistive force and solving the Navier-Stokes equation for representative channels. The model is validated against a large data set of experimental hemiwicking coefficients harvested from the literature and measured in-house using high-speed imaging. The theoretical predictions show excellent agreement with the measured values and improved accuracy compared to previously proposed models. Furthermore, using lattice Boltzmann (LB) simulations, we demonstrate that the present model is applicable over a broad range of geometries. The scaling of velocity with texture geometry, implicit in our model, is compared against experimental data, where good agreement is observed for most practical systems. The analytical expression presented here offers a tool for developing design guidelines for surface chemistry and microstructure selection for liquid propagation on textured surfaces.
To enable rapid development of flexible microelectronic systems, effective thermal management is needed. Flexible Polydimethylsiloxane (PDMS)-based microchannel flow boiling may provide a desirable solution. However, the heat transfer performance of PDMS-based microchannels is diminished by its poor thermophysical properties. The development of PDMS wick is proposed to address this dilemma. Herein, a new PDMS wick structure is designed and integrated in the microfluidic device to significantly enhance its thermal performance by promoting capillary-driven flow. Furthermore, to achieve highly efficient vapor removal, a dedicated vapor pathway is designed in the microfluidic device. Experiments have been conducted to investigate the capillary-assisted evaporation/boiling for mass flux ranging from 70 kg/m2s to 245 kg/m2s on dielectric fluid HFE-7100. The capillary-assisted sustainable and stable thin film evaporation and efficient vapor removal have been demonstrated through the visualization studies. With this new wick design, the liquid rewetting at global and local levels is facilitated through the capillary-driven flow and the efficient vapor removal. This hybrid liquid rewetting mechanism is experimentally demonstrated to significantly enhance the capillary-assisted evaporation/boiling in PDMS-based microchannel. A critical heat flux (CHF) of 14.7 W/cm2 is achieved at a mass flux of 245 kg/m2s. The heat transfer coefficients (HTC) range from 2,000 W/m2K to 9,800 W/m2K. These values are comparable to that in copper/silicon microchannels, with the aforementioned benefits of flexibility. Equally importantly, stable two-phase transport is achieved as well.
Surface tension forces enable a liquid to rise against gravity when wettable tubes or porous media are in contact with the pool of liquid. While the rise dynamics in the media of homogeneous porosity are well known, those in heterogeneous porous media still remain poorly understood. Here, we employ a vertical channel formed by two parallel plates decorated with micropillars, as a simple model of bidisperse porous media, and observe the rise dynamics of various viscous liquids. We find the bulk rise speed to be higher than that in dry smooth channels but equal to that between prewetted smooth channels. As the bulk approaches its equilibrium height, a film emerges ahead of the bulk meniscus, which is driven by the high surface energy of the microdecorated surface. The film extension grows initially like t but later like t1/2, with t being time. We construct theoretical models to predict the critical height where the film emerges and to rationalize the power laws of the film extension. In particular, we show that the dominant viscous resistance to the film extension is provided by the flow from the reservoir through the bulk in the early stages and by the film itself in the late stages. Our study opens a pathway to scrutinize the complicated flow dynamics arising within and across voids of heterogeneous porous media with an easily observable experimental setup of a well-defined geometry.
The control of liquid transport using hierarchical micro-nanostructured surfaces is of significant interest for a broad range of applications, including thermal management, digital lab-on-chip, self-cleaning surfaces, anti-fogging, and water harvesting, among others. Although a variety of fabrication techniques can be utilized to produce micro/nanostructured patterns for controlling liquid transport, each sample usually needs to be patterned and developed separately, making the micro/nanofabrication process tedious and expensive. Here, based on scalable template stripping and chemical oxidation techniques, we demonstrate hierarchical micro-nanostructured surfaces for isotropic or anisotropic liquid transport. Furthermore, the overall structure is thin and flexible, making it ideal for applications where geometry and weight are constrained, such as aerospace, flexible, and wearable devices.
