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.     

Slip-stick wetting and large contact angle hysteresis on wrinkled surfaces

Wetting on a corrugated surface that is formed via wrinkling of a hard skin layer formed by UV oxidation (UVO) of a poly(dimethylsiloxane) (PDMS) slab is studied using advancing and receding water contact angle measurements. The amplitude of the wrinkled pattern can be tuned through the pre-strain of the PDMS prior to surface oxidation. These valleys and peaks in the surface topography lead to anisotropic wetting by water droplets. As the droplet advances, the fluid is free to move along the direction parallel to the wrinkles, but the droplet moving orthogonal to the wrinkles encounters energy barriers due to the topography and slip-stick behavior is observed. As the wrinkle amplitude increases, anisotropy in the sessile droplet increases between parallel and perpendicular directions. For the drops receding perpendicular to the wrinkles formed at high strains, the contact angle tends to decrease steadily towards zero as the drop volume decreases, which can result in apparent hysteresis in the contact angle of over 100°. The wrinkled surfaces can exhibit high sessile and advancing contact angles (>115°), but the receding angle in these cases is generally vanishing as the drop is removed. This effect results in micrometer sized drops remaining in the grooves for these highly wrinkled surfaces, while the flat analogous UVO-treated PDMS shows complete removal of all macroscopic water drops under similar conditions. These wetting characteristics should be considered if these wrinkled surfaces are to be utilized in or as microfluidic devices.     

Dynamic behavior of water droplets on solid surfaces with pillar-type nanostructures

In the present study, we investigated the static and dynamic behavior of water droplets on solid surfaces featuring pillar-type nanostructures by using molecular dynamics simulations. We carried out the computation in two stages. As a result of the first computational stage, an initial water cube reached an equilibrium state at which the water droplet showed different shapes depending on the height and the lateral and gap dimensions of the pillars. In the second computational stage, we applied a constant body force to the static water droplet obtained from the first computational stage and evaluated the dynamic behavior of the water droplet as it slid along the pillar-type surface. The dynamic behavior of the water droplet, which could be classified into three different groups, depended on the static state of the water droplet, the pillar characteristics (e.g., height and the lateral and gap dimensions of the pillars), and the magnitude of the applied body force. We obtained the advancing and receding contact angles and the corresponding contact angle hysteresis of the water droplets, which helped classify the water droplets into the three different groups.     

Sliding of water droplets on hydrophobic surfaces with various hydrophilic region sizes

Four patterned surfaces with hydrophilic areas of different sizes were prepared using photolithography with a smooth octadecyltrimethoxysilane (ODS) hydrophobic coating. The hydrophilic area in the surfaces was aligned hexagonally with a constant area fraction. The sliding angle and contact angle hysteresis of the water droplets increased concomitantly with increasing pattern size. The increase of the contact line distortion between defects at the receding side plays an important role in this trend. The droplet sliding velocity also increased concomitantly with increasing pattern size. This trend was simulated by a simple flow model. The contribution of the interface between the ODS region and the hydrophilic area was deduced from this trend. This study demonstrated the different size dependency of the chemical surface defects for sliding behavior between the critical moment at which a droplet slides down and the period when a droplet is sliding.     

Wetting of nanogrooved polymer surfaces

Molecular dynamics simulations were used to study the wetting of nanogrooved PE and PVC polymer surfaces. The contact angles, equilibrium states, and equilibrium shapes of two nanosized water droplets were analyzed on surfaces with 1D-arranged periodic roughness of various dimensions. The composite solid-liquid contact, which is preferred in practical applications and in which a droplet rests on top of the surface asperities, was observed on the roughest PE surfaces, whereas water filled the similar but slightly deeper grooves on PVC surfaces. The transition from the wetted to composite contact regime occurred when the contact angle with a flat surface reached the value at which the apparent Wenzel and Cassie contact angles are equal. Droplets on grooved PE surfaces with the composite contact exhibited contact angles in agreement with Cassie's equation, but the increase in hydrophobicity on smoother surfaces with the wetted contact was less than expected from Wenzel's equation. The difference between the simulated and theoretical values decreased as the dimensions of the surface grooves increased. Only a slight increase or even a slight decrease in the contact angles was observed on the grooved PVC surfaces, owing to the less hydrophobic nature of the flat PVC surface. On both polymers, the nanodroplet assumed a spherical shape in the composite contact. Only minor anisotropy was observed in the wetted contact on PE surfaces, whereas even a highly anisotropic shape was seen on the grooved PVC surfaces. The contact angle in the direction of the grooves was smaller than that in the perpendicular direction, and the difference between the two angles decreased with the increasing size of the water droplet.     

Displacement of liquid droplets on a surface by a shearing air flow

The motion of droplets on surfaces is crucial to the performance of a wide range of processes; this study examines the initiation of droplet motion through a shearing mechanism generated here by a controlled air flow. Systematic experiments are carried out for a range of fluids and well defined surfaces. A model is postulated that balances surface tension forces at the contact line and the drag force due to the air motion. Experiments reveal that the critical velocity at which droplet motion is initiated depends on the contact angle and the droplet size. Visualizations highlight three modes of motion: (I) the droplet retains a footprint similar to that at the point of motion; (II) a tail exists at the rear of the droplet; (III) a trail remains behind the droplet (that can shed smaller droplets). The predictions of droplet initiation velocity are good for type I motion, in accordance with the assumptions inherent within the model. This model confirms the dominant physics associated with the initiation of droplet motion and provides a useful predictive expression.     

