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Predicting Hemiwicking Dynamics on Textured Substrates
Abstract
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.
... This square root law has been applied widely to model wicking of fluids through porous media 16 and hemiwicking flow through nano/microstructured surfaces 17 in a large number of studies. [18][19][20][21] In most of this past work, however, the diffusion coefficient is an empirical parameter or obtained through scaling laws, but the approach is rarely predictive and specific to the nano/microstructure geometry. Bico et al. 22 estimated the viscosity of the hemiwicking film based on the classic Poiseuille flow on a flat plate and accounted for the viscous effect of the pillar sidewall through an empirical coefficient b, while Zhang et al. 6 treated the pillars as two flat plates and neglected the viscous loss by the substrate. ...
... Ishino et al. 23 proposed two separate diffusion coefficient (i.e., D) correlations by considering that the friction is caused by either the substrate or the pillars, depending on a relation between the height and center-to-center spacing or pitch of the pillars. Hay et al. 24 examined the invasion speed of hemiwicking through a hydraulic diameter formulation to account for the pressure loss, while an empirical parameter labeled as the pillar top angle was used to fit the data of Bico et al. 22 Natarajan et al. 21 and Mai et al. 25 derived analytical solutions for b based on the Bico et al. 22 theory by approximating the pillars as nanochannels and their model predictions achieved good comparisons with experimental results with the exception of a few outliers. Srivastava et al. 26 combined dimensional analysis and finite element simulation (COMSOL) around a single pillar to derive a scaling model, but that work did not consider the viscous losses resulting from multiple micropillars. ...
... As summarized above, models in the existing literature for the prediction of hemiwicking dynamics rely on specific empirical coefficients determined by experiments 29 or simulations. 26 They are only applicable under limited geometric conditions, 21,27 and all existing models treat the dynamic hemiwicking phenomenon with static parameters such as a fixed/average permeability and capillary pressure. ...
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.
... Previous studies have classified the equilibrium state of a droplet on a micro/nanostructured surface into three types: (1) Cassie-Baxter state, in which the droplet does not fill the gaps on the micro/nanostructured surface; (2) Wenzel state, in which the droplet fills the gaps on the surface; and (3) Hemiwicking state, in which liquid spontaneously penetrates through the gaps and continue to expand beyond the contact line of the upper droplet [26][27][28][29][30][31][32]. Fig. 5 illustrates that the droplet spreading on the HD-nanoAu surface is a typical hemiwicking behavior. ...
Immunochromatographic test strips typically consist of sample pad, conjugate pad, nitrocellulose membrane, and absorbent pad. Even minute variations in the assembly of these components can lead to inconsistent sample-reagent interactions, thereby reducing reproducibility. In addition, the nitrocellulose membrane is susceptible to damage during assembly and handling. To address this issue, we propose to replace the sample pad, conjugate pad, and nitrocellulose membrane with hierarchical dendritic gold nanostructure (HD-nanoAu) films to develop a compact integrated immunochromatographic strip. The strip uses quantum dots as a background fluorescence signal and employs fluorescence quenching to detect C-reactive protein (CRP) in human serum. A 5.9 μm thick HD-nanoAu film was electrodeposited on an ITO conductive glass by the constant potential method. The wicking kinetics of the HD-nanoAu film was thoroughly investigated, and the results indicated that the film exhibited favorable wicking properties, with a wicking coefficient of 0.72 μm ms-0.5. The immunochromatographic device was fabricated by etching three interconnected rings on HD-nanoAu/ITO to designate sample/conjugate (S/C), test (T), and control (C) regions. The S/C region was immobilized with mouse anti-human CRP antibody (Ab1) labeled with gold nanoparticles (AuNPs), while the T region was preloaded with polystyrene microspheres decorated with CdSe@ZnS quantum dots (QDs) as background fluorescent material, followed by mouse anti-human CRP antibody (Ab2). The C region was immobilized with goat anti-mouse IgG antibody. After the samples were added to the S/C region, the excellent wicking properties of the HD-nanoAu film facilitated the lateral flow of the CRP-containing sample toward the T and C regions after binding to AuNPs labeled with CRP Ab1. In the T region, CRP-AuNPs-Ab1 formed sandwich immunocomplexes with Ab2, and the fluorescence of QDs was quenched by AuNPs. The ratio of fluorescence intensity in the T region to that in the C region was used to quantify CRP. The T/C fluorescence intensity ratio was negatively correlated with the CRP concentration in the range of 26.67-853.33 ng mL-1 (corresponding to 300-fold diluted human serum), with a correlation coefficient (R2) of 0.98. The limit of detection was 15.0 ng mL-1 (corresponding to 300-fold diluted human serum), and the range of relative standard deviation: 4.48-5.31%, with a recovery rate of 98.22-108.33%. Common interfering substances did not cause significant interference, and the range of relative standard deviation: 1.96-5.51%. This device integrates multiple components of conventional immunochromatographic strips onto a single HD-nanoAu film, resulting in a more compact structure that improves the reproducibility and robustness of detection, making it promising for point-of-care testing applications.
