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.     

Comparison of contact angle hysteresis of different probe liquids on the same solid surface

Advancing and receding contact angles of water, formamide and diiodomethane were measured on 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) layers deposited on three different solid supports—glass, mica and poly(methyl methacrylate). Up to five statistical monolayers were deposited on the surfaces by spreading DPPC solution. It was found that even on five statistical DPPC monolayers, the hysteresis of a given liquid depends on the kind of solid support. Also on the same solid support the contact angle hysteresis is different for each probe liquid used. The AFM images show that the heights of roughness of the DPPC films cannot be the primary cause of the observed hysteresis because the heights are too small to cause the observed hystereses. It is believed that the hysteresis is due to the liquid film present right behind the three-phase solid surface/liquid drop/gas (vapour) contact line and the presence of Derjaguin pressure. The value of contact angle hysteresis depends on both the solid surface and liquid properties as well as on intermolecular interactions between them.     

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.     

Combining hydrodynamics and molecular kinetics to predict dewetting between a small bubble and a solid surface

This paper examined the dewetting between a small air bubble and a solid surface in deionised water. Hydrodynamics was used in conjunction with surface molecular kinetics to model and predict the velocity of the moving contact line as a function of the dynamic macroscopic contact angle. The dewetting hydrodynamics was modelled following the approach developed specifically for drops and bubbles using the (absolute) coordinate system with the origin located at the centre of the contact area, which does not move with the moving contact line. The model provides accurate corrections unavailable in the generic hydrodynamic theories developed by Voinov and Cox, and removes the need for a macroscopic length scale employed in their generic theories. Molecular kinetics was used to determine the contact angle of the inner region close to the contact line, where the hydrodynamic approach breaks down due to the singularity. Unlike the generic hydrodynamic theories, the inner (microscopic) angle in our combined model is not a constant (a fitting parameter) but is a function of the moving contact line velocity and other molecular properties of the interfaces. The combined model agreed with the experimental data and produced physically consistent values for the slip length, molecular jumping distance and frequency. The dissolved gases accumulated at the non-wetting solid-liquid interface may influence the slip length.     

Solid/liquid interfacial tension as a tool to study stability of lysozyme on adsorption to solid surfaces

This work proposes the use of solid/liquid interfacial tension to study the stability of adsorbed lysozyme films on a solid surface using the contact angle of a liquid at the three phase contact line, in the presence of a denaturant, urea.Results suggest a direct correlation between this method with a standard technique like the fluorescence emission spectra and is measured with the same observable error as in the spectral methods. Further the technique provides a simple and direct handle to evaluate the homogeneity and degree of polarity of protein films on solid surfaces.     

The dynamic contact angle I. Dependence of the receding contact angle on velocity in the surfactant-containing three-phase system

Spontaneous three-phase contact (tpc) motion is investigated in order to determine the dependence of the static contact angle on tpc velocity in surfactant-containing systems after recession. To interpret the experimental results, the molecular-kinetic sitechanging theory and the hydrodynamic theory were considered. It is shown that, especially at very high tpc velocities, the experimental results are not thoroughly described by these theories. The deviations are explained as a surfactant transfer from the liquid/gas to the solid/gas interface which, under insufficient afterdiffusion, leads to an increase in surface tension and to a changed surface rheology. This mechanism could be governed by a model.     

A Novel Method for Surface Free-Energy Determination of Powdered Solids

Interfacial solid/liquid interactions play a crucial role in wetting, spreading, and adhesion processes. In the case of a flat solid surface, contact angle measurements are commonly utilized for the determination of the solid surface free energy and its components. However, if such a surface cannot be obtained, then the contact angle can not be measured directly. Usually methods based on imbibition of probe liquids into a thin porous layer or column are applied. In this paper a novel method, also based on the capillary rise, is proposed for the solid surface free-energy components determination. Actually, it is a modification of the thin column wicking method; similar theoretical background can be applied together with that appropriate for the capillary rise method of liquid surface tension determination. The proposed theoretical approach and procedure are verified by using single glass capillaries, and then alumina and ground glass powders were used for the method testing. Thus obtained surface free-energy components for these solids, for both glass and alumina, agree well with the literature values.     

