Evaporation-Driven Micromixing in Sessile Droplets for Miniaturized Absorbance-Based Colorimetry.

We demonstrate the use of an evaporating, sessile droplet on a nonwetting substrate as a miniature micromixing device to conduct sample-dye reactions for absorbance-based colorimetry. The nonwetting substrate supports buoyancy-induced mixing inside the droplet for rapid completion of the measurement. The Bradford assay is used as a proof of concept, where a protein-containing sample is reacted with a reagent dye to measure the protein concentration. Viability of absorbance measurement through the droplet is first established using droplets in which the reactants are mixed prior to their deposition onto the substrate. In a second set of experiments involving in situ mixing, the reagent is directly added to a sessile droplet of the protein-containing sample, allowing the reactants to mix while the absorbance is being measured. Interplay between buoyancy-induced mixing, protein-reagent reaction, and protein adsorption onto the substrate leads to a complex temporal absorbance measurement signal. Videos corresponding to the signal data show that each of these mechanisms dominates during different phases of droplet evolution, causing a signal pattern containing peaks and valleys having a strong monotonic trend with the protein concentration. Overall, the second absorbance peak at which the reaction nears completion is the most sensitive to sample concentration. Heating of the substrate is demonstrated to dramatically speed up the mixing process. These protein concentration measurements, obtained with a simpler system and low reactant volumes, demonstrate that this droplet micromixing concept is a viable alternative to microtiter plates for colorimetric applications.

Re-entrant Cavities Enhance Resilience to the Cassie-to-Wenzel State Transition on Superhydrophobic Surfaces during Electrowetting.

Electrowetting-based droplet actuation has applications in digital microfluidics. Mobility of droplets on surfaces can be enhanced using structured superhydrophobic surfaces that offer inherently low adhesion to droplets in the Cassie state. However, these surfaces must be designed to prevent transition to the Wenzel state (in which droplets are immobile) at high electrowetting actuation voltages. The electrowetting behavior of cylindrical microposts and mushroom-shaped re-entrant microstructures, both of which afford excellent superhydrophobicity, is investigated and compared. A surface-energy-based model is employed to estimate the energy barrier for the Cassie-to-Wenzel transition and thus the electrowetting voltage required to initiate this transition. The mushroom structures are predicted to be more resilient to transition (i.e., transition occurs at a voltage that is up to 1.5 times higher) than microposts. Both types of microstructured surfaces are fabricated and electrowetting experiments performed to demonstrate that mushroom structures indeed inhibit the Cassie-to-Wenzel transition at voltages that induce such transition on the cylindrical microposts.

Enabling Highly Effective Boiling from Superhydrophobic Surfaces.

A variety of industrial applications such as power generation, water distillation, and high-density cooling rely on heat transfer processes involving boiling. Enhancements to the boiling process can improve the energy efficiency and performance across multiple industries. Highly wetting textured surfaces have shown promise in boiling applications since capillary wicking increases the maximum heat flux that can be dissipated. Conversely, highly nonwetting textured (superhydrophobic) surfaces have been largely dismissed for these applications as they have been shown to promote formation of an insulating vapor film that greatly diminishes heat transfer efficiency. The current Letter shows that boiling from a superhydrophobic surface in an initial Wenzel state, in which the surface texture is infiltrated with liquid, results in remarkably low surface superheat with nucleate boiling sustained up to a critical heat flux typical of hydrophilic wetting surfaces, and thus upends this conventional wisdom. Two distinct boiling behaviors are demonstrated on both micro- and nanostructured superhydrophobic surfaces based on the initial wetting state. For an initial surface condition in which vapor occupies the interstices of the surface texture (Cassie-Baxter state), premature film boiling occurs, as has been commonly observed in the literature. However, if the surface texture is infiltrated with liquid (Wenzel state) prior to boiling, drastically improved thermal performance is observed; in this wetting state, the three-phase contact line is pinned during vapor bubble growth, which prevents the development of a vapor film over the surface and maintains efficient nucleate boiling behavior.

