Growth dynamics of water drops on a square-pattern rough hydrophobic surface

Condensation on rough or superhydrophobic substrates can induce wetting behavior that is quite different from that of deposited or impinging drops. We investigate the growth dynamics of water drops in a well-controlled condensation chamber on a model rough hydrophobic surface made of square pillars. After having followed growth laws similar to those observed on flat surfaces, a transition to an air-pocket-like state occurred because of the bridging of the drops between the pillars. Another transition to the more stable Wenzel state is later ensured by a noticeable pillar self-drying process. Condensation ends up in a few large drops in a mixed Wenzel penetration regime. The drops are fed by neighboring channels and the adjacent pillars stay almost dry, a remarkable and seemingly general property of rough hydrophobic substrates.     

Contact line dynamics in drop coalescence and spreading

The dynamics of coalescence of two water sessile drops is investigated and compared with the spreading dynamics of a single drop in partially wetting regime. The composite drop formed due to coalescence relaxes exponentially toward equilibrium with a typical relaxation time that decreases with contact angle. The relaxation time can reach a few tenths of seconds and depends also on the drop size, initial conditions, and surface properties (contact angle, roughness). The relaxation dynamics is larger by 5 to 6 orders of magnitude than the bulk hydrodynamics predicts, due to the high dissipation in the contact line vicinity. The coalescence is initiated at a contact of the drops growing in a condensation chamber or by depositing a small drop at the top of neighboring drops with a syringe, a method also used for the studies of the spreading. The dynamics is systematically faster by an order of magnitude when comparing the syringe deposition with condensation. We explain this faster dynamics by the influence of the unavoidable drop oscillations observed with fast camera filming. Right after the syringe deposition, the drop is vigorously excited by deformation modes, favoring the contact line motion. This excitation is also observed in spreading experiments while it is absent during the condensation-induced coalescence.     

The drop size in membrane emulsification determined from the balance of capillary and hydrodynamic forces

Here, we investigate experimentally and theoretically the factors that determine the size of the emulsion droplets produced by membrane emulsification in "batch regime" (without applied crossflow). Hydrophilic glass membranes of pore diameters between 1 and 10 mum have been used to obtain oil-in-water emulsions. The working surfactant concentrations are high enough to prevent drop coalescence. Under such conditions, the size of the formed drops does not depend on the surfactant type and concentration, on the interfacial tension, or on the increase of viscosity of the inner (oil) phase. The drops are monodisperse when the working transmembrane pressure is slightly above the critical pressure for drop breakup. At higher pressures, the size distribution becomes bimodal: a superposition of a "normal" peak of monodisperse drops and an "anomalous" peak of polydisperse drops is observed. The theoretical model assumes that, at the moment of breakup, the hydrodynamic ejection force acting on the drop is equal to the critical capillary force that corresponds to the stability-instability transition in the drop shape. The derived equations are applied to predict the mean size of the obtained drops in regimes of constant flow rate and constant transmembrane pressure. Agreement between theory and experiment is established for the latter regime, which corresponds to our experimental conditions. The transition from unimodal to bimodal drop size distribution upon increase of the transmembrane pressure can be interpreted in terms of the transition from "dripping" to "jetting" mechanisms of drop detachment.     

Suspension of water droplets on individual pillars

We report results of extensive experimental and numerical studies on the suspension of water drops deposited on cylindrical pillars having circular and square cross sections and different wettabilities. In the case of circular pillars, the drop contact line is pinned to the whole edge contour until the drop collapses due to the action of gravity. In contrast, on square pillars, the drops are suspended on the four corners and spilling along the vertical walls is observed. We have also studied the ability of the two geometries to sustain drops and found that if we compare pillars with the same characteristic size, the square is more efficient in pinning large volumes, while if we normalize the volumes to pillar areas, the opposite is true.     