Thin-film evaporation from micropillar array porous media has gained interest 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 semi-analytical modeling framework to predict the dry-out heat flux accurately for thin-film evaporation from micropillar arrays with 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 literature. We emphasize the importance of predicting an accurate liquid-vapor interface shape on the prediction accuracy for 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.
Inkjet printing of functional inks on textiles to embed passive electronics devices and sensors is a novel approach in the space of wearable electronic-textiles (E-textiles). However, achieving functionality such as conductivity by inkjet printing on textiles is challenged by the porosity and surface roughness of textiles. Nanoparticle based conductive inks frequently cause the blockage/clogging of inkjet printer nozzles making it a less than ideal method for applying these functional materials. It is also very challenging to create a conformal conductive coating and achieve electrically conductive percolation with the inkjet printing of metal nanoparticle inks on rough and porous textile and paper substrates. Herein, a novel reliable and conformal inkjet printing process is demonstrated for printing particle-free reactive silver ink on uncoated polyester textile knit, woven and nonwoven fabrics. The particle-free functional ink can conformally coat individual fibers to create a conductive network within textile structure without changing the feel, texture, durability and mechanical behavior of the textile. It was found that the conductivity and the resolution of the inkjet-printed tracks are directly related with the packing and the tightness of fabric structures and fiber sizes of the fabrics. It is noteworthy that the electrical conductivity of the inkjet-printed conductive coating on pristine PET fibers is improved by an order of magnitude by in-situ heat curing of the textiles surface during printing as the in-situ heat curing process minimizes the wicking of the ink into the textile structures. A minimum sheet resistance of 0.2 ± 0.025 Ω/□ and 0.9 ± 0.02 Ω/□ on polyester woven and polyester knit fabric is achieved, respectively. These findings aim to advance E-textile product design through integration of inkjet printing as a low-cost, scalable and automated manufacturing process.
Heat pipes and vapor chambers act as efficient heat spreaders since they rely on phase change of the coolant. The evaporator design is critical and typically high performance is characterized by the high heat dissipation capability with low thermal resistance. In the past, there have been numerous experimental and modeling studies focused on the design of evaporator wicks of different geometries, but systematic studies to simultaneously optimize both the heat flux and thermal resistance have been limited. In this work, we developed a comprehensive model that considers both aspects to provide design guidelines for evaporator micropillar wicks. We show that capillary limited heat dissipation is best captured with a recently developed numerical model as compared to previous analytical models. We also developed a numerical model to obtain the effective wick thermal conductivity, which is a function of pillar diameter, pitch, and height. Smaller diameters with smaller pitches of the pillars had more thin film area and had larger effective wick thermal conductivities. Our parametric investigations show that trade-offs between lowest thermal resistance and maximum heat carrying load exists, and the actual wick geometry will be dictated by application specific requirements. Finally, we highlight the importance of accurately obtaining the accommodation coefficients to predict the effective wick thermal conductivity. The present work would enable in optimal design of micropillar wicks (with low thermal resistance and high dry-out heat flux) and the same methodology can be extended to other types of wick structures as well.
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.
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 non-uniform behavior due to heterogeneities in surface chemistry or roughness. Here, we demonstrate that such non-uniformities 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 non-axisymmetric 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.
Hemiwicking refers to the spreading of a liquid on a rough hydrophilic surface driven by capillarity. Here, we construct scaling laws to predict the velocity of hemiwicking on a rough substrate and experimentally corroborate them with various arrangements and dimensions of micropillar arrays. At the macroscopic scale, where the wetting front appears parallel to the free surface of the reservoir, the wicking distance is shown to grow diffusively, i.e. like
with
t
being time. We show that our model is consistent with pillar arrays of a wide range of pitch-to-height ratios, either square or skewed. At the microscopic scale, where the meniscus extension from individual pillars at the wetting front is considered, the extension distance begins to grow like
t
but the spreading slows down to behave like
when the meniscus is far from the pillar. Our microscopic flow modelling allows us to find pillar spacing conditions under which the assumption of densely spaced pillars is valid.