Capillary wicking characteristics play an important role in two-phase thermal management devices including heat pipes and vapor chambers, yet three-dimensional (3D) pore-scale simulations of the dynamic capillary wicking process on various micro-structured surfaces have been rare. In this paper, we conduct 3D pore-scale simulations of capillary wicking on three commonly used micro-structured wicks including micro-pillar array, micro-channel, and sintered particles. The micro-scale liquid propagation dynamics and the “stick-slip” behavior of the propagating liquid front are captured using a 3D pseudo-potential multiple-relaxation-time lattice Boltzmann method. Based on the Lucus–Washburn approach and a work-energy approach, we theoretically analyze wickabilities of different micro-structured wicks. Effects of wick geometry and structural parameters on the capillary wicking characteristics are discussed. We demonstrate that an optimal pillar pitch distance exists, which maximizes the wickability of the micro-pillar array. We show that when the porosity is relatively low, the wickability of the micro-channel is higher than that of the micro-pillar array and the sintered particles. When the porosity is large, however, the sintered particles exhibit higher wickability than the micro-pillar array and the micro-channel. We also demonstrate that the capillary pressure of the sintered particles is always higher than that of the micro-pillar array and the micro-channel throughout the porosity range investigated. The numerical simulation results are compared with theoretical predictions. Findings in this work provide guidelines for the designs of porous wick in various two-phase thermal management systems for high heat flux devices.
Throughout the last few decades, a significant amount of research has been conducted on the wetting and deformation of soft materials. Employing high-speed videography, we report the spatiotemporal wetting and hemiwicking velocities for different fluids with micropillar hemiwicking arrays of various pillar geometries, spacing configurations, and Young's moduli ranging from E = 61 kPa to 12 GPa. The wetting and wicking dynamics are analyzed with comparisons to that predicted by contemporary scaling laws or derived analytic solutions. The results show that our analytical models can predict the inertial wetting, deformation, and hemiwicking dynamics within typically <50% of that experimentally observed. For the wide range of sample-fluid couples studied, the upper-limit (maximum) hemiwicking and inertial wetting velocities are typically observed within the narrow ranges of 10~30 mm/s and 0.8~1.6 m/s, respectively. Aside from the ultrasoft (~61 kPa) Ecoflex sample, sample stiffness had no notable effect on the maximum speed that a fluid can wet the non-textured surface region. However, for soft materials with elastic moduli below ~150 kPa, the rapid coupling between transient swelling and elastocapillary deformations leads to recoil wetting and wicking dynamics and notable reductions in the hemiwicking velocity.
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.
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).
A fundamental limitation of liquids on many surfaces is their contact line pinning. This limitation can be overcome by infusing a non-volatile and immiscible liquid or lubricant into texture or roughness created in or applied onto the solid substrate so that the liquid of interest no longer directly contacts the underlying surface. Such slippery liquid infused porous surfaces (SLIPS), also known as lubricant impregnated surfaces, complete remove contact line pinning and contact angle hysteresis. However, although a sessile droplet may rest on such a surface, its contact angle can only be an apparent contact angle because its contact is now with a second liquid and not a solid. Close to the solid the droplet has a wetting ridge with a force balance of the liquid-liquid and liquid-vapor interfacial tensions described by a Neumann’s triangle rather than Young’s law. Here, we show how, provided the lubricant coating is thin and the wetting ridge is small, a surface free energy approach can be used to obtain an apparent contact angle equation analogous to Young’s law using interfacial tensions for the lubricant-vapor and liquid-lubricant and an effective interfacial tension for the combined liquid-lubricant-vapor interfaces. This effective interfacial tension is the sum of the liquid-lubricant and the lubricant-vapor interfacial tensions or the liquid-vapor interfacial tension, for a positive or negative spreading power of the lubricant on the liquid, respectively. Using this approach, we then show Cassie-Baxter, Wenzel, hemi-wicking and other equations for rough, textured or complex geometry surfaces and for electrowetting and dielectrowetting can be used with the Young’s law contact angle replaced by the apparent contact angle from the equivalent smooth lubricant impregnated surface. The resulting equations are consistent with literature data. These results enable equilibrium contact angle theory for sessile droplets on surfaces to be used widely for surfaces that retain a thin and conformal SLIPS coating.