Anomalous contact angle hysteresis of a captive bubble: advancing contact line pinning

Contact angle hysteresis of a sessile drop on a substrate consists of continuous invasion of liquid phase with the advancing angle (θ(a)) and contact line pinning of liquid phase retreat until the receding angle (θ(r)) is reached. Receding pinning is generally attributed to localized defects that are more wettable than the rest of the surface. However, the defect model cannot explain advancing pinning of liquid phase invasion driven by a deflating bubble and continuous retreat of liquid phase driven by the inflating bubble. A simple thermodynamic model based on adhesion hysteresis is proposed to explain anomalous contact angle hysteresis of a captive bubble quantitatively. The adhesion model involves two solid–liquid interfacial tensions (γ(sl) > γ(sl)′). Young’s equation with γ(sl) gives the advancing angle θ(a) while that with γ(sl)′ due to surface rearrangement yields the receding angle θ(r). Our analytical analysis indicates that contact line pinning represents frustration in surface free energy, and the equilibrium shape corresponds to a nondifferential minimum instead of a local minimum. On the basis of our thermodynamic model, Surface Evolver simulations are performed to reproduce both advancing and receding behavior associated with a captive bubble on the acrylic glass.     

The dynamik contact angle II. Investigation of the adsorption mechanism based on the measurement of the preceding contact angles

The structure of the adsorption layer at the solid/gas interface is characterized, as a function of conditioning concentration, by the measurement of preceding contact angles. The contact angles were determined tensiometrically (plate method) and cinema tographically (capillary rise method) in the system glass or mercury/n-dodecyl ammonium chloride solution/air, respectively. In the dependence of contact angle on concentration, four regions are provable. These regions correlate with the surfactants, which are bound to adsorption in a heteropolar mode or by van der Waals forces of interaction, with the formation of layer-like coverage and with bilayers. Special attention was given to the fact that loosely bound surfactants are transferred from the solid/gas interface to the liquid/gas interface and cause a reduction of the preceding contact angle.Publication No. 1077 from the Research Institut of Mineral Processing, Academy of Sciences of the GDR, Freiberg, G.D.R.     

Detachment of deposited colloids by advancing and receding air-water interfaces

Moving air-water interfaces can detach colloidal particles from stationary surfaces. The objective of this study was to quantify the effects of advancing and receding air-water interfaces on colloid detachment as a function of interface velocity. We deposited fluorescent, negatively charged, carboxylate-modified polystyrene colloids (diameter of 1 μm) into a cylindrical glass channel. The colloids were hydrophilic with an advancing air-water contact angle of 60° and a receding contact angle of 40°. After colloid deposition, two air bubbles were sequentially introduced into the glass channel and passed through the channel at different velocities (0.5, 7.7, 72, 982, and 10,800 cm/h). The passage of the bubbles represented a sequence of receding and advancing air-water interfaces. Colloids remaining in the glass channel after each interface passage were visualized with confocal microscopy and quantified by image analysis. The advancing air-water interface was significantly more effective in detaching colloids from the glass surface than the receding interface. Most of the colloids were detached during the first passage of the advancing air-water interface, while the subsequent interface passages did not remove significant amounts of colloids. Forces acting on the colloids calculated from theory corroborate our experimental results, and confirm that the detachment forces (surface tension forces) during the advancing air-water interface movement were stronger than during the receding movement. Theory indicates that, for hydrophilic colloids, the advancing interface movement generally exerts a stronger detachment force than the receding, except when the hysteresis of the colloid-air-water contact angle is small and that of the channel-air-water contact angle is large.     