Anisotropic wetting characteristics on submicrometer-scale periodic grooved surface

Submicrometer-scale periodic structures consisting of parallel grooves were prepared on azobenzene-containing multiarm star polymer films by laser interference. The wetting characteristics on the patterned surfaces were studied by contact angle measurements. Macroscopic distortion of water drops was found on such small-scale surface structures, and the contact angles measured from the direction parallel to the grooves were larger than those measured from the perpendicular direction. A thermodynamic model was developed to calculate the change in the surface free energy as a function of the instantaneous contact angle when the three-phase contact line (TPCL) moves along the two orthogonal directions. It was found that the fluctuations, i.e., energy barriers, on the energy versus contact angle curves are crucial to the analysis of wetting anisotropy and contact angle hysteresis. The calculated advancing and receding contact angles from the energy versus contact angle curves were in good agreement with those measured experimentally. Furthermore, with the groove depth increasing, both the degree of wetting anisotropy and the contact angle hysteresis perpendicular to the grooves increased as a result of the increase in the energy barrier. The theoretical critical value of the groove depth, above which the anisotropic wetting appears, was determined to be 16 nm for the grooved surface with a wavelength of 396 nm. On the other hand, the effect of the groove wavelength on the contact angle hysteresis perpendicular to the grooves was also interpreted on the basis of the thermodynamic model. That is, with the wavelength decreasing, the contact angle hysteresis increased due to the increase in the number of energy barriers. These results may provide theoretical evidence for the design and application of anisotropic wetting surface.     

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.     

Sliding behavior of liquid droplets on tilted Langmuir-Blodgett surfaces

The sliding behavior of liquid droplets on inclined Langmuir-Blodgett surfaces was investigated. The critical sliding angle defined as the tilt angle of the surface at which the drop slides down as well as the advancing and receding contact angles was measured for five different liquids on five surfaces. In addition, the contact line geometry was analyzed at critical sliding angle. The experimental relationship between the surface tension forces resulting from contact angle hysteresis and the weight of the drop was compared to theoretical predictions. Even though the shape of the drop bases was found as skewed ellipses, a model assuming parallel-sided elongated drops is shown to describe reasonably the experimental values. This result probably indicates the main influence of the capillary forces at the rear and front edges of the drop with respect to that exerted on the lateral sides.     

Anisotropic drop morphologies on corrugated surfaces

The spreading of liquid drops on surfaces corrugated with micrometer-scale parallel grooves is studied both experimentally and numerically. Because of the surface patterning, the typical final drop shape is no longer spherical. The elongation direction can be either parallel or perpendicular to the direction of the grooves, depending on the initial drop conditions. We interpret this result as a consequence of both the anisotropy of the contact line movement over the surface and the difference in the motion of the advancing and receding contact lines. Parallel to the grooves, we find little hysteresis due to the surface patterning and that the average contact angle approximately conforms to Wenzel's law as long as the drop radius is much larger than the typical length scale of the grooves. Perpendicular to the grooves, the contact line can be pinned at the edges of the ridges, leading to large contact angle hysteresis.     

Droplet compression and relaxation by a superhydrophobic surface: contact angle hysteresis

In this article, the contact angle hysteresis (CAH) of acrylic glass is experimentally and theoretically studied through the compression-relaxation process of droplets by using a superhydrophobic surface with negligible CAH effect. In contrast to the existing technique in which the volume of the droplet changes during the measurement of CAH, this procedure is carried out at a constant volume of the droplet. By observing the base diameter (BD) and the contact angle (CA) of the droplet during the compression-relaxation process, the wetting behavior of the droplet can be divided into two regimes, the contact line withdrawal and the contact line pinning regimes, depending on the gap thickness (H) at the end of the compression process. During the compression process, both regimes possess similar droplet behavior; the contact line will move outward and the BD will expand while the CA remains at the advancing angle. During the relaxation process, the two regimes are significantly different. In the contact line withdrawal regime, the contact line will withdraw with the CA remaining at the receding angle. In the contact line pinning regime, however, the contact line will be pinned at the final position and the CA will decline to a certain value higher than the receding angle. Furthermore, the advancing pinning behavior can also be realized through a successive compression-relaxation process. On the basis of the liquid-induced defects model, Surface Evolver simulations are performed to reproduce the behavior of the droplet during the compression-relaxation process; both contact line withdrawal and pinning regimes can also be identified. The results of the experiment and simulation agree with each other very well.     

Two-dimensional fluidics based on differential lyophobicity and gravity

We have prepared planar fluidics devices using binary chemical patterns consisting of hydrophobic "roads" on which water droplets slide easily and more hydrophobic "curbs" that direct droplet motion. Contact angle and contact angle hysteresis both control the motion of liquid droplets on surfaces. The difference between the advancing contact angles of the two regions prevents the liquid from crossing the interface between them. The low hysteresis of the roads allows facile movement. Gravity (slight tilting of samples) forces droplets to move effortlessly in defined pathways even though the difference in contact angles is not large and both regions are hydrophobic.     

