Fog deposition and accumulation on smooth and textured hydrophobic surfaces

We investigated the deposition and accumulation of droplets on both smooth substrates and substrates textured with square pillars, which were tens of micrometers in size. After being coated with a hydrophobic monolayer, substrates were placed in an air flow with a sedimenting suspension of micrometer-sized water droplets (i.e., fog). We imaged the accumulation of water and measured the evolution of the mean drop size. On smooth substrates, the deposition process was qualitatively similar to condensation, but differences in length scale revealed a transient regime not reported in condensation experiments. Based on previous simulation results, we defined a time-scale characterizing the transition to steady-state behavior. On textured substrates, square pillars promoted spatial ordering of accumulated drops. Furthermore, texture regulated drop growth: first enhancing coalescence when the mean drop size was smaller than the pillar, and then inhibiting coalescence when drops were comparable to the pillar size. This inhibition led to a monodisperse drop regime, in which drop sizes varied by less than 5%. When these monodisperse drops grew sufficiently large, they coalesced and could either remain suspended on pillars (i.e., Cassie-Baxter state) or wet the substrate (i.e., Wenzel state).     

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.     

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.     

Stability of the Shape of a Viscous Drop under Buoyancy-Driven Translation in a Hele-Shaw Cell

It has been shown (N. R. Gupta, A. Nadim, H. Haj-Hariri, and A. Borhan, J. Colloid Interface Sci. 218, 338 1999) that a circular drop translating in a Hele-Shaw cell under the action of gravity is linearly stable for nonzero interfacial tension. In this paper, we use the boundary integral method to examine the nonlinear evolution of the shape of initially noncircular drops translating in a Hele-Shaw cell. For prolate initial deformations, it is found that the drop reverts to a circular shape for all finite Bond numbers considered. Initially oblate drops, on the other hand, are found to become unstable and break up if the initial shape perturbation is of sufficiently large magnitude. The critical conditions for the onset of drop breakup are examined in terms of the magnitude of the initial deformation as a function of Bond number. Two branches of marginal stability are identified and the effects of viscosity ratio and asymmetric initial perturbations on the stability diagram are discussed. Copyright 2000 Academic Press.     

Mimicking the stenocara beetle--dewetting of drops from a patterned superhydrophobic surface

This paper describes the preparation of superhydrophobic surfaces that have been selectively patterned with circular hydrophilic domains. These materials mimicked the back of the stenocara beetle and collected drops of water if exposed to mist or fog. Under the effect of gravity, the drops dewetted from the hydrophilic regions once a critical volume had been reached. The surface energy in the hydrophilic regions was carefully controlled and assumed various values, allowing us to study the behavior of drops as a function of the superhydrophobic/hydrophilic contrast. We have investigated the development of drops and quantitatively analyzed the critical volumes as a function of several parameters.     

Spreading Dynamics of Polydimethylsiloxane Drops: Crossover from Laplace to Van der Waals Spreading

The spreading dynamics of small polydimethylsiloxane (PDMS) drops was studied on substrates with varying surface energies. For experimental parameters near the wetting transition, we observed small PDMS drops of different drop volumes as a function of time using interference video microscopy. While for large drops the contact angle θ decreases with the well-established power-law relation θ approximately t(-0.3) (Tanner's law), the effect of dispersive van der Waals (VW) interactions must be taken into account when interpreting the evolution of small drops. Two signatures of the VW forces are observed. For a positive Hamaker constant, the disjoining pressure acts as an additional driving force, leading to an acceleration of droplet spreading as soon as the drop height becomes comparable to the range of the VW interactions. In addition, a precursor film forms ahead of the contact line, leading to an apparent volume loss, particularly noticeable for very small drops. Contact line pinning may be a problem and we describe its effect on our experimental results. We present a theory that discusses the interplay of surface tension and VW forces in the case of a spreading drop. This model predicts a new spreading regime for very thin drops, in agreement with our experimental results. Copyright 2001 Academic Press.     

Wetting on the microscale: shape of a liquid drop on a microstructured surface at different length scales

Describing wetting of a liquid on a rough or structured surface is a challenge because of the wide range of involved length scales. Nano- and micrometer-sized textures cause pinning of the contact line, reflected in a hysteresis of the contact angle. To investigate contact angles at different length scales, we imaged water drops on arrays of 5 μm high poly(dimethylsiloxane) micropillars. The drops were imaged by laser scanning confocal microscopy (LSCM), which allowed us to quantitatively analyze the local and large-scale drop profile simultaneously. Deviations of the shape of drops from a sphere decay at two different length scales. Close to the pillars, the amplitude of deviations decays exponentially within 1-2 μm. The drop profile approached a sphere at a length scale 1 order of magnitude larger than the pillars' height. The height and position dependence of the contact angles can be understood from the interplay of pinning of the contact line, the principal curvatures set by the topography of the substrate, and the minimization of the air-water interfaces.     

