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.     

Droplet spreading on microstriped surfaces

When a droplet of fluid is deposited on a surface with chemical and/or topological patterns, its static shape is highly dependent on the 2D distribution of the patterns. In the case of chemical stripes, three distinct spreading regimes have been observed as a function of wettability contrast between the two kind of stripes. For low wettability contrast, the droplet spreads with the same [corrected] velocity normal and parallel to the stripes [corrected] and the macroscopic contact angle is close to Cassie's contact angle. When the wettability contrast is intermediate/high, the resulting shape of the droplets is elongated. In the intermediate wettability contrast regime, an ideal situation shows stick and slip behavior of the contact line, during which the contact line jumps from one stripe to another. For a high wettability contrast, the confinement of the fluid between two chemical stripes leads to a 2D spreading.     

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.     

Smart design of stripe-patterned gradient surfaces to control droplet motion

The motion of droplets under the influence of lithographically created anisotropic chemically defined patterns is described and discussed. The patterns employed in our experiments consist of stripes of alternating wettability: hydrophobic stripes are created via fluorinated self-assembled monolayers, and for hydrophilic stripes, the SiO(2) substrate is used. The energy gradient required to induce the motion of the droplets is created by varying the relative widths of the stripes in such a way that the fraction of the hydrophilic area increases. The anisotropic patterns create a preferential direction for liquid spreading parallel to the stripes and confine motion to the perpendicular direction, giving rise to markedly higher velocities as compared to nonstructured surface energy gradients. Consequently, the influence of the distinct pattern features on the overall motion as well as suggestions for design improvements from an application point of view are discussed.     

Novel combination of hydrophilic/hydrophobic surface for large wettability difference and its application to liquid manipulation

This paper reports a novel combination of hydrophilic/hydrophobic materials for the evolution of liquid manipulation. Droplet generation based on a hydrophilic/hydrophobic mechanism is a promising method for highly accurate liquid manipulations. Although several droplet manipulation devices utilizing hydrophilic/hydrophobic patterns have been reported, it has been difficult to split fluid into droplets solely through hydrophilic/hydrophobic patterns in a microchannel. In this study, a material combination for fabricating hydrophilic/hydrophobic patterns was investigated and their wettability difference was enhanced for droplet generation. To improve hydrophilicity, we attempted to increase the surface area of silicon oxide through pulsed plasma chemical vapor deposition (PPCVD). To improve hydrophobicity, the damage to the hydrophobic patterns in the fabrication process was reduced. We successfully enhanced the difference in contact angles from 54.3° to 86.6° by combining the developed hydrophilic material and hydrophobic material. The developed material combination could successfully split fluid into a quantitative droplet of 14.1 nL in a microfluidic chip. Because the developed hydrophilic/hydrophobic combination enables the formation of a droplet with desirable shape in microchannels, the developed hydrophilic/hydrophobic combination is a promising component for lab-on-a-chip applications.     

Droplet morphologies on particles with macroscopic surface roughness

The equilibrium configuration of liquid droplets on the surface of macroscopically rough solid particles was determined by numerical simulations using the volume-of-fluid (VOF) method. The fractional surface coverage of the particle as a function of the droplet size, equilibrium contact angle, and the particle surface roughness amplitude and correlation length has been systematically investigated. Droplet size and contact angle were found to generally have a stronger effect on surface coverage than particle surface roughness. Because of droplet coalescence, a relatively large variation in surface coverage was observed for any given total liquid volume, particularly for larger values of the equilibrium contact angle.     

Nanoparticles of varying hydrophobicity at the emulsion droplet-water interface: adsorption and coalescence stability

The coalescence stability of poly(dimethylsiloxane) emulsion droplets in the presence of silica nanoparticles ( approximately 50 nm) of varying contact angles has been investigated. Nanoparticle adsorption isotherms were determined by depletion from solution. The coalescence kinetics (determined under coagulation conditions at high salt concentration) and the physical structure of coalesced droplets were determined from optical microscopy. Fully hydrated silica nanoparticles adsorb with low affinity, reaching a maximum surface coverage that corresponds to a close packed monolayer, based on the effective particle radius and controlled by the salt concentration. Adsorbed layers of hydrophilic nanoparticles introduce a barrier to coalescence of approximately 1 kT, only slightly reduce the coalescence kinetics, and form kinetically unstable networks at high salt concentrations. Chemically hydrophobized silica nanoparticles, over a wide range of contact angles (25 to >90 degrees ), adsorb at the droplet interface with high affinity and to coverages equivalent to close-packed multilayers. Adsorption isotherms are independent of the contact angle, suggesting that hydrophobic attraction overcomes electrostatic repulsion in all cases. The highly structured and rigid adsorbed layers significantly reduce coalescence kinetics: at or above monolayer surface coverage, stable flocculated networks of droplets form and, regardless of their wettability, particles are not detached from the interface during coalescence. At sub-monolayer nanoparticle coverages, limited coalescence is observed and interfacial saturation restricts the droplet size increase. When the nanoparticle interfacial coverage is >0.7 and <1.0, mesophase-like microstructures have been noted, the physical form and stability of which depends on the contact angle. Adsorbed nanoparticle layers at monolayer coverage and composed of a mixture of nanoparticles with different hydrophobisation levels form stable networks of droplets, whereas mixtures of hydrophobized and hydrophilic nanoparticles do not effectively stabilize emulsion droplets.     