Enhanced Antimicrobial Efficacy of Bimetallic Porous CuO Microspheres Decorated with Ag Nanoparticles.

The antimicrobial action of porous CuO microspheres (µCuO), Ag nanoparticles (nAg), and bimetallic porous CuO microspheres decorated with Ag nanoparticles (µCuO/nAg) was evaluated against surrogate microorganisms representative of pathogens commonly implicated in foodborne and healthcare-associated human infections. This work addressed the Gram-negative bacteria E. coli (Escherichia coli O157:H7-GFP B6-914), Salmonella (Salmonella enterica serovar enteritidis phage-type PT21), and the Gram-positive bacteria Listeria (Listeria innocua), as well as environmental microorganisms derived from local river water. Compared to particles composed only of CuO or Ag, the bimetallic porous µCuO/nAg particle exhibits enhanced antimicrobial efficacy. The antimicrobial action of bimetallic porous µCuO/nAg particles is dose-dependent, with 50 µg/mL particle concentration completely inhibiting the growth of both the Gram-negative (Salmonella) and the Gram-positive (Listeria) bacteria after 6 h. To assess the mechanism of antimicrobial action, the changes in surface morphologies of bacteria treated with the particles were observed using scanning electron microscopy. In the case of the Gram-negative bacteria, the bacterial cell membrane is damaged, likely due to the release of metal ions from the particles; however, particle-induced cell membrane damage is not observed for Gram-positive bacteria. Collectively, results from this work shed further light on possible mechanisms of antimicrobial action of micro-/nanoparticles and highlight the potential for bimetallic particle-based inhibition of microbial infections.

Multiscale Modeling of the Three-Dimensional Meniscus Shape of a Wetting Liquid Film on Micro-/Nanostructured Surfaces.

The design of structured surfaces for increasing the heat flux dissipated during boiling and evaporation processes via enhanced liquid rewetting requires prediction of the liquid meniscus shape on these surfaces. In this study, a general continuum model is developed to predict the three-dimensional meniscus shape of liquid films on micro/nanostructured surfaces based on a minimization of the system free energy that includes solid-liquid van der Waals interaction energy, surface energy, and gravitational potential. The continuum model is validated at the nanoscale against molecular dynamics simulations of water films on gold surfaces with pyramidal indentations, and against experimental measurements of water films on silicon V-groove channels at the microscale. The validated model is used to investigate the effect of film thickness and surface structure depth on the meniscus shape. The meniscus is shown to become more conformal with the surface structure as the film thickness decreases and the structure depth increases. Assuming small interface slope and small variation in film thickness, the continuum model can be linearized to obtain an explicit expression for the meniscus shape. The error of this linearized model is quantitatively assessed and shown to increase with increasing structure depth and decreasing structure pitch. The model developed can be used for accurate prediction of three-dimensional meniscus shape on structured surfaces with micro/nano-scale features, which is necessary for determining the liquid delivery rate and heat flux dissipated during thin-film evaporation. The linearized model is useful for rapid prediction of meniscus shape when the structure depth is smaller than or comparable to the liquid film thickness.

A Wettability Metric for Characterization of Capillary Flow on Textured Superhydrophilic Surfaces.

Surface wettability is typically characterized by measuring the static contact angle of a sessile droplet placed on the surface. For extremely wetting surfaces on which liquid spontaneously spreads into a thin liquid film, the near-zero static contact angle is not amenable to measurement and does not fully describe the wetting behavior. There are unmet needs in microfluidics, boiling heat transfer enhancement, and antifogging applications for a metric to characterize highly wetting (i.e., superhydrophilic) textured surfaces based on their capillary-driven liquid pumping performance, as a supplement to the contact angle for this highly wetting regime. To describe the wetting behavior, the textured surface can be approximated as a thin porous layer through which the liquid spreads. An analytical model is developed for the volumetric flow in this layer, which reveals a single superhydrophilicity metric that captures the wetting behavior for a given liquid. A simple experimental approach is proposed to characterize this metric by measuring the volumetric liquid intake into the surface from a filled capillary tube. This approach is validated by characterizing micropillared superhydrophilic surfaces of known geometry; the predicted and measured wetting behaviors show good agreement. The metric proposed in this study offers a simple approach for accurately characterizing and differentiating highly wetting surfaces based on their liquid pumping ability.