Morphologically driven dynamic wickability is essential for determining the hydrodynamic status of solid-liquid interface. We demonstrate that the dynamic wicking can play an integral role in supplying and propagating liquid through the interface, and govern the critical heat flux (CHF) against surface dry-out during boiling heat transfer. For the quantitative control of wicking, we manipulate the characteristic lengths of hexagonally arranged nanopillars within sub-micron range through nanosphere lithography combined with top-down metal-assisted chemical etching. Strong hemi-wicking over the manipulated interface (i.e., wicking coefficients) of 1.28 mm/s0.5 leads to 164% improvement of CHF compared to no wicking. As a theoretical guideline, our wickability-CHF model can make a perfect agreement with improved CHF, which cannot be predicted by the classic models pertaining to just wettability and roughness effects, independently.
This paper presents a comparative study between theoretical predictions and experimental results of a flat-plate solar collector with heat pipes. The theoretical model for the heat pipe solar collector is based upon the method by Duffie and Beckman (1980), modified to use heat pipes for energy transport. The methanol filled heat pipes are self-contained devices whose evaporators are inserted under pressure in the flat plate of the solar collector and the heat exchange is carried out at their condensers. The evaporators contain a wick of one mesh layer to ensure a better distribution of the working fluid. The condensers are wickless and inclined 15 deg more than the inclination of the evaporators to facilitate the return of the condensate to the evaporators. The time constant of the heat pipe solar collector was calculated and found to be about 23 minutes. Also presented in this paper are comparative experimental results of the proposed solar collector and a conventional commercial solar collector. The two collectors were tested simultaneously. The instantaneous efficiencies of the heat pipe solar collector are lower than the conventional collector in the morning and higher when the heat pipes reach their operating temperatures.
Non-wetting surfaces containing micro/nanotextures impregnated with lubricating liquids have recently been shown to exhibit superior non-wetting performance compared to superhydrophobic surfaces that rely on stable air–liquid interfaces. Here we examine the fundamental physico-chemical hydrodynamics that arise when droplets, immiscible with the lubricant, are placed on and allowed to move along these surfaces. We find that these four-phase systems show novel contact line morphology comprising a finite annular ridge of the lubricant pulled above the surface texture and consequently as many as three distinct 3-phase contact lines. We show that these distinct morphologies not only govern the contact line pinning that controls droplets' initial resistance to movement but also the level of viscous dissipation and hence their sliding velocity once the droplets begin to move.
Ice repellent coatings have been studied and keenly sought after for many years, where any advances in the durability of such coatings will result in huge energy savings across many fields. Progress in creating anti-ice and anti-frost surfaces has been particularly rapid since the discovery and development of slippery, liquid infused porous surfaces (SLIPS). Here we use SLIPS-coated differential scanning calorimeter (DSC) pans to investigate the effects of the surface modification on the nucleation of supercooled water. This investigation is inherently different from previous studies which looked at the adhesion of ice to SLIPS surfaces, or the formation of ice under high humidity conditions. Given the stochastic nature of nucleation of ice from supercooled water, multiple runs on the same sample are needed to determine if a given surface coating has a real and statistically significant effect on the nucleation temperature. We have cycled supercooling to freezing and then thawing of deionized water in hydrophilic (untreated aluminum), hydrophobic, superhydrophobic, and SLIPS-treated DSC pans multiple times to determine the effects of surface treatment on the nucleation and subsequent growth of ice. We find that SLIPS coatings lower the nucleation temperature of supercooled water in contact with statistical significance and show no deterioration or change in the coating performance even after 150 freeze-thaw cycles.
We present results showing how water drops, produced by ink-jet printing,
spread on surfaces patterned with lattices of diamond or triangular posts.