The mass transport capacity, i.e., the capillary limit, of homogeneous wicks is limited by the inverse relation between the capillary pressure and permeability. Hybrid wicks with two or more distinct pore sizes have been proposed as alternative geometries to enhance the capillary limit. In this study, the impact of the two hybridization schemes - in-plane and out-of-plane schemes - on the capillary transport of hybrid wicks is studied. Experimental data from in-plane hybrid wicks in conjunction with a theoretical model show that local changes in the curvature of the liquid-vapor meniscus (i.e., pore size) do not result in a higher mass flow rate than that of a comparable homogeneous wick. Instead, a global change in the curvature of the liquid-vapor meniscus (as occurring in out-of-plane hybrid wicks) is necessary for obtaining mass flow rates greater than that of a homogeneous wick. Therefore, the physics of capillary limit and dryout in out-of-plane hybrid wicks are investigated using a hybrid wick consisting of a 1-µm-thick highly porous mesh suspended over a homogeneous array of micropillars. A study of the dryout process within the structure revealed that the presence of the mesh strongly alters the dryout mechanism. Visualization studies showed that out-of-plane hybrid wicks remain operational only as long as the liquid is constrained within the mesh pores; recession of the meniscus just below the mesh results in instantaneous local dryout. To maintain liquid within the mesh structure, the mesh thickness was increased and it was determined that the mesh thickness plays the key role in performance of an out-of-plane hybrid wick.
Wicking, the absorption of liquid into narrow spaces without the assistance of external forces, has drawn much attention due to its potential applications in many engineering fields. Increase surface roughness using micro/nanostructures can improve capillary action to enhance wicking. However, reducing the structure length scale can also result in significant viscous forces to impede wicking. In this work, we demonstrated enhanced wicking dynamics by using nanostructures with three-dimensional (3D) hierarchical features to increase surface area while limiting the obstruction of liquid flow. The proposed structures is engineered using a combination of interference lithography and chemical synthesis of ZnO nanowires, where structures at two length scales are independently designed to control wicking behavior. The fabricated hierarchical 3D structures are tested for water and ethanol wicking properties, demonstrating improved wicking dynamics with intermediate nanowire lengths. The experimental data agrees with the derived fluid model based on the balance of capillary and vicious forces. The hierarchical wicking structures can find applications in water harvesting surfaces, microfluidics, and integrated heat exchangers.
The generation of concentrated heat loads in advanced microprocessors, GaN electronics, and solar cells present significant thermal management challenges in defense, space and commercial applications. Liquid to vapor phase-change strategies are promising due to the high latent heat of vaporization of the working fluid. In particular, thin-film evaporation has received increased interest owing to advances in micro/nanofabrication and the potential to dissipate high heat fluxes by increasing the evaporative meniscus area. Yet, predictive tools to design various wicking structures are limited due to the complexity of the thermal–fluidic transport. In this work, we performed systematic experiments to characterize capillary-limited thin-film evaporation from silicon micropillar wicks in the absence of nucleate boiling. The insights gained from experiments were used to model the capillary pressure, permeability, and thermal resistance. Accordingly, we developed a semi-analytical model to determine the capillary-limited dryout heat flux and wall temperature with ±20% accuracy, compared to our experiments. The model provides a versatile platform to design and optimize micropillar wicks for next generation thermal management devices.
We captured interesting static and dynamic behavior of the liquid-vapor interface in well-defined silicon micropillar arrays during thermally driven evaporation of water from the microstructured surface. The 3-D shape of the meniscus was characterized via laser interferometry where bright and dark fringes result from the interference of incident and reflected monochromatic light due to a variable thickness thin liquid film (FIG. 1). During steady state evaporation experiments, water was supplied to the sample with a syringe pump at 10 μL/min. FIG. 2a and 2b show a SEM image of a typical fabricated micropillar array and a schematic of the experimental setup, respectively.