Pressure dependence of the contact angle

When a liquid and its vapor contact a smooth, homogeneous surface, Gibbsian thermodynamics indicates that the contact angle depends on the pressure at the three-phase line of an isothermal system. When a recently proposed adsorption isotherm for a solid-vapor interface is combined with the equilibrium conditions and the system is assumed to be in a cylinder where the liquid-vapor interface can be approximated as spherical, the contact-angle-pressure relation can be made explicit. It indicates that a range of contact angles can be observed on a smooth homogeneous surface by changing the pressure at the three-phase line, but it also indicates that the adsorption at the solid-liquid interface is negative, and leads to the prediction that the contact angle increases with pressure. The predicted dependence of the contact angle on pressure is investigated experimentally in a system that has an independent mechanism for determining when thermodynamic equilibrium is reached. The predictions are in agreement with the measurements. The results provide a possible explanation for contact angle hysteresis.     

Effect of Surface Depressions on Wetting and Interactions between Hydrophobic Pore Array Surfaces

The surface structure is known to significantly affect the long-range capillary forces between hydrophobic surfaces in aqueous solutions. It is, however, not clear how small depressions in the surface will affect the interaction. To clarify this, we have used the AFM colloidal probe technique to measure interactions between hydrophobic microstructured pore array surfaces and a hydrophobic colloidal probe. The pore array surfaces were designed to display two different pore spacings, 1.4 and 4.0 μm, each with four different pore depths ranging from 0.2 to 12.0 μm. Water contact angles measured on the pore array surfaces are lower than expected from the Cassie-Baxter and Wenzel models and not affected by the pore depth. This suggests that the position of the three-phase contact line, and not the interactions underneath the droplet, determines the contact angle. Confocal Raman microscopy was used to investigate whether water penetrates into the pores. This is of importance for capillary forces where both the movement of the three-phase contact line and the situation at the solid/liquid interface influence the stability of bridging cavities. By analyzing the shape of the force curves, we distinguish whether the cavity between the probe and the surfaces was formed on a flat part of the surface or in close proximity to a pore. The pore depth and pore spacing were both found to statistically influence the distance at which cavities form as surfaces approach each other and the distance at which cavities rupture during retraction.     

Small solid particles and liquid lenses at fluid/fluid interfaces

The behaviour of small solid particles and liquid droplets at fluid interfaces is of wide interest, in part because of the roles they play in the stability of foams and emulsions. Here we focus on solid particles at liquid interfaces, both singly and in highly structured monolayers. We briefly mention small oil lenses on water in connection with the determination of line tension, τ. Particles are surface-active in the sense that they often adhere quite strongly to liquid surfaces, although of course they are not usually amphiphilic. The three-phase contact line around a particle at an interface is associated with an excess free energy resulting in a tendency of the line to contract (positive τ, which is a 1D analogue of surface tension) or to expand (negative τ). Positive line tension acts so as to push the contact angle of a particle with the fluid interface further away from 90°, i.e. to force the particle towards the more “wetting” of the two bulk phases. It also leads to activation barriers to entry and departure of particles from an interface. The behaviour of particle monolayers at octane/water interfaces is also discussed . It is found that, for monodisperse spherical polystyrene particles containing ionisable sulphate groups at the surface, highly ordered monolayers are formed. This appears to result from very long range electrostatic repulsion mediated through the oil phase. Surface pressure–surface area isotherms are discussed for particle monolayers and it is shown, using light microscopy, that at monolayer “collapse” particles are not expelled from the monolayers but rather the monolayer folds, remaining intact. This has an important bearing on methods, involving the use of the Langmuir trough, for the experimental determination of contact angles and line tensions in particulate systems. Received: 18 July 1999/Accepted: 30 August 1999     

Single DNA molecules as probes for interrogating silica surfaces after various chemical treatments

We examined the adsorption of single YOYO-1-labeled λ-DNA molecules at glass surfaces after treatment with various chemical cleaning methods by using total internal reflection fluorescence microscopy (TIRFM). The characteristics of these surfaces were further assessed using contact angle (CA) measurements and atomic force microscopy (AFM). By recording the real-time dynamic motion of DNA molecules at the liquid/solid interface, subtle differences in adsorption affinities were revealed. The results indicate that the driving force for adsorption of DNA molecules on glass surfaces is mainly hydrophobic interaction. We also found that surface topography plays a role in the adsorption dynamics.     