Considering post widths typically ~7 m and lattice spacings between 15-40 m, we
observe drop shapes with 3,4 and 6-fold symmetry, depending on both the
symmetry of the lattice and the shape of the posts. This is a result of the
different mechanisms of interface pinning and depinning which depend on the
direction of the contact line motion with respect to the post shape. Lattice
Boltzmann simulations are used to describe these mechanisms in detail for
triangular posts. We also follow the motion of the contact line as the drops
evaporate showing that they tend to return to their original shape. To explain
this we show that the easy direction for movement is the same for spreading and
drying drops. We compare the behaviour of small drops with that of larger drops
created by jetting several drops at the same position. We find that the contact
line motion is unexpectedly insensitive to drop volume, even when a spherical
cap of fluid forms above the posts. The findings are relevant to microfluidic
applications and to the control of drop shapes in ink-jet printing.
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.
Bacteria primarily exist in robust, surface-associated communities known as biofilms, ubiquitous in both natural and anthropogenic environments. Mature biofilms resist a wide range of antimicrobial treatments and pose persistent pathogenic threats. Treatment of adherent biofilm is difficult, costly, and, in medical systems such as catheters or implants, frequently impossible. At the same time, strategies for biofilm prevention based on surface chemistry treatments or surface microstructure have been found to only transiently affect initial attachment. Here we report that Slippery Liquid-Infused Porous Surfaces (SLIPS) prevent 99.6% of Pseudomonas aeruginosa biofilm attachment over a 7-d period, as well as Staphylococcus aureus (97.2%) and Escherichia coli (96%), under both static and physiologically realistic flow conditions. In contrast, both polytetrafluoroethylene and a range of nanostructured superhydrophobic surfaces accumulate biofilm within hours. SLIPS show approximately 35 times the reduction of attached biofilm versus best case scenario, state-of-the-art PEGylated surface, and over a far longer timeframe. We screen for and exclude as a factor cytotoxicity of the SLIPS liquid, a fluorinated oil immobilized on a structured substrate. The inability of biofilm to firmly attach to the surface and its effective removal under mild flow conditions (about 1 cm/s) are a result of the unique, nonadhesive, "slippery" character of the smooth liquid interface, which does not degrade over the experimental timeframe. We show that SLIPS-based antibiofilm surfaces are stable in submerged, extreme pH, salinity, and UV environments. They are low-cost, passive, simple to manufacture, and can be formed on arbitrary surfaces. We anticipate that our findings will enable a broad range of antibiofilm solutions in the clinical, industrial, and consumer spaces.
Writing with ink involves the supply of liquid from a pen onto a porous hydrophilic solid surface, paper. The resulting linewidth depends on the pen speed and the physicochemical properties of the ink and paper. Here we quantify the dynamics of this process using a combination of experiment and theory. Our experiments are carried out using a minimal pen, a long narrow tube that serves as a reservoir of liquid, which can write on a model of paper, a hydrophilic micropillar array. A minimal theory for the rate of wicking or spreading of the liquid is given by balancing the capillary force that drives the liquid flow and the resistance associated with flow through the porous substrate. This allows us to predict the shape of the front and the width of the line laid out by the pen, with results that are corroborated by our experiments.
Creating a robust synthetic surface that repels various liquids would have broad technological implications for areas ranging from biomedical devices and fuel transport to architecture but has proved extremely challenging. Inspirations from natural nonwetting structures, particularly the leaves of the lotus, have led to the development of liquid-repellent microtextured surfaces that rely on the formation of a stable air-liquid interface. Despite over a decade of intense research, these surfaces are, however, still plagued with problems that restrict their practical applications: limited oleophobicity with high contact angle hysteresis, failure under pressure and upon physical damage, inability to self-heal and high production cost. To address these challenges, here we report a strategy to create self-healing, slippery liquid-infused porous surface(s) (SLIPS) with exceptional liquid- and ice-repellency, pressure stability and enhanced optical transparency. Our approach-inspired by Nepenthes pitcher plants-is conceptually different from the lotus effect, because we use nano/microstructured substrates to lock in place the infused lubricating fluid. We define the requirements for which the lubricant forms a stable, defect-free and inert 'slippery' interface. This surface outperforms its natural counterparts and state-of-the-art synthetic liquid-repellent surfaces in its capability to repel various simple and complex liquids (water, hydrocarbons, crude oil and blood), maintain low contact angle hysteresis (<2.5°), quickly restore liquid-repellency after physical damage (within 0.1-1 s), resist ice adhesion, and function at high pressures (up to about 680 atm). We show that these properties are insensitive to the precise geometry of the underlying substrate, making our approach applicable to various inexpensive, low-surface-energy structured materials (such as porous Teflon membrane). We envision that these slippery surfaces will be useful in fluid handling and transportation, optical sensing, medicine, and as self-cleaning and anti-fouling materials operating in extreme environments.