When water wicks through the micropillar array, the meniscus in a unit cell (four pillars in FIG. 1) assumes an equilibrium shape depending on the location from the liquid source/reservoir and the ambient conditions (ambient evaporation at Qin = 0 W). At this point, the meniscus is pinned at the top of the pillars. As the evaporation rate increases due the applied heat flux, the meniscus increases in curvature, thus increasing the capillary pressure to sustain the higher evaporation rate. This is evidenced by the increasing number of fringes in the unit cell when Qin is increased (0 W, 0.11 W, 0.44 W, and 0.99 W, FIG. 1a-1d respectively). Beyond a maximum curvature, the meniscus de-pins from the pillar top surface and recedes within the unit cell. This occurs when the capillary pressure generated at this curvature, cannot balance the viscous loss resulting from flow through the micropillar array. We observed that this receding shape was independent of the applied heat, and only depended on the micropillar array geometry and the intrinsic wettability of the material. Representative meniscus profiles along the diagonal direction of the unit cell obtained from image analysis of FIG. 1 at various Qin are shown in FIG. 2c.
This article, the second of a two-part study, is aimed at finding optimal micropillar wick geometries and their theoretical performance limits. For the first time, the theoretical optimization results are experimentally verified. The permeability and capillary pressure models determined in the first part of this study are utilized in the optimization process. First, the existence of optimality is ascertained through constrained parametric sweeps of the individual variables in the wick performance model, which reveal the presence of optimal values of each variable for a specific combination of the other variables. Then, the overall optimization of wicks is accomplished through a genetic algorithm. It is established that a unique optimal geometry, i.e. a combination of diameter, spacing and height, exists at each wicking length. Finally, these results are used to determine the theoretical performance limits of micropillar array wicks. The results suggest that the theoretical performance limit is 3-4 times greater than the highest performance reported in the literature.
The fundamentals of wetting and wicking are reviewed. Wetting is the displacement of a fiber-air interface with a fiber-liquid interface. Wicking is the spontaneous flow of a liquid in a porous substrate, driven by capillary forces. Because capillary forces are caused by wetting, wicking is a result of spontaneous wetting in a capillary system. Fiber wettability is therefore a prerequisite for the occurrence of wicking. The inter action of liquids with textile fabrics may involve one or several physical phenomena. On basis of the relative amount of liquid involved and the mode of the liquid-fabric contact, the wicking processes can be divided into two groups: wicking from an infinite liquid reservoir (immersion, transplanar wicking, and longitudinal wicking), and wicking from a finite (limited) liquid reservoir (a single drop wicking into a fabric). According to fiber-liquid interactions, each of the four wicking processes can be divided into four categories: capillary penetration only, simultaneous capillary penetration and imbibition by the fibers (diffusion of the liquid into the interior of the fibers), capillary penetration and adsorption of a surfactant on fibers, and simultaneous cap illary penetration, imbibition by the fibers, and adsorption of a surfactant on fibers. When designing tests to simulate liquid-textile interactions of a practical process, it is essential to understand the primary processes involved and their kinetics.
The tribological phenomena of adhesion, friction, and wear arise when solid objects make contact. As the size of devices shrinks to micro- and nanoscales, the surface-to-volume ratio increases and the effects of body forces (gravity and inertia) become insignificant compared with those of surface forces (van der Waals, capillary, electrostatic, and chemical bonding). In microelectromechanical systems (MEMS), tribological and static interfacial forces are comparable with forces driving device motion. In this situation, macroscale lubrication and wear mitigation methods, such as the use of bulk fluids and micrometer thick coatings, are ineffective; new nano-engineering approaches must be employed for MEMS devices with moving structures. We review fundamental tribological problems related to micro- and nanoscale mechanical contacts and developments in MEMS lubrications.
