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.     

Static and dynamic contact angles of water droplet on a solid surface using molecular dynamics simulation

The present study investigates the variation of static contact angle of a water droplet in equilibrium with a solid surface in the absence of a body force and the dynamic contact angles of water droplet moving on a solid surface for different characteristic energies using the molecular dynamics simulation. With increasing characteristic energy, the static contact angle in equilibrium with a solid surface in the absence of a body force decreases because the hydrophobic surface changes its characteristics to the hydrophilic surface. In order to consider the effect of moving water droplet on the dynamic contact angles, we apply the constant acceleration to an individual oxygen and hydrogen atom. In the presence of a body force, the water droplet changes its shape with larger advancing contact angle than the receding angle. The dynamic contact angles are compared with the static contact angle in order to see the effect of the presence of a body force.     

Analysis of droplet evaporation on a superhydrophobic surface

The evaporation process for small, 1-2-mm-diameter droplets of water from patterned polymer surfaces is followed and characterized. The surfaces consist of circular pillars (5-15 microm diameter) of SU-8 photoresist arranged in square lattice patterns such that the center-to-center separation between pillars is 20-30 microm. These types of surface provide superhydrophobic systems with theoretical initial Cassie-Baxter contact angles for water droplets of up to 140-167 degrees, which are significantly larger than can be achieved by smooth hydrophobic surfaces. Experiments show that on these SU-8 textured surfaces water droplets initially evaporate in a pinned contact line mode, before the contact line recedes in a stepwise fashion jumping from pillar to pillar. Provided the droplets of water are deposited without too much pressure from the needle, the initial state appears to correspond to a Cassie-Baxter one with the droplet sitting upon the tops of the pillars. In some cases, but not all, a collapse of the droplet into the pillar structure occurs abruptly. For these collapsed droplets, further evaporation occurs with a completely pinned contact area consistent with a Wenzel-type state. It is shown that a simple quantitative analysis based on the diffusion of water vapor into the surrounding atmosphere can be performed, and estimates of the product of the diffusion coefficient and the concentration difference (saturation minus ambient) are obtained.     

Dynamic effects of bouncing water droplets on superhydrophobic surfaces

Superhydrophobic surfaces have considerable technological potential for various applications due to their extreme water repellent properties. Superhydrophobic surfaces may be generated by the use of hydrophobic coating, roughness, and air pockets between solid and liquid. Dynamic effects, such as the bouncing of a droplet, can destroy the composite solid-air-liquid interface. The relationship between the impact velocity of a droplet and the geometric parameters affects the transition from the solid-air-liquid interface to the solid-liquid interface. Therefore, it is necessary to study the dynamic effect of droplets under various impact velocities. We studied the dynamic impact behavior of water droplets on micropatterned silicon surfaces with pillars of two different diameters and heights and with varying pitch values. A criterion for the transition from the Cassie and Baxter regime to the Wenzel regime based on the relationship between the impact velocity and the parameter of patterned surfaces is proposed. The trends are explained based on the experimental data and the proposed transition criterion. For comparison, the dynamic impact behavior of water droplets on nanopatterned surfaces was investigated. The wetting behavior under various impact velocities on multiwalled nanotube arrays also was investigated. The physics of wetting phenomena for bouncing water droplet studies here is of fundamental importance in the geometrical design of superhydrophobic surfaces.     

仿生表面液固界面摩擦力的动态调控

仿生超疏水材料在自清洁、防雾抗冰、油水分离、集水等领域有着重要应用;而在不同疏水状态之间的转换将大大促进仿生超疏水材料在智能技术领域的应用.利用软印刷技术将玫瑰花表面微观结构转印到聚氨酯弹性体PU膜表面,利用机械应力实现表面微结构的动态实时调控,实现了表面微观结构在各向同性与各向异性之间的可逆转换;利用毛细管投影传感技...     

Methodology for calculating the volume of condensate droplets on topographically modified, microgrooved surfaces

Liquid droplets on micropatterned surfaces consisting of parallel grooves tens of micrometers in width and depth are considered, and a method for calculating the droplet volume on these surfaces is presented. This model, which utilizes the elongated and parallel-sided nature of droplets condensed on these microgrooved surfaces, requires inputs from two droplet images at ? = 0° and ? = 90°--namely, the droplet major axis, minor axis, height, and two contact angles. In this method, a circular cross-sectional area is extruded the length of the droplet where the chord of the extruded circle is fixed by the width of the droplet. The maximum apparent contact angle is assumed to occur along the side of the droplet because of the surface energy barrier to wetting imposed by the grooves--a behavior that was observed experimentally. When applied to water droplets condensed onto a microgrooved aluminum surface, this method was shown to calculate the actual droplet volume to within 10% for 88% of the droplets analyzed. This method is useful for estimating the volume of retained droplets on topographically modified, anisotropic surfaces where both heat and mass transfer occur and the surface microchannels are aligned parallel to gravity to assist in condensate drainage.     