Characterization of Coalescence-Induced Droplet Jumping Height on Hierarchical Superhydrophobic Surfaces.

Coalescence-induced condensate droplet jumping from superhydrophobic surfaces can be exploited in condensation heat-transfer enhancement, imparting self-cleaning behavior to surfaces, anti-icing coatings, and other industrial uses. An intriguing application would exploit this phenomenon to achieve thermal rectification using a sealed vapor chamber with opposing superhydrophilic and superhydrophobic surfaces. During forward operation, continuous evaporation occurs from the heated superhydrophilic evaporator surface; self-propelled jumping returns the condensate droplets from the cooler superhydrophobic surface to the evaporator, allowing passive recirculation of the working fluid without a reliance on gravity or capillary wicking for fluid return. In reverse operation, when the superhydrophobic surface is heated, the absence of a mechanism for fluid return from the cooler superhydrophilic side to the evaporator restricts heat transport across the (low conductivity) vapor gap. The effectiveness of this jumping-droplet thermal diode can be enhanced by maximizing the distance between the opposing superhydrophobic and superhydrophilic surfaces. It is, therefore, important to investigate the height to which the condensate droplets jump from the superhydrophobic surfaces such that replenishment of liquid to the superhydrophilic surface is maintained. In this study, we systematically investigate the height to which the condensate droplets jump from the hierarchical superhydrophobic surfaces having truncated microcones coated with nanostructures. The condensate droplet jumping height increases with a decrease in microcone pitch. A general theoretical model that accounts for surface adhesion, line tension, and initial wetting states of multiple coalescing droplets of different radii is used to predict and explain the experimentally observed trend of droplet jumping height with surface roughness. The insights provided regarding the effect of surface topography on droplet jumping height are critical to the design of high-performance thermal diode devices.

In Vitro Multitissue Interface Model Supports Rapid Vasculogenesis and Mechanistic Study of Vascularization across Tissue Compartments.

A significant challenge facing tissue engineers is the design and development of complex multitissue systems, including vascularized tissue-tissue interfaces. While conventional in vitro models focus on either vasculogenesis (de novo formation of blood vessels) or angiogenesis (vessels sprouting from existing vessels or endothelial monolayers), successful therapeutic vascularization strategies will likely rely on coordinated integration of both processes. To address this challenge, we developed a novel in vitro multitissue interface model in which human endothelial colony forming cell (ECFC)-encapsulated tissue spheres are embedded within a surrounding tissue microenvironment. This highly reproducible approach exploits biphilic surfaces (nanostructured surfaces with distinct superhydrophobic and hydrophilic regions) to (i) support tissue compartments with user-specified matrix composition and physical properties as well as cell type and density and (ii) introduce boundary conditions that prevent the cell-mediated tissue contraction routinely observed with conventional three-dimensional monodispersion cultures. This multitissue interface model was applied to test the hypothesis that independent control of cell-extracellular matrix (ECM) and cell-cell interactions would affect vascularization within the tissue sphere as well as across the tissue-tissue interface. We found that high-cell-density tissue spheres containing 5 × 10(6) ECFCs/mL exhibit rapid and robust vasculogenesis, forming highly interconnected, stable (as indicated by type IV collagen deposition) vessel networks within only 3 days. Addition of adipose-derived stromal cells (ASCs) in the surrounding tissue further enhanced vasculogenesis within the sphere as well as angiogenic vessel elongation across the tissue-tissue boundary, with both effects being dependent on the ASC density. Overall, results show that the ECFC density and ECFC-ASC crosstalk, in terms of paracrine and mechanophysical signaling, are critical determinants of vascularization within a given tissue compartment and across tissue interfaces. This new in vitro multitissue interface model and the associated mechanistic insights it yields provide guiding principles for the design and optimization of multitissue vascularization strategies for research and clinical applications.