Contact-angle hysteresis on super-hydrophobic surfaces

The relationship between perturbations to contact angles on a rough or textured surface and the super-hydrophobic enhancement of the equilibrium contact angle is discussed theoretically. Two models are considered. In the first (Wenzel) case, the super-hydrophobic surface has a very high contact angle and the droplet completely contacts the surface upon which it rests. In the second (Cassie-Baxter) case, the super-hydrophobic surface has a very high contact angle, but the droplet bridges across surface protrusions. The theoretical treatment emphasizes the concept of contact-angle amplification or attenuation and distinguishes between the increases in contact angles due to roughening or texturing surfaces and perturbations to the resulting contact angles. The theory is applied to predicting contact-angle hysteresis on rough surfaces from the hysteresis observable on smooth surfaces and is therefore relevant to predicting roll-off angles for droplets on tilted surfaces. The theory quantitatively predicts a "sticky" surface for Wenzel-type surfaces and a "slippy" surface for Cassie-Baxter-type surfaces.     

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.     

Evaporative properties and pinning strength of laser-ablated, hydrophilic sites on lotus-leaf-like, nanostructured surfaces

Wetting, evaporative, and pinning strength properties of hydrophilic sites on superhydrophobic, nanostructured surfaces were examined. Understanding these properties is important for surface characterization and designing features in self-cleaning, lotus-leaf-like surfaces. Laser-ablated, hydrophilic spots between 250 mum and 2 mm in diameter were prepared on silicon nanowire (NW) superhydrophobic surfaces. For larger circumference pinning sites, initial contact angle measurements resemble the contact angle of the surface within the pinning site: 65-69 degrees . As the drop volume is increased, the contact angles approach the contact angle of the NW surface without pinning sites: 171-176 degrees . The behavior of water droplets on the pinning sites is governed by how much of the water droplet is being influenced by the superhydrophobic NW surfaces versus the hydrophilic areas. During the evaporation of sinapic acid solution, drops are pinned by the spots except for the smaller circumference sites. Pinning strengths of the hydrophilic sites are a linear function of the pinning spot circumference. Protein samples prepared and deposited on the pinning sites for analysis by matrix-assisted laser desorption ionization indicate an improvement in sensitivity from that of a standard plate analysis by a factor of 5.     

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.     

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.     

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.     

Fabrication of flexible gold films with periodic sub-micrometer roughness and their wettability control by modification of SAM

Flexible honeycomb gold films supported by polymer sheets are fabricated by using polystyrene particle monolayers. The surfaces of the flexible gold films are covered with self-assembled monolayers (SAMs) of hydrophobic or hydrophilic thiol compounds, and the wettability of the modified surface is evaluated by measurements of the contact angles of water droplets. The contact angle of the film covered with hydrophobic SAM is ca. 150 degrees, which is greater than the value of 112 degrees for a flat gold surface, while the values for hydrophilic SAM are below 10 degrees.     

Microparticle sampling by electrowetting-actuated droplet sweeping

This paper describes a new microparticle sampler where particles can be efficiently swept from a solid surface and sampled into a liquid medium using moving droplets actuated by the electrowetting principle. We successfully demonstrate that super hydrophilic (2 microm and 7.9 microm diameter glass beads of about 14 degrees contact angle), intermediate hydrophilic (7.5 microm diameter polystyrene beads of about 70 degrees contact angle), and super hydrophobic (7.9 microm diameter Teflon-coated glass beads and 3 microm size PTFE particles of over 110 degrees contact angles) particles on a solid surface are picked up by electrowetting-actuated moving droplets. For the glass beads as well as the polystyrene beads, the sampling efficiencies are over 93%, in particular over 98% for the 7.9 microm glass beads. For the PTFE particles, however, the sampling efficiency is measured at around 70%, relatively lower than that of the glass and polystyrene beads. This is due mainly to the non-uniformity in particle size and the particle hydrophobicity. In this case, the collected particles staying (adsorbing) on the air-to-water interface hinder the droplet from advancing. This particle sampler requires an extremely small amount of liquid volume (about 500 nanoliters) and will thus be highly compatible and easily integrated with lab-on-a-chip systems for follow-up biological/chemical analyses.     

Shape-gradient composite surfaces: water droplets move uphill

The approach of water droplets self-running horizontally and uphill without any other forces was proposed by patterning the shape-gradient hydrophilic material (i.e., mica) to the hydrophobic matrix (i.e., wax or low-density polyethylene (LDPE)). The shape-gradient composite surface is the best one to drive water droplet self-running both at the high velocity and the maximal distance among four different geometrical mica/wax composite surfaces. The driving force for the water droplets self-running includes: (1) the great difference in wettability of surface materials, (2) the low contact angle hysteresis of surface materials, and (3) the space limitation of the shape-gradient transportation area. Furthermore, the average velocity and the maximal distance of the self-running were mainly determined by the gradient angle (alpha), the droplet volume, and the difference of the contact angle hysteresis. Theoretical analysis is in agreement with the experimental results.     

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.     

Characterizing the surface quality and droplet interface shape for microarray plates

The variation in the surface quality of microarray plates was examined by measuring the contact angles of 480 droplets on five microarray plates. It was found that the measured contact angle did not accurately predict the droplet shape for moderate Bond numbers (~0.5 ≤ N(B) ≤ 5). By defining an apparent contact angle using the ratio of the contact radius to the height, the variance in the predicted interface shape decreased by greater than a factor of 3 for both local and globally averaged characteristics. The error in the predicted droplet height was also reduced by 3 orders of magnitude.     

Dynamic behavior of polymer surface and the time dependence of contact angle

The increased attention has been focused on the re-searches of soft materials proposed by Pierre-Gilles de Gennes, a Nobel Prize Laureate in Physics. A special issue of “Science” on soft surfaces was published in 2002 to review specific surface properti…     

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.