Exceptional superhydrophobicity and low velocity impact icephobicity of acetone-functionalized carbon nanotube films

We present a simple method to produce carbon nanotube-based films with exceptional superhydrophobicity and impact icephobicity by depositing acetone-treated single-walled carbon nanotubes on glass substrates. This method is scalable and can be adopted for any substrate, both flexible and rigid. These films have indicated a high contact angle, in the vicinity of 170°, proved both by static and dynamic analysis processes. The dynamic evaporation studies indicated that a droplet deposited on the treated films evaporated in the constant contact angle mode for more than 80% of the total evaporation time, which is definitely a characteristic of superhydrophobic surfaces. Furthermore, the acetone-functionalized films showed a strong ability to mitigate ice accretion from supercooled water droplets (-8 °C), when the droplets were found to bounce off the films tilted at 30°. The untreated nanotube films did not indicate similar behavior, and the supercooled water droplets remained attached to the films' surfaces. Such studies could be the foundation of highly versatile technologies for both water and ice mitigation.     

Sliding variability of droplets on a hydrophobic incline due to surface entrained air bubbles

The ability of a liquid droplet to move on an incline has important ramifications in discrete volume fluidic devices. By taking advantage of the spontaneous and copious formation of visible air bubbles within water droplets on a polytetrafluoroethylene (PTFE) surface, we uncovered a direct correlation between their presence and the ability of droplets to slide down an incline. We forward two possible mechanisms to account for this behavior. The first is attributed to the air bubbles creating regions where additional solid-liquid-vapor phase interfaces are present; wherein due to the buoyancy force acting upwards, the orientation of the contact angles of each bubble (which should also be in hysteresis but in the opposite direction of the hysteresis at the droplet rim contact lines) dictate that the net force of the bubbles in the droplet act down an incline. We show here that this mechanism cannot fully account for the bubble enhanced sliding behavior. The second mechanism is based on the occurrence of the droplet front advancing first, causing the droplet to elongate and thus allowing the receding contact line to partially sweep inwards over the bubbles. This causes a series of point-wise disruptions on the contact line that permits the droplet to slide down more readily. The relatively short time of ～180s during which these micron sized bubbles decrease in size indicates a possibility of this mechanism contributing to a transient means to reduce the retention force of droplets that reside on hydrophobic surfaces.     

Modeling of wetting: a study of nanowetting at rough and heterogeneous surfaces

Molecular dynamics simulations were performed to study the behavior of nanoscale water droplets at solid surfaces. Simulations of droplets on heterogeneous patterned surfaces show that the relative sizes of the domains and the droplets play an important role as do the interactions between the solid and the liquid, particularly when the domain width is comparable to the droplet radius. For pillar surfaces, a transition is observed between the Wenzel and the Cassie and Baxter regimes with increasing pillar height. The effects of pillar width and the gap between the pillars were also examined. The simulations show clearly the importance of the detailed topography and composition of the solid surface.     

Evaporative characteristics of sessile nanofluid droplet on micro‐structured heated surface

Micro‐structure patterned substrates attract our attention due to the special and programmable wettabilities. The interaction between the liquid and micro/nano structures gives rise to controllable spreading and thus evaporation. For exploration of the application versatility, the introduction of nanoparticles in liquid droplet results in interaction among particles, liquid and microstructures. In addition, temperature of the substrates strongly affects the spreading of the contact line and the evaporative property. The evaporation of sessile droplets of nanofluids on a micro‐grooved solid surface is investigated in terms of liquid and surface properties. The patterned nickel surface used in the experiments is designed and fabricated with circular and rectangular shaped pillars whose size ratios between interval and pillars is fixed at 5. The behavior is firstly compared between nanofluid and pure liquid on substrates at room temperature. For pure water droplet, the drying time is relatively longer due to the receding of contact line which slows down the liquid evaporation. Higher concentrations of nanoparticles tend to increase the total evaporation time. With varying concentrations of graphite at nano scale from 0.02% to 0.18% with an interval at 0.04% in water droplets and the heating temperature from 22 to 85°C, the wetting and evaporation of the sessile droplets are systematically studied with discussion on the impact parameters and the resulted liquid dynamics as well as the stain. The interaction among the phases together with the heating strongly affects the internal circulation inside the droplet, the evaporative rate and the pattern of particles deposition.     