Marangoni Convection in Evaporating Organic Liquid Droplets on a Nonwetting Substrate.

We quantitatively characterize the flow field inside organic liquid droplets evaporating on a nonwetting substrate. A mushroom-structured surface yields the desired nonwetting behavior with methanol droplets, while use of a cooled substrate (5-15 °C) slows the rate of evaporation to allow quasi-static particle image velocimetry. Visualization reveals a toroidal vortex within the droplet that is characteristic of surface tension-driven flow; we demonstrate by means of a scaling analysis that this recirculating flow is Marangoni convection. The velocities in the droplet are on the order of 10-45 mm/s. Thus, unlike in the case of evaporation on wetting substrates where Marangoni convection can be ignored for the purpose of estimating the evaporation rate, advection due to the surface tension-driven flow plays a dominant role in the heat transfer within an evaporating droplet on a nonwetting substrate because of the large height-to-radius aspect ratio of the droplet. We formulate a reduced-order model that includes advective transport within the droplet for prediction of organic liquid droplet evaporation on a nonwetting substrate and confirm that the predicted temperature differential across the height of the droplet matches experiments.

Coalescence-Induced Jumping of Multiple Condensate Droplets on Hierarchical Superhydrophobic Surfaces.

Coalescence-induced jumping of condensate droplets from a superhydrophobic surface with hierarchical micro/nanoscale roughness is quantitatively characterized. Experimental observations show that the condensate droplet jumping is induced by coalescence of multiple droplets of different sizes, and that the coalesced droplet trajectories typically deviate from the surface normal. A depth-from-defocus image processing technique is developed to track the out-of-plane displacement of the jumping droplets, so as to accurately measure the droplet size and velocity. The results demonstrate that the highest jumping velocity is achieved when two droplets coalesce. The jumping velocity decreases gradually with an increase in the number of coalescing droplets, despite the greater potential surface energy released upon coalescence. A general theoretical model that accounts for viscous dissipation, surface adhesion, line tension, the initial droplet wetting states, and the number and sizes of the coalescing droplets is developed to explain the trends of droplet jumping velocity observed in the experiments.

Water and Ethanol Droplet Wetting Transition during Evaporation on Omniphobic Surfaces.

Omniphobic surfaces with reentrant microstructures have been investigated for a range of applications, but the evaporation of high- and low-surface-tension liquid droplets placed on such surfaces has not been rigorously studied. In this work, we develop a technique to fabricate omniphobic surfaces on copper substrates to allow for a systematic examination of the effects of surface topography on the evaporation dynamics of water and ethanol droplets. Compared to a water droplet, the ethanol droplet not only evaporates faster, but also inhibits Cassie-to-Wenzel wetting transitions on surfaces with certain geometries. We use an interfacial energy-based description of the system, including the transition energy barrier and triple line energy, to explain the underlying transition mechanism and behaviour observed. Suppression of the wetting transition during evaporation of droplets provides an important metric for evaluating the robustness of omniphobic surfaces requiring such functionality.

Influence of surface wettability on transport mechanisms governing water droplet evaporation.