We present and interpret lattice Boltzmann simulations of thick films spreading on surfaces patterned with polygonal posts. We show that the mechanism of pinning and depinning differs with the direction of advance, and demonstrate that this leads to anisotropic spreading within a certain range of material contact angles.
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.
Roughening a hydrophobic surface enhances its nonwetting properties into superhydrophobicity. For liquids other than water, roughness can induce a complete rollup of a droplet. However, topographic effects can also enhance partial wetting by a given liquid into complete wetting to create superwetting. In this work, a model system of spreading droplets of a nonvolatile liquid on surfaces having lithographically produced pillars is used to show that superwetting also modifies the dynamics of spreading. The edge speed-dynamic contact angle relation is shown to obey a simple power law, and such power laws are shown to apply to naturally occurring surfaces.
Micropatterned surfaces have been studied extensively as model systems to understand influences of topographic or chemical heterogeneities on wetting phenomena. Such surfaces yield specific wetting or hydrodynamic effects, for example, ultrahydrophobic surfaces, 'fakir' droplets, tunable electrowetting, slip in the presence of surface heterogeneities and so on. In addition, chemical patterns allow control of the locus, size and shape of droplets by pinning the contact lines at predetermined locations. Applications include the design of 'self-cleaning' surfaces and hydrophilic spots to automate the deposition of probes on DNA chips. Here, we discuss wetting on topographically patterned but chemically homogeneous surfaces and demonstrate mechanisms of shape selection during imbibition of the texture. We obtain different deterministic final shapes of the spreading droplets, including octagons, squares, hexagons and circles. The shape selection depends on the topographic features and the liquid through its equilibrium contact angle. Considerations of the dynamics provide a 'shape' diagram that summarizes our observations and suggest rules for a designer's tool box.
In some cases water droplets can completely wet microstructured superhydrophobic surfaces. The dynamics of this rapid process is analyzed by ultrahigh-speed imaging. Depending on the scales of the microstructure, the wetting fronts propagate smoothly and circularly or-more interestingly-in a stepwise manner, leading to a growing square-shaped wetted area: entering a new row perpendicular to the direction of front propagation takes milliseconds, whereas once this has happened, the row itself fills in microseconds ("zipping"). Numerical simulations confirm this view and are in quantitative agreement with the experiments.
Viable tumour-derived epithelial cells (circulating tumour cells or CTCs) have been identified in peripheral blood from cancer patients and are probably the origin of intractable metastatic disease. Although extremely rare, CTCs represent a potential alternative to invasive biopsies as a source of tumour tissue for the detection, characterization and monitoring of non-haematologic cancers. The ability to identify, isolate, propagate and molecularly characterize CTC subpopulations could further the discovery of cancer stem cell biomarkers and expand the understanding of the biology of metastasis. Current strategies for isolating CTCs are limited to complex analytic approaches that generate very low yield and purity. Here we describe the development of a unique microfluidic platform (the 'CTC-chip') capable of efficient and selective separation of viable CTCs from peripheral whole blood samples, mediated by the interaction of target CTCs with antibody (EpCAM)-coated microposts under precisely controlled laminar flow conditions, and without requisite pre-labelling or processing of samples. The CTC-chip successfully identified CTCs in the peripheral blood of patients with metastatic lung, prostate, pancreatic, breast and colon cancer in 115 of 116 (99%) samples, with a range of 5-1,281 CTCs per ml and approximately 50% purity. In addition, CTCs were isolated in 7/7 patients with early-stage prostate cancer. Given the high sensitivity and specificity of the CTC-chip, we tested its potential utility in monitoring response to anti-cancer therapy. In a small cohort of patients with metastatic cancer undergoing systemic treatment, temporal changes in CTC numbers correlated reasonably well with the clinical course of disease as measured by standard radiographic methods. Thus, the CTC-chip provides a new and effective tool for accurate identification and measurement of CTCs in patients with cancer. It has broad implications in advancing both cancer biology research and clinical cancer management, including the detection, diagnosis and monitoring of cancer.
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.