Electrowetting dynamics of microfluidic actuation

When voltage is suddenly applied to vertical, parallel dielectric-coated electrodes dipped into a liquid with finite conductivity, the liquid responds by rising up to reach a new hydrostatic equilibrium height. On the microfluidic scale, the dominating mechanism impeding this electromechanically induced actuation appears to be a dynamic friction force that is directly proportional to the velocity of the contact line moving along the solid surface. This mechanism has its origin in the molecular dynamics of the liquid coming into contact with the solid surface. A simple reduced-order model for the rising column of liquid is used to quantify the magnitude of this frictional effect by providing estimates for the contact line friction coefficient. Above some critical threshold of voltage, the electromechanical force is clamped, presumably by the same mechanism responsible for contact angle saturation and previously reported static height-of-rise limits. The important distinction for the dynamic case is that the onset of the saturation effect is delayed in time until the column has risen more than about halfway to its static equilibrium height.     

Probing with a laser sheet the contact angle distribution along a contact line

An optical method for probing contact angle distribution along contact lines of any shape using a laser sheet is proposed. This method is applied to a dry patch formed inside a film flowing along an inclined plane, both liquid and solid being transparent. Falling normally to the plane, a laser sheet cuts the contact line and is moved along this line. Distortions of the sheet trace observed on a screen put below the plane allow us to extract the contact angle distribution and the local line inclination along the line. Our results show that the contact angle around a dry patch is nearly constant and equal to the static advancing angle, at least when the evolution of its shape is followed for increasing flow rates. This supports a model of dry patch shape recently proposed by Podgorski and co-workers. Preliminary results obtained for decreasing flow are also qualitatively observed.     

Recent progress in the determination of solid surface tensions from contact angles

Advancing contact angles of different liquids measured on the same solid surface fall very close to a smooth curve when plotted as a function of liquid surface tension, i.e., gamma(lv)costheta versus gamma(lv). Changing the solid surface, and hence gamma(sv), shifts the curve in a regular manner. These patterns suggest that gamma(lv)costheta depends only on gamma(lv) and gamma(sv). Thus, an "equation of state for the interfacial tensions" was developed to facilitate the determination of solid surface tensions from contact angles in conjunction with Young's equation. However, a close examination of the smooth curves showed that contact angles typically show a scatter of 1-3 degrees around the curves. The existence of the deviations introduces an element of uncertainty in the determination of solid surface tensions. Establishing that (i) contact angles are exclusively a material property of the coating polymer and do not depend on experimental procedures and that (ii) contact angle measurements with a sophisticated methodology, axisymmetric drop shape analysis (ADSA), are highly reproducible guarantees that the deviations are not experimental errors and must have physical causes. The contact angles of a large number of liquids on the films of four different fluoropolymers were studied to identify the causes of the deviations. Specific molecular interactions at solid-vapor and/or solid-liquid interfaces account for the minor contact angle deviations. Such interactions take place in different ways. Adsorption of vapor of the test liquid onto the solid surface is apparently the only process that influences the solid-vapor interfacial tension (gamma(sv)). The molecular interactions taking place at the solid-liquid interface are more diverse and complicated. Parallel alignment of liquid molecules at the solid surface, reorganization of liquid molecules at the solid-liquid interface, change in the configuration of polymer chains due to contact with certain probe liquids, and intermolecular interactions between solid and liquid molecules cause the solid-liquid interfacial (gamma(sl)) tension to be different from that predicted by the equation of state, i.e., gamma(sl) is not a precise function of gamma(lv) and gamma(sv). In other words, the experimental contact angles deviate from the "ideal" contact angle pattern. Specific criteria are proposed to identify probe liquids which eliminate specific molecular interactions. Octamethylcyclotetrasiloxane (OMCTS) and decamethylcyclopentasiloxane (DMCPS) are shown to meet those criteria, and therefore are the most suitable liquids to characterize surface tensions of low energy fluoropolymer films with an accuracy of +/-0.2 mJ/m2.     