Modeling Cassie–Baxter State on Superhydrophobic Surfaces

The goal of this work is to study the Cassie–Baxter state on the microstructure hydrophobic surfaces. The dependence of the energy barrier on the drop size, contact angle, the gap between the pillars, and pillar width is investigated. We consider the drop in three dimensions using a numerical approach to minimize the free energy of the drop in any situations. Numerical results are obtained for the wetting of a hydrophobic surface textured with a square lattice of pillars. According to the results, we found that the curvature increases allowing the liquid to touch the surface below the posts as the drop loses volume or decreased the contact angle with fixed drop volume. In the situations we considered, the pillar diagonal length is very critical and sensitive to the details of the surface patterning when the drop volume is larger.     

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.     

Fabrication, surface properties, and origin of superoleophobicity for a model textured surface

Inspired by the superhydrophobic effect displayed in nature, we set out to mimic the interplay between the chemistry and physics in the lotus leaf to see if the same design principle can be applied to control wetting and adhesion between toners and inks on various printing surfaces. Since toners and inks are organic materials, superoleophobicity has become our design target. In this work, we report the design and fabrication of a model superoleophobic surface on silicon wafer. The model surface was created by photolithography, consisting of texture made of arrays of ～3 μm diameter pillars, ～7 μm in height with a center-to-center spacing of 6 μm. The surface was then made oleophobic with a fluorosilane coating, FOTS, synthesized by the molecular vapor deposition technique with tridecafluoro-1,1,2,2-tetrahydrooctyltrichlorosilane. Contact angle measurement shows that the surface exhibits super repellency toward water and oil (hexadecane) with a water and hexadecane contact angles at 156° and 158°, respectively. Since the sliding angles for both liquids are also very small (～10°), we conclude that the model surface is both superhydrophobic and superoleophobic. By comparing with the contact angle data of the bare silicon surfaces (both smooth and textured), we also conclude that the superoleophobicity is a result of both surface texturing and fluorination. Results from investigations of the effects of surface modification and pillar geometry indicate that both surface oleophobicity and pillar geometry are contributors to the superoleophobicity. More specifically, we found that superoleophobicity can only be attained on our model textured surface when the flat surface coating has a relatively high oleophobicity (i.e., with a hexadecane contact angle of >73°). SEM examination of the pillars with higher magnification reveals that the side wall in each pillar is not smooth; rather it consists of a ～300 nm wavy structure (due to the Bosch etching process) from top to bottom. Comparable textured surfaces with (a) smooth straight side wall pillars and (b) straight side wall pillars with a 500 nm re-entrant structure made of SiO(2) were fabricated and the surfaces were made oleophobic with FOTS analogously. Contact angle data indicate that only the textured surfaces with the re-entrant pillar structure are both superoleophobic and superhydrophobic. The result suggests that the wavy structure at the top of each pillar is the main geometrical contributor to the superoleophobic property observed in the model surface.     

Silica particle-stabilized emulsions of silicone oil and water: aspects of emulsification

A study of the emulsification of silicone oil and water in the presence of partially hydrophobic, monodisperse silica nanoparticles is described. Emulsification involves the fragmentation of bulk liquids and the resulting large drops and the coalescence of some of those drops. The influence of particle concentration, oil/water ratio, and emulsification time on the relative extents of fragmentation and coalescence during the formation of emulsions, prepared using either batch or continuous methods, has been investigated. For batch emulsions, the average drop diameter decreases with increasing particle concentration as the extent of limited coalescence is reduced. Increasing the oil volume fraction in the emulsion at fixed aqueous particle concentration results in an increase in the average drop diameter together with a dramatic lowering of the uniformity of the drop size distribution as coalescence becomes increasingly significant until catastrophic phase inversion occurs. For low oil volume fractions (phi(o)), fragmentation dominates during emulsification since the mean drop size decreases with emulsification time. For higher phi(o) close to conditions of phase inversion, coalescence becomes more prevalent and the drop size increases with time with stable multiple emulsions forming as a result.     