Penetration of Liquids into Cylindrical Capillaries.—The rate of penetration into a small capillary of radius r is shown to be: dldt=P(r2+4εr)8ηl, where P is the driving pressure, ε the coefficient of slip and η the viscosity. By integrating this expression, the distance penetrated by a liquid flowing under capillary pressure alone into a horizontal capillary or one with small internal surface is found to be the square root of (γrt·cosθ2η), where γ is the surface tension and θ the angle of contact. The quantity (γcosθ2η) is called the coefficient of penetrance or the penetrativity of the liquid.
Solutions for the slow flow past a square and a hexagonal array of cylinders are determined using a somewhat non-conventional numerical method. The calculated values of the drag on a cylinder as a function of c, the volume fraction of the cylinders, are shown to be in excellent agreement with the corresponding asymptotic expressions for c ⪡ 1 and for , the maximum volume fraction. These solutions are then used to calculate the average temperature difference between the bulk and the cylinders which are heated uniformly under conditions of small Reynolds and Péclet numbers.
If a rough surface is put in contact with a wetting liquid, the roughness may be spontaneously invaded depending on the surface pattern and the wetting properties of the liquid. Here, we study the conditions for observing such an imbibition and present practical achievements where the wetting properties of the surface can be predicted and tuned by the design of a solid texture. The contact angle of a drop on such a surface (where solid and liquid coexist) is discussed. Finally, the dynamics of the liquid film is found to obey a diffusive-type law, as in the case of porous wicking.
Recent achievements in the construction of surfaces with special wettabilities, such as superhydrophobicity, superhydrophilicity, superoleophobicity, superoleophilicity, superamphiphilicity, superamphiphobicity, superhydrophobicity/superoleophilicity, and reversible switching between superhydrophobicity and superhydrophilicity, are presented. Particular attention is paid to superhydrophobic surfaces created via various methods and surfaces with reversible superhydrophobicity and superhydrophilicity that are driven by various kinds of external stimuli. The control of the surface micro-/nanostructure and the chemical composition is critical for these special properties. These surfaces with controllable wettability are of great importance for both fundamental research and practical applications.
The capillary rise of liquid on a surface, or "wicking", has potential applications in biological and industrial processes such as drug delivery, oil recovery, and integrated circuit chip cooling. This paper presents a theoretical study on the dynamics of wicking on silicon nanopillars based on a balance between the driving capillary forces and viscous dissipation forces. Our model predicts that the invasion of the liquid front follows a diffusion process and strongly depends on the structural geometry. The model is validated against experimental observations of wicking in silicon nanopillars with different heights synthesized by interference lithography and metal-assisted chemical etching techniques. Excellent agreement between theoretical and experimental results, from both our samples and data published in the literature, was achieved.
We discuss in this review how the roughness of a solid impacts its wettability. We see in particular that both the apparent contact angle and the contact an-gle hysteresis can be dramatically affected by the presence of roughness. Ow-ing to the development of refined methods for setting very well-controlled micro-or nanotextures on a solid, these effects are being exploited to induce novel wetting properties, such as spontaneous filmification, superhydropho-bicity, superoleophobicity, and interfacial slip, that could not be achieved without roughness.
A calculation is given of the viscous force, exerted by a flowing fluid on a dense swarm of particles. The model underlying
these calculations is that of a spherical particle embedded in a porous mass. The flow through this porous mass is decribed
by a modification of Darcy's equation. Such a modification was necessary in order to obtain consistent boundary conditions.
A relation between permeability and particle size and density is obtained. Our results are compared with an experimental relation
due to Carman.