Hypothesis:
A disturbance such as a microparticle on the pathway of a spreading droplet has shown the tremendous ability to accelerate locally the motion of the macroscopic contact line (Mu et al., 2017). Although this ability has been linked to the particle-liquid interaction, the physical mechanisms behind it are still poorly understood despite its academic interest and the scope of numerous industrial applications in need of fast wetting.
Experiments:
In order to better understand the mechanisms behind the particle-liquid interaction, we numerically investigate the pressure and velocity fields in the liquid film. The results are compared to experiments assessing the temporal shape variation of the liquid-film meniscus from which pressure difference around the particle is evaluated.
Findings:
The particle-induced acceleration of the film front depends both on the shape of the meniscus that forms around the particle foot and the liquid "reservoir" in the film that can be pumped thanks to the presence of the particle. The study validates the presence of three stages of pressure difference between the upstream and downstream regions of the meniscus around the particle, which leads to the local acceleration/deceleration of the macroscopic contact line. We indicate that asymmetric meniscus around the particle foot produces a net pressure force driving liquid and accelerating the liquid-film front.
Wicking in hierarchical micro/nanostructured surfaces has gained significant attention due to its potential applications in thermal management, moisture capturing, drug delivery, and oil recovery. While some studies have shown that hierarchical structures enhance wicking over micro-structured surfaces, others have found very limited wicking improvement. In this study, we demonstrate the importance of micropatterns on wicking enhancement in hierarchical surfaces using ZnO nanorods grown on silicon micropillars of varying spacings and heights. The wicking front over hierarchical surfaces is found to follow a two-stage motion, where wicking is faster around micropillars, but slower in between adjacent pillar rows and the latter stage dictates the wicking enhancement in hierarchical surfaces. The competition between the added capillary action and friction due to nanostructures in these two different wicking stages results in a strong dependence of wicking enhancement on the height and spacing of the micropillars. A scaling model for the propagation coefficient is developed for wicking in hierarchical surfaces considering nanostructures in both wicking stages and the model agrees well with the experiments. This microstructure-controlled two-stage wicking characteristic sheds light on a more effective design of hierarchical micro/nanostructured surfaces for wicking enhancement.
Wetting process of a high energy surface can be accelerated locally through the capillary interaction of a liquid advancing front with a micro-object introduced to the surface (Mu et al., 2017, J. Fluid Mech. 830:R1). We demonstrate that a linear array of micro-pillars embedded in a fully wettable substrate can produce quick propagation of liquid along the array. It is observed that multiple interactions of a liquid front with pillars can induce the motion of liquid a hundred times faster than in the absence of pillars.
Many of the distinctive and useful phenomena of soft matter come from its interaction with interfaces. Examples are the peeling of a strip of adhesive tape or the coating of a surface or the curling of a fibre via capillary forces or the electrically driven ow along a microchannel, or the collapse of a porous sponge. These interfacial phenomena are distinct from the intrinsic behaviour of a soft material like a gel or a microemulsion. Yet many forms of interfacial phenomena can be understood via common principles valid for many forms of soft matter. Our goal in organizing this school was to give students a grasp of these common principles and their many ramifications and possibilities. The school comprised over fifty 90-minute lectures over four weeks in July 2013. Four four-lecture courses by Howard Stone, Michael Cates, David Nelson, and L. Mahadevan served as an anchor for the program. A number of shorter courses and seminars rounded out the school.This volume presents lecture notes prepared by the speakers and submitted for publication after the school. The lectures are grouped under two main themes: Hydrodynamics and interfaces, and Soft matter.
This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation.
To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.
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.
This work explores capillary flow through micropillar arrays with rectangular pillar arrangements. The effects of these configurations on permeability and capillary pressure are investigated for heat pipe wick applications. The permeability is described in terms of three dimensionless parameters: , and , where l and S are the edge-to-edge spacings in the x- and y-directions, respectively. The two analytical permeability models considered are Hale et al. (2014) [20] and the Brinkman equation using specifically the permeability derived by Tamayol and Bahrami (2009) [19]. Permeability results from numerical simulations are also presented. The surface energy minimization program called Surface Evolver is used to calculate the capillary pressure within the arrays. Mass flow rates are first derived from a combination of array permeability and capillary pressure, and then used to predict the capillary limit of heat pipes equipped with these wicks. Rectangular arrays exhibited the ability to maintain high capillary pressures even at high porosities, which increased the overall cooling capacity above square arrays. The increase was on the order of 1.5× in the absence of gravity and 5×-7× in the presence of gravity, depending on the exact ratio considered.