Prediction and manipulation of the evaporation of small droplets is a fundamental problem with importance in a variety of microfluidic, microfabrication, and biomedical applications. A vapor-diffusion-based model has been widely employed to predict the interfacial evaporation rate; however, its scope of applicability is limited due to incorporation of a number of simplifying assumptions of the physical behavior. Two key transport mechanisms besides vapor diffusion-evaporative cooling and natural convection in the surrounding gas-are investigated here as a function of the substrate wettability using an augmented droplet evaporation model. Three regimes are distinguished by the instantaneous contact angle (CA). In Regime I (CA ≲ 60°), the flat droplet shape results in a small thermal resistance between the liquid-vapor interface and substrate, which mitigates the effect of evaporative cooling; upward gas-phase natural convection enhances evaporation. In Regime II (60 ≲ CA ≲ 90°), evaporative cooling at the interface suppresses evaporation with increasing contact angle and counterbalances the gas-phase convection enhancement. Because effects of the evaporative cooling and gas-phase convection mechanisms largely neutralize each other, the vapor-diffusion-based model can predict the overall evaporation rates in this regime. In Regime III (CA ≳ 90°), evaporative cooling suppresses the evaporation rate significantly and reverses entirely the direction of natural convection induced by vapor concentration gradients in the gas phase. Delineation of these counteracting mechanisms reconciles previous debate (founded on single-surface experiments or models that consider only a subset of the governing transport mechanisms) regarding the applicability of the classic vapor-diffusion model. The vapor diffusion-based model cannot predict the local evaporation flux along the interface for high contact angle (CA ≥ 90°) when evaporative cooling is strong and the temperature gradient along the interface determines the peak local evaporation flux.

Droplet evaporation on heated hydrophobic and superhydrophobic surfaces.

The evaporation characteristics of sessile water droplets on smooth hydrophobic and structured superhydrophobic heated surfaces are experimentally investigated. Droplets placed on the hierarchical superhydrophobic surface subtend a very high contact angle (∼160°) and demonstrate low roll-off angle (∼1°), while the hydrophobic substrate supports corresponding values of 120° and ∼10°. The substrates are heated to different constant temperatures in the range of 40-60 °C, which causes the droplet to evaporate much faster than in the case of natural evaporation without heating. The geometric parameters of the droplet, such as contact angle, contact radius, and volume evolution over time, are experimentally tracked. The droplets are observed to evaporate primarily in a constant-contact-angle mode where the contact line slides along the surface. The measurements are compared with predictions from a model based on diffusion of vapor into the ambient that assumes isothermal conditions. This vapor-diffusion-only model captures the qualitative evaporation characteristics on both test substrates, but reasonable quantitative agreement is achieved only for the hydrophobic surface. The superhydrophobic surface demonstrates significant deviation between the measured evaporation rate and that obtained using the vapor-diffusion-only model, with the difference being amplified as the substrate temperature is increased. A simple model considering thermal diffusion through the droplet is used to highlight the important role of evaporative cooling at the droplet interface in determining the droplet evaporation characteristics on superhydrophobic surfaces.

Buoyancy-induced on-the-spot mixing in droplets evaporating on nonwetting surfaces.

We investigate hitherto-unexplored flow characteristics inside a sessile droplet evaporating on heated hydrophobic and superhydrophobic surfaces and propose the use of evaporation-induced flow as a means to promote efficient "on-the-spot" mixing in microliter-sized droplets. Evaporative cooling at the droplet interface establishes a temperature gradient that induces buoyancy-driven convection inside the droplet. An asymmetric single-roll flow pattern is observed on the superhydrophobic substrate, in stark contrast with the axisymmetric toroidal flow pattern that develops on the hydrophobic substrate. The difference in flow patterns is attributed to the larger height-to-diameter aspect ratio of the droplet (of the same volume) on the superhydrophobic substrate, which dictates a single asymmetric vortex as the stable buoyancy-induced convection mode. A scaling analysis relates the observed velocities inside the droplet to the Rayleigh number. On account of the difference in flow patterns, Rayleigh numbers, and the reduced solid-liquid contact area, the flow velocity is an order of magnitude higher in droplets evaporating on a superhydrophobic substrate as compared to hydrophobic substrates. Flow velocities in all cases are shown to increase with substrate temperature and droplet size: The characteristic time required for mixing of a dye in an evaporating sessile droplet is reduced by ∼8 times on a superhydrophobic surface when the substrate temperature is increased from 40 to 60 °C. The mixing rate is ∼15 times faster on the superhydrophobic substrate compared to the hydrophobic surface maintained at the same temperature of 60 °C.