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.     

The dynamics of impacting water droplets on alkanethiol self-assembled monolayers with co-adsorbed CH3 and CO2H terminal groups

The impact of water droplets (diameter 3.6 mm) at a fixed Weber number of 59 on solid surfaces with precisely tailored surface wettabilities was studied experimentally using a high-speed imaging camera at 2500 frames per second. Solid surface wettability was varied using four fractional mixtures of self-assembled monolayers of 1-octadecanethiol and 16-mercaptohexadecanoic acid. The surfaces so obtained are characterized for contact angle and chemical functionality using the axisymmetric drop shape analysis profile (ADSA-P) technique and Fourier transform infrared spectroscopy (FT-IR). Our results correlate the wetting effects of the impacting droplets with the surface energy and contact angle measurements of the tailored surfaces. Literature models for the maximum spreading diameter are employed and compared with those from our experiments. An equation is also proposed for the maximum spreading diameter which makes use of the correct contact angles and results in the least error among the models considered. As a consequence of Young's equation, the correct contact angles to be used for droplet impact dynamics should be the corresponding advancing angles on a smooth substrate of interest. We also conclude that accurate examination of literature models requires careful experimentation on impact dynamic data on well-prepared and characterized surfaces such as those presented here.     

Analysis of the relationship between liquid droplet size and contact angle

The purpose of this paper is to present a consistent theoretical concept that can explain the various physical phenomena associated with the effect of droplet size on contact angle for droplets on solid surfaces, and with the geometry of the liquid/gas/solid contact line in general. Two droplet geometries have been considered: uniformly elongated droplets and axisymmetric droplets. It has been shown that the contact angle for elongated droplets is size-independent and, thus, satisfies the Young equation for constant material and interfacial properties. On the other hand, whereas the contact angle for axisymmetric droplets is size-dependent and does not satisfy the original Young equation, it is shown that this contact angle can still be predicted for any combination of droplet and substrate materials, and a given mass of the droplet. The theoretical work has been combined with the development of numerical schemes of solving the Laplace-Young equation for various droplet geometries. The proposed approach has been applied to different material/substrate combinations and validated against several sets of experimental data. As a result, a method has been developed for predicting the contact angle of both long and axisymmetric sessile droplets of arbitrary sizes for given liquid/solid/gas properties.     

Modeling contact angle hysteresis of a liquid droplet sitting on a cosine wave-like pattern surface

A liquid droplet sitting on a hydrophobic surface with a cosine wave-like square-array pattern in the Wenzel state is simulated by using the Surface Evolver to determine the contact angle. For a fixed drop volume, multiple metastable states are obtained at two different surface roughnesses. Unusual and non-circular shape of the three-phase contact line of a liquid droplet sitting on the model surface is observed due to corrugation and distortion of the contact line by structure of the roughness. The contact angle varies along the contact line for each metastable state. The maximum and minimum contact angles among the multiple metastable states at a fixed viewing angle correspond to the advancing and the receding contact angles, respectively. It is interesting to observe that the advancing/receding contact angles (and contact angle hysteresis) are a function of viewing angle. In addition, the receding (or advancing) contact angles at different viewing angles are determined at different metastable states. The contact angle of minimum energy among the multiple metastable states is defined as the most stable (equilibrium) contact angle. The Wenzel model is not able to describe the contact angle along the three-phase contact line. The contact angle hysteresis at different drop volumes is determined. The number of the metastable states increases with increasing drop volume. Drop volume effect on the contact angles is also discussed.     

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.     

Effect of nonionic surfactant on wetting behavior of an evaporating drop under a reduced pressure environment

The evaporation of sessile drops at reduced pressure is investigated. The evaporation of water droplets on aluminum and PTFE surfaces at reduced pressure was compared. It was found that water droplets on an aluminum surface exhibit a 'depinning jump' at subatmospheric pressures. This is when a pinned droplet suddenly depins, with an increase in contact angle and a simultaneous decrease in the base width. The evaporation of sessile water droplets with a nonionic surfactant (Triton X-100) added to an aluminum surface was then studied. The initial contact angle exhibited a minimum at 0.001 wt% Triton X-100. A maximum in the evaporation rate was also observed at the same concentration. Droplets with low surfactant concentrations are found to exhibit the 'depinning jump.' It is thought that the local concentration of the surfactant causes a gradient of surface tension. The balance at the contact angle is dictated by complex phenomena, including surfactant diffusion and adsorption processes at interfaces. Due to the strong evaporation near the triple line, an accumulation of the surfactant will lead to a surface tension gradient along the interface. The gradient of surface tension will influence the wetting behavior (Marangoni effect). At low surfactant concentrations the contact line depins under the strong effect of surface tension gradient that develops spontaneously over the droplet interface due to surfactant accumulation near the triple line. The maximum evaporation rate corresponds to a minimum contact angle for a pinned droplet.