Electrowetting-based microdrop tensiometer

We performed electrowetting (EW) contact angle measurements to determine the interfacial tension between aqueous drops laden with various inorganic and organic solutes and various ambient oils. Using low frequency AC voltage, we obtained interfacial tensions from 5 to 72 mJ/m 2, in close agreement with macroscopic tensiometry for drop volumes between 20 and 2000 nL. In addition to the conventional EW geometry, we demonstrate the possibility of performing "contact-less" measurements without any loss of accuracy using interdigitated coplanar electrodes.     

Microfluidic approach for rapid multicomponent interfacial tensiometry

We report a microfluidic instrument to rapidly measure the interfacial tension of multi-component immiscible liquids. The measurement principle rests upon the deformation and retraction dynamics of drops under extensional flow and was implemented for the first time in microfluidics (S. D. Hudson et al., Appl. Phys. Lett., 2005, 87, 081905 (ref. )). Here we describe in detail the instrument design and physics and extend this principle to investigate multicomponent mixtures, specifically two-component drops of adjustable composition. This approach provides fast real-time sigma measurements (on the order of 1 s), the possibility of rapidly adjusting drop composition and utilizes small sample volumes (approximately 10 microL). The tensiometer operation is illustrated with water drops and binary drops (water/ethylene glycol mixtures) in silicone oils. The technique should be particularly valuable for high-throughput characterization of complex fluids.     

A numerical study of the effect of insoluble surfactants on the stability of a viscous drop translating in a Hele-Shaw cell

A circular drop is a linearly stable solution for the buoyancy-driven motion of drops in a Hele-Shaw cell [Gupta et al. J. Colloid Interface Sci.218(1), 338 (1999)]. In the absence of surface-active agents, an initially prolate drop always goes to a steady circular shape while initially oblate drops exhibit complex dynamics [Gupta et al. J. Colloid Interface Sci.222, 107 (2000)]. In this study, the effect of insoluble surfactant impurities on the critical conditions for drop breakup is explored by using the Langmuir adsorption framework in conjunction with a physically based expression for the depth-averaged tangential stress exerted on a two-phase interface in a Hele-Shaw cell. It is shown that the presence of surfactants can have both a stabilizing and a destabilizing effect on the shape of the drop, depending on the Bond number, the magnitude of the initial perturbation, and the strength of surface convection. Similar to the clean drop dynamics, two marginally stable branches are found. Increasing the surface Peclet number results in the stabilization of the main branch while the secondary branch shifts to higher Bond numbers. The mode of breakup is also found to be strongly influenced by the strength of surface convection.     

Liquid drops on vertical and inclined surfaces; II. A method for approximating drop shapes

In this article, a new method is proposed to approximate the shapes of liquid drops on vertical and inclined surfaces. Based on observations from Part I, the profile of a drop at a given azimuthal angle is approximated by two circles sharing a common tangent at the maximum height. The drop volume is obtained by integrating all profiles over the circumference of the base. The volume is thus described as a function of the contact angles and the three-phase contact line. The new method accurately predicts the volumes of drops tested in Part I and independent measurements from the literature. Simplifying the drop shape to a spherical cap can lead to a 75% error in drop-volume prediction. The proposed method is used to study the effect of drop parameters on volume prediction. The two-circle geometry can also be used to measure contact angles from profile images.     

Modeling contact angle hysteresis on chemically patterned and superhydrophobic surfaces

We investigate contact angle hysteresis on chemically patterned and superhydrophobic surfaces, as the drop volume is quasistatically increased and decreased. We consider both two (cylindrical drops) and three (spherical drops) dimensions using analytical and numerical approaches to minimize the free energy of the drop. In two dimensions, we find, in agreement with other authors, a slip, jump, stick motion of the contact line. In three dimensions, this behavior persists, but the position and magnitude of the contact line jumps are sensitive to the details of the surface patterning. In two dimensions, we identify analytically the advancing and receding contact angles on the different surfaces, and we use numerical insights to argue that these provide bounds for the three-dimensional cases. We present explicit simulations to show that a simple average over the disorder is not sufficient to predict the details of the contact angle hysteresis and to support an explanation for the low contact angle hysteresis of suspended drops on superhydrophobic surfaces.     