Assessment of water droplet evaporation mechanisms on hydrophobic and superhydrophobic substrates.

Evaporation rates are predicted and important transport mechanisms identified for evaporation of water droplets on hydrophobic (contact angle ~110°) and superhydrophobic (contact angle ~160°) substrates. Analytical models for droplet evaporation in the literature are usually simplified to include only vapor diffusion in the gas domain, and the system is assumed to be isothermal. In the comprehensive model developed in this study, evaporative cooling of the interface is accounted for, and vapor concentration is coupled to local temperature at the interface. Conjugate heat and mass transfer are solved in the solid substrate, liquid droplet, and surrounding gas. Buoyancy-driven convective flows in the droplet and vapor domains are also simulated. The influences of evaporative cooling and convection on the evaporation characteristics are determined quantitatively. The liquid-vapor interface temperature drop induced by evaporative cooling suppresses evaporation, while gas-phase natural convection acts to enhance evaporation. While the effects of these competing transport mechanisms are observed to counterbalance for evaporation on a hydrophobic surface, the stronger influence of evaporative cooling on a superhydrophobic surface accounts for an overprediction of experimental evaporation rates by ~20% with vapor diffusion-based models. The local evaporation fluxes along the liquid-vapor interface for both hydrophobic and superhydrophobic substrates are investigated. The highest local evaporation flux occurs at the three-phase contact line region due to proximity to the higher temperature substrate, rather than at the relatively colder droplet top; vapor diffusion-based models predict the opposite. The numerically calculated evaporation rates agree with experimental results to within 2% for superhydrophobic substrates and 3% for hydrophobic substrates. The large deviations between past analytical models and the experimental data are therefore reconciled with the comprehensive model developed here.

Nanotextured superhydrophobic electrodes enable detection of attomolar-scale DNA concentration within a droplet by non-faradaic impedance spectroscopy.

Label-free, rapid detection of biomolecules in microliter volumes of highly diluted solutions (sub-femtomolar) is of essential importance for numerous applications in medical diagnostics, food safety, and chem-bio sensing for homeland security. At ultra-low concentrations, regardless of the sensitivity of the detection approach, the sensor response time is limited by physical diffusion of molecules towards the sensor surface. We have developed a fast, low cost, non-faradaic impedance sensing method for detection of synthetic DNA molecules in DI water at attomolar levels by beating the diffusion limit through evaporation of a micro-liter droplet of DNA on a nanotextured superhydrophobic electrode array. Continuous monitoring of the impedance of individual droplets as a function of evaporation time is exploited to dramatically improve the sensitivity and robustness of detection. Formation of the nanostructures on the electrode surface not only increases the surface hydrophobicity, but also allows robust pinning of the droplet contact area to the sensor surface. These two features are critical for performing highly stable impedance measurements as the droplet evaporates. Using this scheme, the detection limit of conventional non-faradaic methods is improved by five orders of magnitude. The proposed platform represents a step-forward towards realization of ultra-sensitive lab-on-chip biomolecule detectors for real time point-of-care application. Further works are however needed to ultimately realize the full potential of the proposed approach to appraise biological samples in complex buffer solutions rather than in DI water.

Droplet evaporation dynamics on a superhydrophobic surface with negligible hysteresis.