Generation of Water-In-Oil-In-Water (W/O/W) Double Emulsions by Microfluidics

Novel compartment microparticles prepared with double emulsion droplets as templates provide a protected internal space for material encapsulation. The effect of three-phase flow rate on the micro-droplet generation of double emulsion mechanism is available for reference to produce precise size and highly monodisperse particles. The influence of three-phase flow rate on the formation mode and size of the emulsion droplets is investigated by combination of experiment and numerical simulation. The size of compound droplets decreases and frequency increases with the increasing outer fluid flow rate. The monodispersity of the double emulsion reduces due to transition from dripping to narrowing jetting regime. Outer droplet size increases with the increasing flow rate of the middle fluid, whereas inner droplet size is the opposite. The frequency increases and then stabilizes, which leads to a widening regime. When Q₂/Q₁ > 6, the multi-core type double emulsion droplets are produced. Droplet coalescence occurs when surfactants is not involved. As Q₁ increases, there is an increasing tendency for inner drop size. The outer drop size is proportional to the sum of the inner and middle flow rate, and that is irrelevant to Q₁/Q₂. For drop size, the ratio of core-shell and internal structure is precisely controlled by adjusting three-phase flow rate respectively.     

Condensation on ultrahydrophobic surfaces and its effect on droplet mobility: ultrahydrophobic surfaces are not always water repellant

The condensation of water was studied on topography-based ultrahydrophobic surfaces containing hydrophobized silicon pillars. Optical microscopy showed that water nucleated and grew both on top of and between the pillars. As condensation progressed, water between the pillars became unstable and was forced upward to the surface. Macroscopic water droplets on top of the pillars coalesced with condensed water that remained between the pillars, pinning the droplets at their three-phase contact line. Dynamic contact angle measurements on ultrahydrophobic surfaces wet with condensation revealed a dramatic increase in hysteresis compared to that on dry surfaces, leading to a corresponding decrease in water drop mobility.     

Anomalous melting of overheated smectic films

The formation of droplets of a nematic phase in free-standing smectic films (FSSFs) overheated above the temperature of the bulk smectic–nematic transition is studied theoretically. Contrary to the bulk systems the film melting is strongly influenced by its confinement between two free surfaces. By using the general thermodynamic approach to the stability of FSSF, we determined the gain in the free energy related with the formation of the nematic droplets, the value of the critical work and the critical size of the drops. The necessary material for initial drops growth is provided by the thermally exited dislocation loops. The further drops growth occurs through merging of the droplets of different size under influence of the capillary forces. These forces arise due to gradients of the surface energy of the film around the drops. At smaller distances an additional interaction of the fluctuation origin appears (pseudo-Casimir), which also favour the drops coalescence. The scenarios of the drop size evolution and of the dynamics of the process are in good agreement with experiments.     

Effect of emulsion drop-size distribution upon coalescence in simple shear flow: a population balance study

A population balance is used to examine the effect of the shape of the initial drop-size distribution of an emulsion upon its short and long-time evolution in simple shear flow. Initial distributions that are monodisperse, multidisperse, lognormal, bimodal, multimodal, and step functions are considered. At short times, it is shown that the rate of coalescence decreases by up to 25% for step distributions and up to 75% for lognormal distributions as the width of the distribution increases. Bimodal, multidisperse and multimodal distributions show intermediate decreases in the rate of coalescence, between these two values, with increases in the distribution width. Furthermore, it is found that the initial rate of coalescence is strongly dependent upon the presence of large drops. As the number fraction of large droplets within the distribution increases, the rate of coalescence also increases. At long times, all distributions move toward an asymptotic distribution shape in which the frequency of drops decreases algebraically with drop diameter at small drop diameters, and decreases exponentially with drop diameter at large drop diameters. Though portions of each distribution showed the expected asymptotic scaling behavior at long times, each asymptotic distribution nevertheless retains 'fingerprints' of the respective initial distribution. Overall, the rate of coalescence for a system is bounded by the initial rate, which is a function of the initial distribution shape, and the asymptotic rate, which is dependent upon the long-time scaling behavior. Finally, it is shown that the resolution with which the drop-size distribution of an emulsion is experimentally measured can have a significant effect upon predicted rates of coalescence.     