Size-selective sliding of sessile drops on a slightly inclined plane using low-frequency AC electrowetting

When placed on an inclined solid plane, drops often stick to the solid surface due to pinning forces caused by contact angle hysteresis. When the drop size or the plane's incline angle is small, the drop is difficult to slide due to a decrease in gravitational force. Here we demonstrate that small drops (0.4-9 μL) on a slightly inclined plane (~12°, Teflon and parylene-C surface) can be mobilized through patterned electrodes by applying low-frequency ac electrowetting under 400 Hz (110-180 V(rms)), which has a mechanism different from that of the high-frequency ac method that induces sliding by reducing contact angle hysteresis. We attribute the sliding motion of our method to a combination of contact angle hysteresis and interfacial oscillation driven by ac electrowetting instead of the minimization of contact angle hysteresis at a high frequency. We investigated the effects of ac frequency on the sliding motion and terminal sliding of drops; the terminal sliding velocity is greatest at resonance frequency. Varying the electrowetting number (0.21-0.56) at a fixed frequency (40 Hz) for 5 μL drops, we found an empirical relationship between the electrowetting number and the terminal sliding velocity. Using the relationship between the drop size and ac frequency, we can selectively slide drops of a specific size or merge two drops along an inclined plane. This simple method will help with constructing microfluidic platforms with sorting, merging, transporting, and mixing of drops without a programmable control of electrical signals. Also, this method has a potential in heat transfer applications because heat removal capacity can be enhanced significantly through drop oscillation.     

Replacing the solid needle by a liquid one when measuring static and advancing contact angles

In general, the optical determination of static and advancing contact angle is made on drops applied or extended, respectively, onto a substrate through the use of thin solid needles. Although this method is used extensively, this way of dosing can be time consuming, cumbersome and if not performed meticulously can lead to erroneous results. Herein, we present an alternative way of applying drops onto substrates using a liquid jet produced by a liquid pressure dosing system acting as a “liquid needle”. We performed a comparative static contact angle study on 14 different surfaces with two different liquids (water and diiodomethane) utilizing two different ways of dosing: the conventional solid and a novel liquid needle-based technique. We found, for all but one sample, that the obtained results on μl size drops were comparable within the experimental error bars provided the liquid needle is thin enough. Observed differences are explained by the special characteristics of either way of dosing. In addition, we demonstrate how the liquid pressure-based dosing system facilitates high-speed optical advancing contact angle measurement by expanding a drop from 0.1 to 22 μl within less than 1.2 s but yet providing constant contact angle versus drop base diameter curves. The obtained results were compared with data from tensiometric dynamic Wilhelmy contact angle measurements. These data, in conjunction with sequences of live images of the dosing process of the liquid pressure dosing system, illustrate how this system can replace the solid needle by a liquid needle.     

Three-dimensional equilibrium shapes of drops on hysteretic surfaces

In this paper, we study equilibrium three-dimensional shapes of drops on hysteretic surfaces. We develop a function coupled with the publicly available surface energy minimization code Surface Evolver to handle contact angle hysteresis. The function incorporates a model for the mobility of the triple line into Surface Evolver. The only inputs to the model are the advancing and receding contact angles of the surface. We demonstrate this model’s versatility by studying three problems in which parts of the triple line advance while other parts either recede or remain stationary. The first problem focuses on the three-dimensional shape of a static pendant drop on a vertical surface. We predict the finite drop volume when impending sliding motion is observed. In the second problem, we examine the equilibrium shapes of coalescing sessile drops on hysteretic surfaces. Finally, we study coalescing puddles in which gravity plays a leading role in determining the equilibrium puddle shape along with hysteresis.     

Evidence for the existence of an effective interfacial tension between miscible fluids. 2. Dodecyl acrylate-poly(dodecyl acrylate) in a spinning drop tensiometer

We studied drops of dodecyl acrylate in poly(dodecyl acrylate) (molecular weight of 25,000) in a spinning drop tensiometer to determine whether an effective interfacial tension (EIT) existed between these two miscible fluids. We found convincing evidence. We estimated the mechanical relaxation time from an immiscible analogue (1-propanol and poly(dodecyl acrylate)) and showed that the dodecyl acrylate drops maintained quasi-steady diameters long after this relaxation period. Drops continuously grew in length and became more diffuse, but the width of the transition zone did not grow with t(1/2) as expected from Fick's law although this system had been shown to follow Fick's law in a static configuration (Antrim, D.; Bunton, P.; Lewis, L. L.; Zoltowski, B. D.; Pojman, J. A. J. Phys. Chem. B 2005, 109, 11842-11849). The EIT was determined from Vonnegut's equation, EIT = (Deltarho)omega(2)r(3)/4; both the inner and outer diameters were measured, yielding values of 0.002 and 0.02 mN m(-1), respectively. The EIT was found to be independent of the rotation rate above 6000 rpm and independent of the initial drop volume. The EIT was found to decrease with temperature and increase with the difference in concentration between the monomer drop and polymer-monomer fluid. The square gradient parameter, k, was determined from EIT = k(Deltac(2)/delta), where Deltac is the difference in mole fraction and delta is the width of the transition zone. The square gradient parameter was on the order of 10(-9) N. The square gradient parameter was found to decrease with temperature, to be independent of concentration, and to increase with the molecular weight of the polymer.     