An empirically validated analytical model of droplet dynamics in electrowetting on dielectric devices

Explicit analytical models that describe the capillary force on confined droplets actuated in electrowetting on dielectric devices and the reduction in that force by contact angle hysteresis as a function of the three-dimensional shape of the droplet interface are presented. These models are used to develop an analytical model for the transient position and velocity of the droplet. An order of magnitude analysis showed that droplet motion could be modeled using the driving capillary force opposed by contact angle hysteresis, wall shear, and contact line friction. Droplet dynamics were found to be a function of gap height, droplet radius, surface tension, fluid density, the initial and deformed contact angles, contact angle hysteresis, and friction coefficients pertaining to viscous wall friction and contact line friction. The first four parameters describe the device geometry and fluid properties; the remaining parameters were determined experimentally. Images of the droplet during motion were used to determine the evolution of the shape, position, and velocity of the droplet with time. Comparisons between the measured and predicted results show that the proposed model provides good accuracy over a range of practical voltages and droplet aspect ratios.     

Dynamics of water droplets detached from porous surfaces of relevance to PEM fuel cells

The detachment of liquid droplets from porous material surfaces used with proton exchange membrane (PEM) fuel cells under the influence of a cross-flowing air is investigated computationally and experimentally. CCD images taken on a purpose-built transparent fuel cell have revealed that the water produced within the PEM is forming droplets on the surface of the gas-diffusion layer. These droplets are swept away if the velocity of the flowing air is above a critical value for a given droplet size. Static and dynamic contact angle measurements for three different carbon gas-diffusion layer materials obtained inside a transparent air-channel test model have been used as input to the numerical model; the latter is based on a Navier–Stokes equations flow solver incorporating the volume of fluid (VOF) two-phase flow methodology. Variable contact angle values around the gas–liquid–solid contact-line as well as their dynamic change during the droplet shape deformation process, have allowed estimation of the adhesion force between the liquid droplet and the solid surface and successful prediction of the separation line at which droplets loose their contact from the solid surface under the influence of the air stream flowing around them. Parametric studies highlight the relevant importance of various factors affecting the detachment of the liquid droplets from the solid surface.     

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.     

Control over wettability of polyethylene glycol surfaces using capillary lithography

We demonstrate that wettability of poly(ethylene glycol) (PEG) surfaces can be controlled using nanostructures with various geometrical features. Capillary lithography was used to fabricate PEG nanostructures using a new ultraviolet (UV) curable mold consisting of functionalized polyurethane with acrylate group (MINS101m, Minuta Tech.). Two distinct wetting states were observed depending of the height of nanostructures. At relatively lower heights (< 300 nm for 150 nm pillars with 500 nm spacing), the initial contact angle of water was less than 80 degrees and the water droplet easily invaded into the surface grooves, leading to a reduced contact angle at equilibrium (Wenzel state). At relatively higher heights (> 400 nm for 150 nm pillars with 500 nm spacing), on the other hand, the nanostructured PEG surface showed hydrophobic nature and no significant change in contact angle was observed with time (Cassie state). The presence of two wetting states was also confirmed by dynamic wetting properties and contact-angle hysteresis. The wetting transition from hydrophilic (bare PEG surface) to hydrophobic (PEG nanostructures) was described by the Cassie-Baxter equation assuming that enhanced hydrophobicity is due to the heterogeneous wetting mediated by an air pocket on the surface. The measured contact angles in the Cassie state were increased with increasing air fraction, in agreement with the theoretical prediction.     

Wetting phenomena on micro-grooved aluminum surfaces and modeling of the critical droplet size

The behavior of water droplets on aluminum surfaces with parallel grooves tens of microns in width and depth is considered, and a mechanistic model is developed for predicting the critical droplet size-droplets at incipient sliding due to gravity. The critical droplet size is nearly 50% smaller on micro-grooved surfaces than on the same surface without micro-grooves. The application of existing models fails to predict this behavior, and a new model based on empiricism is developed. The new model provides reasonable predictions of the critical droplet size for a given inclination angle, advancing contact angle, and maximum contact angle. When the grooves are aligned parallel to gravity, the maximum apparent contact angle does not occur at the advancing front but rather along the side of the droplet because of contact-line pinning. Droplets on these surfaces are elongated and possess a parallel-sided base contour shape. Novel data are provided for droplets in a Wenzel state, a Cassie-Baxter state, and combined state on micro-grooved surfaces, and the ability of the empirical model to handle these variations is explored. These findings may be important to a broad range of engineering applications.     

Voltage control of droplet interface bilayer lipid membrane dimensions

A novel approach to control the area of anchor-free droplet interface bilayer (DIB) lipid membranes is presented. Unsupported DIB lipid membranes are formed at the interface of phospholipid-coated aqueous droplets dispensed in dodecane oil. Using electrodes inserted into the droplets, an external voltage is applied which modulates the effective DIB area. Electrical (capacitance or current) and optical (imaging of DIB lateral length) recordings were simultaneously performed. Alpha-hemolysin (αHL) single channel insertions into the DIB were recorded. Currents across the DIB were measured as a function of voltage and αHL concentration in the droplets. Nonlinear response is observed for current, DIB lateral length and area, and capacitance with respect to voltage. Voltage induced changes in interfacial tension modulated the DIB-oil contact angle and the membrane contact length, which provided control of membrane dimensions. Comparison of these results is made to the electrowetting effect, which is also governed by effect of voltage on the interfacial tension. This approach provides active control of the number of ion channels inserted into the DIB.     