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.
We investigate the wicking in granular media by considering layers of grains at the surface of a liquid and discuss the critical contact angle below which spontaneous impregnation takes place. This angle is found to be on the order of 55° for monodisperse layers, significantly smaller than 90°, the threshold value for penetrating assemblies of tubes. Owing to geometry, impregnating grains is more demanding than impregnating tubes. We also consider the additional effects of polydispersity and pressure on this wetting transition and discuss the corresponding shift observed for the critical contact angle.
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.
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.
After a brief presentation of the classical laws of wetting, we review different phenomenological descriptions of rough wetting, i.e., show how these classical laws must be modified on rough solids. This introduces the questions of hemi-wicking (can a film propagate inside the texture of a solid ?), rough films (is it possible for a liquid film to follow the roughness of a solid ?) and super-hydrophobicity (how can a solid be designed to become water repellent ?).
We discuss quantitatively the wetting of a solid textured by a designed roughness. Both the hydrophilic and the hydrophobic case are described, together with possible implications for the wetting of porous materials.
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.
Controlling surface wettability and liquid spreading on patterned surfaces is of significant interest for a broad range of applications, including DNA microarrays, digital lab-on-a-chip, anti-fogging and fog-harvesting, inkjet printing and thin-film lubrication. Advancements in surface engineering, with the fabrication of various micro/nanoscale topographic features, and selective chemical patterning on surfaces, have enhanced surface wettability and enabled control of the liquid film thickness and final wetted shape. In addition, groove geometries and patterned surface chemistries have produced anisotropic wetting, where contact-angle variations in different directions resulted in elongated droplet shapes. In all of these studies, however, the wetting behaviour preserves left-right symmetry. Here, we demonstrate that we can harness the design of asymmetric nanostructured surfaces to achieve uni-directional liquid spreading, where the liquid propagates in a single preferred direction and pins in all others. Through experiments and modelling, we determined that the spreading characteristic is dependent on the degree of nanostructure asymmetry, the height-to-spacing ratio of the nanostructures and the intrinsic contact angle. The theory, based on an energy argument, provides excellent agreement with experimental data. The insights gained from this work offer new opportunities to tailor advanced nanostructures to achieve active control of complex flow patterns and wetting on demand.
We present a microfluidic particle-trap array that utilizes negative dielectrophoresis (nDEP) force and hydrodynamic force. The traps are located at the stagnation points of cylindrical pillars arranged in a regular array, and they can function as both single-particle traps (capable of discriminating particles based on size) and multiparticle traps (capable of controlling the number of particles trapped). By adjusting the relative strength of the nDEP and hydrodynamic forces, we are able to control the number of trapped particles accurately. We have used 5 microm polystyrene beads to validate and demonstrate the capability of this new particle-trap design. Pulsed nDEP was used to increase the selectivity and stability. Good correlation between simulation and the experimental results was obtained.
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.
Structuring Liquid Using Functionalized Surfaces for Effective Carbon Capture
- M S Yeganeh
- S P Deighton
- M Siskin
- A Jaishankar
- C Maldarelli
- P Bertolini
- A R Konicek
- B Natarajan
- J L Vreeland
- A Jusufi
Yeganeh, M. S.; Deighton, S. P.; Siskin, M.; Jaishankar, A.;
Maldarelli, C.; Bertolini, P.; Konicek, A. R.; Natarajan, B.; Vreeland, J.
L.; Jusufi, A. Structuring Liquid Using Functionalized Surfaces for
Effective Carbon Capture. Nature, submitted for publication, 2020.
Soft Interfaces: Lecture Notes of the Les Houches Summer School
- L Bocquet
- D Queŕe
- T A Witten
- L F Cugliandolo
Bocquet, L.; Queŕe, D.; Witten, T. A.; Cugliandolo, L. F. Soft
Interfaces: Lecture Notes of the Les Houches Summer School; Oxford
University Press, 2017; Vol. 98.
The Lattice Boltzmann Method
- T Kruger
- H Kusumaatmaja
- A Kuzmin
- O Shardt
- G Silva
- E M Viggen
Kruger, T.; Kusumaatmaja, H.; Kuzmin, A.; Shardt, O.; Silva,
G.; Viggen, E. M. The Lattice Boltzmann Method; Springer
International Publishing, 2017; Vol. 10, pp 4−15.