Liquid dynamics in micropillar arrays have received significant fundamental interest and have offered opportunities for the development of advanced microfluidic, thermal management, and energy-harvesting devices. However, a comprehensive understanding of complex liquid behavior and the effect on macroscopic propagation rates in micropillar arrays is needed. In this work, we investigated the microscopic sweeping behavior of the liquid front along the spreading direction in micropillar arrays where the sweeping distance scales with the one-fifth power of time. We explain the scaling with a simplified model that captures the capillary pressure gradient at the liquid front. Furthermore, we show that such microscopic dynamics is the mechanism that decreases the macroscopic propagation rate. This effect is a result of the reduction in the interfacial energy difference used to generate the capillary pressure, which is explained with an energy-based model and corroborated with experiments. The results indicate the importance of accounting for the microscopic dynamics of the liquid on microstructured surfaces, particularly in sparse geometries.
Prediction and optimization of liquid propagation rates in micropillar arrays are important for various lab-on-a-chip, biomedical, and thermal management applications. In this work, a semianalytical model based on the balance between capillary pressure and viscous resistance was developed to predict liquid propagation rates in micropillar arrays with height-to-period ratios greater than 1 and diameter-to-period ratios less than 0.57. These geometries represent the most useful regimes for practical applications requiring large propagation rates. The capillary pressure was obtained using an energy approach where the meniscus shape was predicted using Surface Evolver simulations and experimentally verified by interference microscopy. The combined viscous resistance of the pillars and the substrate was determined using Brinkman's equation with a numerically obtained permeability and corroborated with finite element simulations. The model shows excellent agreement with one-dimensional propagation experiments of deionized water in silicon micropillar arrays, highlighting the importance of accurately capturing the details of the meniscus shape and the viscous losses. Furthermore, an effective propagation coefficient was obtained through dimensionless analysis that is functionally dependent only on the micropillar geometry. The work offers design guidelines to obtain optimal liquid propagation rates on micropillar surfaces.
Many applications would benefit from an understanding of the physical mechanism behind fluid movement on rough surfaces, including the movement of water or contaminants within an unsaturated rock fracture. Presented is a theoretical investigation of the effect of surface roughness on fluid spreading. It is known that surface roughness enhances the effects of hydrophobic or hydrophilic behavior, as well as allowing for faster spreading of a hydrophilic fluid. A model is presented based on the classification of the regimes of spreading that occur when fluid encounters a rough surface: microscopic precursor film, mesoscopic invasion of roughness and macroscopic reaction to external forces. A theoretical relationship is developed for the physical mechanisms that drive mesoscopic invasion, which is used to guide a discussion of the implications of the theory on spreading conditions. Development of the analytical equation is based on a balance between capillary forces and frictional resistive forces. Chemical heterogeneity is ignored. The effect of various methods for estimating viscous dissipation is compared to available data from fluid rise on roughness experiments. Methods that account more accurately for roughness shape better explain the data as they account for more surface friction; the best fit was found for a hydraulic diameter approximation. The analytical solution implies the existence of a critical contact angle that is a function of roughness geometry, below which fluid will spread and above which fluid will resist spreading. The resulting equation predicts movement of a liquid invasion front with a square root of time dependence, mathematically resembling a diffusive process.
In this paper, a batch microfabrication process is presented for creating high aspect ratio, micron-sized helical and toroidal inductors with Q greater than or equal to 50 at multi-GHz frequencies. With a maximum processing temperature of only 220°C, the inductors can be fabricated on top of standard CMOS wafers. This process can also be used to create "inductor chiplets", which are polymer-encapsulated inductors with the same form factor as an EIA (Electronics Industries Association) standard 0201 surface mount device. The chiplets can be assembled onto CMOS wafers using a fluidic microassembly technique. This technique allows for multiple electrical interconnects to the inductor chiplets. The 40-μm gap between the substrate and assembled inductor increases the Q by a factor of ∼3 compared to as-fabricated inductors. Assembled and as-fabricated inductors have been characterized on similar substrates and have maximum Q values of 50 and 15 with resonant frequencies of 10 GHz and 9 GHz, respectively. Performance of the assembled inductors is nearly comparable to that of inductors as fabricated and tested on quartz substrates.