Biomimetic superhydrophobic and highly oleophobic cotton textiles

We report a biomimetic procedure to prepare superhydrophobic cotton textiles. By in situ introducing silica particles to cotton fibers to generate a dual-size surface roughness, followed by hydrophobization with polydimethylsiloxane (PDMS), normally hydrophilic cotton has been easily turned superhydrophobic, which exhibits a static water contact angle of 155 degrees for a 10 microL droplet. The roll-off angle of water droplets depends on the droplet volume, ranging from 7 degrees for a droplet of 50 microL to 20 degrees for a 7 microL droplet. When a perfluoroalkyl chain is introduced to the silica particle surface, the superhydrophobic textile also becomes highly oleophobic, as demonstrated by a static contact angle of 140 degrees and a roll-off angle of 24 degrees for a 15 microL sunflower oil droplet.     

Interfacial oil droplets

Very small, discrete oil droplets can form at the solid-liquid interface. We demonstrate this effect through formation of decane droplets at the interface between an aqueous ethanol solution and silicon wafers that have been made hydrophobic through self-assembly of octadecyltrichlorosilane (OTS). The droplets have a lens-like shape; the shape is approximately a spherical cap with a contact angle < 25 degrees. The heights of the droplets are about 2-50 nm, and diameters at the three-phase boundary are about 100-600 nm in 25% ethanol solution. The size and contact angle can be varied by changing the ethanol concentration. The contact angle of the very small droplets (height < 20 nm) is similar to the contact angle of macroscopic droplets (height approximately equal to 1 mm), so the line tension is very small. The droplets are only stable for a few hours: they gradually lose mass, presumably through Ostwald ripening. The drop perimeter is not pinned during ripening but retreats across the solid. We form the droplets by direct adsorption from an emulsion; evidence for adsorption is obtained by comparing the drop volumes in bulk to the volumes at the interface. The droplet sizes are obtained by dynamic light scattering and atomic force microscopy.     

Mean-field theory of liquid droplets on roughened solid surfaces: application to superhydrophobicity

We present calculations of the density distributions and contact angles of liquid droplets on roughened solid surfaces for a lattice gas model solved in a mean-field approximation. For the case of a smooth surface, this approach yields contact angles that are well described by Young's equation. We consider rough surfaces created by placing an ordered array of pillars on a surface, modeling so-called superhydrophobic surfaces, and we have made calculations for a range of pillar heights. The apparent contact angle follows two regimes as the pillar height increases. In the first regime, the liquid penetrates the interpillar volume, and the contact angle increases with pillar height before reaching a constant value. This behavior is similar to that described by the Wenzel equation for contact angles on rough surfaces, although the contact angles are underestimated. In the second regime, the liquid does not penetrate the interpillar volume substantially, and the contact angle is independent of the pillar height. This situation is similar to that envisaged in the Cassie-Baxter equation for contact angles on heterogeneous surfaces, but the contact angles are overestimated by this equation. For larger pillar heights, two states of the droplet can be observed, one Wenzel-like and the other Cassie-like.     

Water wetting transition parameters of perfluorinated substrates with periodically distributed flat-top microscale obstacles

Superhydrophobicity is obtained on photolithographically structured silicon surfaces consisting of flat-top pillars after a perfluorosilanization treatment. Systematic static contact angle measurements were carried out on these surfaces as a function of pillar parameters that geometrically determine the surface roughness, including pillar height, diameter, top perimeter, overall filling factor, and disposition. In line with thermodynamics models, two regimes of static contact angles are observed varying each parameter independently: the "Cassie" regime, in which the water drop sits suspended on top of the pillars (referred to as composite), corresponding to experimental contact angles greater than 140-150 degrees, and the "Wenzel" regime, in which water completely wets the asperities (referred to as wetted), corresponding to lower experimental contact angles. A transition between the Cassie and Wenzel regimes corresponds to a set of well-defined parameters. By smoothly depositing water drops on the surfaces, this transition is observed for surface parameter values far from the calculated ones for the thermodynamic transition, therefore offering evidence for the existence of metastable composite states. For all studied parameters, the position of the experimental transition correlates well with a rough estimation of the energy barrier to be overcome from a composite metastable state in order to reach the thermodynamically favored Wenzel state. This energy barrier is estimated as the surface energy variation between the Cassie state and the hypothetical composite state with complete filling of the surface asperities by water, keeping the contact angle constant.