We report on experiments of droplet evaporation on a structured superhydrophobic surface that displays very high contact angle (CA ∼ 160 deg), and negligible contact angle hysteresis (<1 deg). The droplet evaporation is observed to occur in a constant-contact-angle mode, with contact radius shrinking for almost the entire duration of evaporation. Experiments conducted on Teflon-coated smooth surface (CA ∼ 120 deg) as a baseline also support an evaporation process that is dominated by a constant-contact-angle mode. The experimental results are compared with an isothermal diffusion model for droplet evaporation from the literature. Good agreement is observed for the Teflon-coated smooth surface between the analytical expression and experimental results in terms of the total time for evaporation, transient volume, contact angle, and contact radius. However, for the structured superhydrophobic surface, the experiments indicate that the time taken for complete evaporation of the droplet is greater than the predicted time, across all droplet volumes. This disparity is attributed primarily to the evaporative cooling at the droplet interface due to the high aspect ratio of the droplet and also the lower effective thermal conductivity of the substrate due to the presence of air gaps. This hypothesis is verified by numerically evaluating the temperature distribution along the droplet interface. We propose a generalized relation for predicting the instantaneous volume of droplets with initial CA > 90 deg, irrespective of the mode of evaporation.

Hybrid surface design for robust superhydrophobicity.

Surfaces may be rendered superhydrophobic by engineering the surface morphology to control the extent of the liquid-air interface and by the use of low-surface-energy coatings. The droplet state on a superhydrophobic surface under static and dynamic conditions may be explained in terms of the relative magnitudes of the wetting and antiwetting pressures acting at the liquid-air interface on the substrate. In this paper, we discuss the design and fabrication of hollow hybrid superhydrophobic surfaces which incorporate both communicating and noncommunicating air gaps. The surface design is analytically shown to exhibit higher capillary (or nonwetting) pressure compared to solid pillars with only communicating air gaps. Six hybrid surfaces are fabricated with different surface parameters selected such that the Cassie state of a droplet is energetically favorable. The robustness of the surfaces is tested under dynamic impingement conditions, and droplet dynamics are explained using pressure-based transitions between Cassie and Wenzel states. During droplet impingement, the effective water hammer pressure acting due to the sudden change in the velocity of the droplet is determined experimentally and is found to be at least 2 orders of magnitude less than values reported in the literature. The experiments show that the water hammer pressure depends on the surface morphology and capillary pressure of the surface. We propose that the observed reduction in shock pressure may be attributed to the presence of air gaps in the substrate. This feature allows liquid deformation and hence avoids the sudden stoppage of the droplet motion as opposed to droplet behavior on smooth surfaces.

Electrowetting-induced dewetting transitions on superhydrophobic surfaces.

We develop and demonstrate the use of electrowetting to achieve the dewetting (Wenzel-to-Cassie transition) of superhydrophobic surfaces. We effect this transition by means of an opposing flat plate and a three-electrode system; the liquid droplet is completely pulled out of its wetted Wenzel state upon the application of a suitable voltage. We also experimentally quantify the dissipative forces preventing the dewetting transition. The energy associated with these nonconservative forces is comparable to the interfacial energies.

Dynamics of droplet motion under electrowetting actuation.

The static shape of droplets under electrowetting actuation is well understood. The steady-state shape of the droplet is obtained on the basis of the balance of surface tension and electrowetting forces, and the change in the apparent contact angle is well characterized by the Young-Lippmann equation. However, the transient droplet shape behavior when a voltage is suddenly applied across a droplet has received less attention. Additional dynamic frictional forces are at play during this transient process. We present a model to predict this transient behavior of the droplet shape under electrowetting actuation. The droplet shape is modeled using the volume of fluid method. The electrowetting and dynamic frictional forces are included as an effective dynamic contact angle through a force balance at the contact line. The model is used to predict the transient behavior of water droplets on smooth hydrophobic surfaces under electrowetting actuation. The predictions of the transient behavior of droplet shape and contact radius are in excellent agreement with our experimental measurements. The internal fluid motion is explained, and the droplet motion is shown to initiate from the contact line. An approximate mathematical model is also developed to understand the physics of the droplet motion and to describe the overall droplet motion and the contact line velocities.