Factors affecting the spontaneous motion of condensate drops on superhydrophobic copper surfaces

The coalescence-induced condensate drop motion on some superhydrophobic surfaces (SHSs) has attracted increasing attention because of its potential applications in sustained dropwise condensation, water collection, anti-icing, and anticorrosion. However, an investigation of the mechanism of such self-propelled motion including the factors for designing such SHSs is still limited. In this article, we fabricated a series of superhydrophobic copper surfaces with nanoribbon structures using wet chemical oxidation followed by fluorization treatment. We then systematically studied the influence of surface roughness and the chemical properties of as-prepared surfaces on the spontaneous motion of condensate drops. We quantified the "frequency" of the condensate drop motion based on microscopic sequential images and showed that the trend of this frequency varied with the nanoribbon structure and extent of fluorination. More obvious spontaneous condensate drop motion was observed on surfaces with a higher extent of fluorization and nanostructures possessing sufficiently narrow spacing and higher perpendicularity. We attribute this enhanced drop mobility to the stable Cassie state of condensate drops in the dynamic dropwise condensation process that is determined by the nanoscale morphology and local surface energy.     

Solubilization of thermotropic liquid crystal compounds in aqueous surfactant solutions

We study the micellar solubilization of three thermotropic liquid crystal compounds by immersing single drops in aqueous solutions of the ionic surfactant tetradecyltrimethylammonium bromide. For both nematic and isotropic drops, we observe a linear decrease of the drop size with time as well as convective flows and self-propelled motions. The solubilization is accompanied by the appearance of small aqueous droplets within the nematic or isotropic drop. At low temperatures, nematic drops expell small nematic droplets into the aqueous environment. Smectic drops show the spontaneous formation of filament-like structures which resemble the myelin figures observed in lyotropic lamellar systems. In all cases, the liquid crystal drops become completely solubilized, provided the weight fraction of the liquid crystal in the system is not larger than a few percent. The solubilization of the liquid crystal drops is compared with earlier studies of the solubilization of alkanes in ionic surfactant solutions.     

Non-aqueous phase liquid drop formation within a water saturated fracture

This work focuses on the mechanisms of non-aqueous phase liquid (NAPL) drop formation within a single fracture fed from a NAPL reservoir by way of a circular orifice, such as a pore. The fracture is assumed to be fully saturated, the relative wettability of the system is assumed water-wet, and the water velocity profile within the fracture is described by a Poiseuille flow. The size of the NAPL drops is investigated for various water flow velocities and NAPL entrance diameters. A force balancing method was used to determine the radii of detached drops. The drop sizes calculated from the model developed here are shown to be in agreement with available experimental drop size data. It is shown that at low Reynolds numbers the buoyancy force is the dominant force acting on the drop during the formation process and at high Reynolds numbers the viscous forces dominate. A simplified expression relating the geometry of the fractured system to the drop radii is developed from the model equations, and it is shown to predict drop radii that match well with both the model simulations and the available experimental data.     

Electrophoresis of a concentrated aqueous dispersion of non-Newtonian drops

The electrophoresis of a concentrated dispersion of non-Newtonian drops in an aqueous medium, which has not been investigated theoretically in the literature, is analyzed under conditions of low zeta potential and weak applied electric field. The results obtained provide a theoretical basis for the characterization of the nature of an emulsion and a microemulsion system. A Carreau fluid, which has wide applications in practice, is chosen for the non-Newtonian drops, and the unit cell model of Kuwabara is adopted to simulate a dispersion. The effects of the key parameters of a dispersion, including its concentration, the shear-thinning nature of the drop fluid, and the thickness of the double layer, on the electrophoretic behavior of a drop are discussed. In general, the more significant the shear-thinning nature of the drop fluid is, the larger the mobility is, and this effect is pronounced as the thickness of the double layer decreases. However, if the double layer is sufficiently thick, this effect becomes negligible. In general, the higher the concentration of drops is, the smaller the mobility is; however, if the double layer is either sufficiently thin or sufficiently thick, this effect becomes unimportant.