Stability of emulsified heavy oil: the combined effects of deterministic DLVO forces and random surface charges

When dispersed in aqueous solution, droplets of bitumen (extra heavy oil) are known to acquire negative surface charges. The resulting electrostatic repulsion, according to traditional DLVO theory, is far too strong for any droplet coalescence to occur. However, from experience it is known that bitumen droplets do coalesce in aqueous suspensions. Furthermore, the process appears to be random, with the probability of coalescence increasing sharply with the drop size. To explain these facts, we modeled the bitumen-water interface as a heterogeneous surface comprising charged "patches"; the zeta potentials of the patches constitute a random variable that is assumed to be Gaussian. The traditional DLVO theory, according to this model, remains sound on the local scale (i.e., for patches interacting across an intervening water layer). Such a theory can predict the probabilities of coalescence in remarkable detail. A parameter central to this theory is the lateral extent of the charged patches, which was estimated to be in the neighborhood of 0.6 μm.     

Optofluidic encapsulation of crystalline colloidal arrays into spherical membrane

Double emulsion droplets encapsulating crystalline colloidal arrays (CCAs) with a narrow size distribution were produced using an optofluidic device. The shell phase of the double emulsion was a photocurable resin that was photopolymerized downstream of the fluidic channel within 1 s after drop generation. The present optofluidic synthesis scheme was very effective for fabricating highly monodisperse spherical CCAs that were made structurally stable by in situ photopolymerization of the encapsulating shells. The shell thickness and the number of core emulsion drops could be controlled by varying the flow rates of the three coflowing streams in the dripping regime. The spherical CCAs confined in the shell exhibited distinct diffraction patterns in the visible range, in contrast to conventional film-type CCAs. As a result of their structure, the spherical CCAs exhibited photonic band gaps for normal incident light independent of the position on the spherical surface. This property was induced by heterogeneous nucleation at the smooth wall of the spherical emulsion drop during crystallization into a face-centered cubic (fcc) structure. On the other hand, the solidified shells did not permit the penetration of ionic species, enabling the CCAs to maintain their structure in a continuous aqueous phase of high ionic strength for at least 1 month. In addition, the evaporation of water molecules inside the shell was slowed considerably when the core-shell microparticles were exposed to air: It took approximately 6 h for a suspension encapsulated in a thick shell to evaporate completely, which is approximately 1000 times longer than the evaporation time for water droplets with the same volume. Finally, the spherical CCAs additionally exhibited enhanced stability against external electric fields. The spherical geometry and high dielectric constant of the suspension contributed to reducing the electric field inside the shell, thereby inhibiting the electrophoretic movement of the charged particles.     

Shear-induced coalescence of emulsified oil drops

Crude oil droplets, when suspended in water, possess negative surface charges which give rise to double-layer repulsive forces between the drops. According to conventional DLVO theory, the magnitude of this repulsion (based on the measured zeta potential) is more than sufficient to prevent coalescence of the droplets. Indeed, when two such droplets were brought together on direct (i.e., "head-on") approach, coalescence was rarely observed. Upon oblique approach, however, the same droplets were seen to coalesce readily. An oblique encounter must necessarily give rise to lateral relative motion-or shearing-between the droplet surfaces. It is speculated that, if the charge distributions at the droplet surfaces were heterogeneous, lateral shearing would facilitate many encounters between surface patches of different zeta potentials across the intervening water film. If the repulsion across any local region were sufficiently weak to allow formation of an oil bridge across the water film, coalescence of the drops would follow inevitably. With the hypothesis of surface heterogeneity, it is not necessary to invoke any additional colloidal interactions (such as "hydrophobic forces") to account for the observed droplet-droplet coalescence. This finding may have important implications for the underlying mechanisms of emulsion stability in general and the commercial extraction of bitumen from oil sands in particular.     