Equilibrium contact angles of liquid droplets on ideal rough solids

This work proposes a theoretical model for predicting the apparent equilibrium contact angle of a liquid on an ideal rough surface that is homogeneous and has a negligible body force, line tension, or contact angle hysteresis between solid and liquid. The model is derived from the conservation equations and the free-energy minimization theory for the changes of state of liquid droplets. The work of adhesion is expressed as the contact angles in the wetting process of the liquid droplets. Equilibrium contact angles of liquid droplets for rough surfaces are expressed as functions of the area ratios for the solid, liquid, and surrounding gas and the roughness ratio and wetting ratio of the liquid on the solid for the partially and fully wet states. It is found that the ideal critical angle for accentuating the contact angles by the surface roughness is 48°. The present model is compared with existing experimental data and the classical Wenzel and Cassie-Baxter models and agrees with most of the experimental data for various surfaces and liquids better than does the Wenzel model and accounts for trends that the Wenzel model cannot explain.     

Calculating the surface tension between a flat solid and a liquid: a theoretical and computer simulation study of three topologically different methods

We discuss three topologically different methods for calculating the surface tension between a flat solid and a liquid from theoretical and computer simulation viewpoints. The first method, commonly used in experiments, measures the contact angle at which a static droplet of liquid rests on a solid surface. We present a new analysis algorithm for this method and explore the effects of line tension on the contact angle. The second method, commonly used computer simulations, uses the pressure tensor through the virial in a system where a thick, infinitely extended slab of liquid rests on a solid surface. The third method, which is original to this paper and is closest to the thermodynamic definition of surface tension, applies to a spherical solid in contact with liquid in which the flat solid is recovered by extrapolating the sphere radius to infinity. We find that the second and third methods agree with each other, while the first method systematically underestimates surface tension values.     

Effect of surface mobility on the particle sliding along a bubble or a solid sphere

The sliding velocity of glass beads on a spherical surface, made either of an air bubble or of a glass sphere held stationary, is measured to investigate the effect of surface mobility on the particle sliding velocity. The sliding process is recorded with a digital camera and analyzed frame by frame. The sliding glass bead was found to accelerate with increasing angular position on the collector's surface. It reaches a maximum velocity at an angular position of about 100 degrees and then, under certain conditions, the glass bead leaves the surface of the collector. The sliding velocity of the glass bead depends strongly on the surface mobility of a bubble, decreasing with decreasing surface mobility. By a mobile surface we mean one which cannot set up resistive forces to an applied stress on the surface. The sliding velocity on a rigid surface, such as a glass sphere, is much lower than that on a mobile bubble surface. The sliding velocity can be described through a modified Stokes equation. A numerical factor in the modified Stokes equation is determined by fitting the experimental data and is found to increase with decreasing surface mobility. Hydrophobic glass beads sliding on a hydrophobic glass sphere were found to stick at the point of impact without sliding if the initial angular position of the impact is less than some specific angle, which is defined as the critical sticking angle. The sticking of the glass beads can be attributed to the capillary contracting force created by the formation of a cavity due to spontaneous receding of the nonwetting liquid from the contact zone. The relationship between the critical sticking angle and the particle size is established based on the Yushchenko [J. Colloid Interface Sci. 96 (1983) 307] analysis.