Deposition of Oil Drops on a Glass Substrate in Relation to the Process of Washing

The attachment of emulsion drops to glass substrates is investigated in relation to the redeposition of oil drops in the process of washing. It turns out that the drops of a surfactant-stabilized oil-in-water emulsion cannot be attached to an immersed glass plate simply by the buoyancy force. However, the same drops can be deposited on the plate when the latter is pulled out of the emulsion, i.e., when the drops are pressed against the substrate by a receding meniscus. We measured the amount of the oily deposit as a function of the pH, ionic strength, and composition of an amphoteric-anionic surfactant mixture. The enhanced oil deposition at low pH correlates with the domain in which the emulsion drops and the solid substrate bear opposite electric charges. This was established by zeta-potential measurements with oil drops and glass particles. The anionic surfactant brings negative surface charge to the oil droplets and suppresses the oil deposition on the negatively charged glass. With the increase of the fraction of the amphoteric surfactant in the mixture, the zeta-potential is converted from negative to positive, and the oil deposition grows almost linearly with the potential. In general, the deposition of oil drops by a receding meniscus is governed by an interplay of electrostatic and hydrodynamic factors. Copyright 2000 Academic Press.     

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.     

Effect of Emulsifier Type on the Characterization of O/W Emulsions Using a Spectroscopy Technique

The droplet size distribution (DSD) of emulsions is the result of two competitive effects that take place during emulsification process, i.e., drop breakup and drop coalescence, and it is influenced by the formulation and composition variables, i.e., nature and amount of emulsifier, mixing characteristics, and emulsion preparation, all of which affect the emulsion stability. The aim of this study is to characterize oil-in-water (O/W) emulsions (droplet size and stability) in terms of surfactant concentration and surfactant composition (sodium dodecyl benzene sulphonate (SDBS)/Tween 80 mixture). Ultraviolet-visible (UV-vis) transmission spectroscopy has been applied to obtain droplet size and stability of the emulsions and the verification of emulsion stability with the relative cleared volume technique (time required for a certain amount of emulsion to separate as a cleared phase). It is demonstrated that the DSD of the emulsions is a function of the oil concentration and the surfactant composition with higher stability for emulsions prepared with higher SDBS ratio and lower relative cleared volume with the time. Results also show that smaller oil droplets are generated with increasing Tween 80 ratio and emulsifier concentration.     

Model for drop coalescence in a locally isotropic turbulent flow field

The proposed model views drop coalescence in a turbulent flow field as a two-step process consisting of formation of a doublet due to drop collisions followed by coalescence of the individual droplets in a doublet due to the drainage of the intervening film of continuous phase under the action of colloidal (van der Waals and electrostatic) and random turbulent forces. The turbulent flow field was assumed to be locally isotropic. A first-passage-time analysis was employed for the random process of intervening continuous-phase film thickness between the two drops of a doublet in order to evaluate the first two moments of coalescence-time distribution of the doublet. The average drop coalescence time of the doublet was dependent on the barrier for coalescence due to the net repulsive force (net effect of colloidal repulsive and turbulent attractive forces). The predicted average drop coalescence time was found to be smaller for larger turbulent energy dissipation rates, smaller surface potentials, larger drop sizes, larger ionic strengths, and larger drop size ratios of unequal-sized drop pairs. The predicted average drop coalescence time was found to decrease whenever the ratio of average turbulent force to repulsive force barrier became larger. The calculated coalescence-time distribution was broader, with a higher standard deviation, at lower energy dissipation rates, higher surface potentials, smaller drop sizes, and smaller size ratios of unequal drop pairs. The model predictions of average coalescence-rate constants for tetradecane-in-water emulsions stabilized by sodium dodecyl sulfate (SDS) in a high-pressure homogenizer agreed fairly well with the inferred experimental values as reported by Narsimhan and Goel (J. Colloid Interface Sci. 238 (2001) 420-432) at different homogenizer pressures and SDS concentrations.