Droplets wetting on filament rails: Surface energy and morphology transition

The morphology of liquid droplets wetting on filaments depends on the filament configuration, droplet volume, and contact angle. A stable morphology is the one that minimizes the potential energy of the droplet–filament system, while morphology transition may happen when an intermediate state exists which corresponds to a higher potential energy. This paper aims to explore such morphology transition of droplet wetting on filament rails made of two parallel identical microfilaments. Detailed numerical simulations were performed to extract the surface energy of the droplet–filament system at varying filament spacings, droplet volumes, and contact angles. Critical conditions of the morphology transition between two symmetrical wetting morphologies (i.e., liquid droplet bridge and barrel-shaped droplet) were determined. A family of characteristic curves in terms of the dimensionless droplet volume vs the filament spacing at varying contact angles was obtained, which can be used as a universal law to govern the morphology transition for such droplet–filament rail systems. The results and concepts presented in this work can be extended to broad wetting systems and utilized for the analysis and design of microfluidic devices and testers based on droplet–filament systems.     

Collective behavior during the exit of a wetting liquid through a network of channels

The exit of a wetting fluid from a thin microchannel into a sudden expansion is studied experimentally. In the case of the exit from a single channel, the advancing interface converges to a parabolic shape after an initial transient, in accordance with the lubrication limit analysis of a spreading drop. The experiments are then repeated for the exit from two parallel channels. At early times, the two exiting drops behave independently and display the same evolution as a single exiting droplet, while at late times we recover a single parabolic profile. The transition between the early and late states is due to the merging of the two drops, which is associated with a sudden increase in the flow rate. This is the signature of a collective effect which acts to redistribute the fluid spatially. Finally, the experiment is generalized to the case of seven parallel channels where a cascade of two-by-two mergings is observed, indicating that local interactions dominate the dynamics which lead to the global state of the system.     

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

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

Condensation and wetting transitions on microstructured ultra-hydrophobic surfaces

On rough surfaces, two distinct wetting modes can appear. These two states are usually described by the theories of Cassie (drops suspended on top of roughness features) and Wenzel (drops impaled on roughness features). Whereas the wetting transition from the Cassie to the Wenzel state has been relatively well studied both experimentally and theoretically, the question of whether metastable Wenzel drops exist and how they transition to the Cassie state has remained open. In this work, we study the wetting behavior of microstructured post surfaces coated with a hydrophobic fluoropolymer. Through condensation, the formation of metastable Wenzel droplets is induced. We show that under certain conditions drops can transition from the Wenzel to the Cassie state.     

Characterization of rough surfaces with vibrated drops

Wetting transitions were studied with vertically-vibrated drops on various artificial and natural rough substrates. Alternative pathways of wetting transitions were observed. The model of wetting transition is presented. Multiple minima of the Gibbs free energy of a drop deposited on a rough surface explain alternative pathways of wetting transitions. We demonstrate that a wetting transition occurs when the constant force resulting from vibrations, Laplace and hydrostatic pressure acts on the triple line. It is shown that the final wetting states are mainly the Cassie impregnating wetting state with water penetrating the pores in the outer vicinity of the droplet or the Wenzel state with water inside the pores under the droplet whereas the substrate ahead the drop is dry.     

Effects of geometrical characteristics of surface roughness on droplet wetting

Surface roughness is known to alter the wettability on a solid substrate. In general, either Wenzel or Cassie-Baxter theory is adopted to describe the apparent contact angle. Following the minimum free energy pathway associated with the imbibition process, we have derived a generalized expression for the apparent contact angle on a textured surface and the liquid-gas contact area within the groove that plays a key role. Depending on the geometrical characteristics of the grooves, the surface wetting falls into three regimes: (i) single stable state which is either Wenzel (completely wetted roughness) or Cassie-Baxter (completely nonwetted roughness) state, (ii) two stable states (Wenzel and Cassie-Baxter) separated by an energy barrier, and (iii) single stable state with partially wetted roughness. The sufficient condition for each regime is derived and several groove geometries are given to show the free energy path. Alteration in the geometric parameters may lead to the wetting crossover. We also show that the Cassie-Baxter can occur at a hydrophilic surface for particular pore shapes.     

Patterned nonadhesive surfaces: superhydrophobicity and wetting regime transitions

Nonadhesive and water-repellent surfaces are required for many tribological applications. We study mechanisms of wetting of patterned superhydrophobic Si surfaces, including the transition between various wetting regimes during microdroplet evaporation in environmental scanning electron microscopy (ESEM) and for contact angle and contact angle hysteresis measurements. Wetting involves interactions at different scale levels: macroscale (water droplet size), microscale (surface texture size), and nanoscale (molecular size). We propose a generalized formulation of the Wenzel and Cassie equations that is consistent with the broad range of experimental data. We show that the contact angle hysteresis involves two different mechanisms and how the transition from the metastable partially wetted (Cassie) state to the homogeneously wetted (Wenzel) state depends upon droplet size and surface pattern parameters.     

Theoretical consideration of wetting on a cylindrical pillar defect: pinning energy and penetrating phenomena

Wetting on a cylindrical pillar defect is discussed in terms of the free-energy difference ΔG. Wetting is divided into wetting on a flat surface, a pinning effect at the apex of the defect, and wetting on a pillar wall. First, we confirmed that ΔG between before and after ideal wetting on a flat surface can be derived as a function of the contact angle θ in which the free-energy minimum is obtained as the equilibrium contact angle θ(eq) described by Young's and Wenzel's laws. Second, the pinning effect at the apex in the cross section of the pillar defect is discussed in ΔG, where the pinning effect is shown to originate from the energy barrier by an increase in the air-liquid interfacial area of a pinned droplet induced by deformation. Next, the ΔG profiles of wetting on the pillar wall are drawn based on the theory of Carroll (Carroll, B. J. J. Colloid Interface Sci.1976, 57, 488-495) to better understand the ΔG profile during penetration. Differences in the manner of wetting between the wetting state on a flat surface and the pillar wall are reflected in ΔG. Finally, penetration of a droplet into a pillar defect is comprehensively discussed on the basis of wetting on a flat surface and a pillar wall. If we consider a simple manner of penetration, another type of energy barrier resulting from an anomalous deformation of the air-liquid interface of the penetrating droplet can be theoretically suggested. Consequently, two types of energy barrier are found. These energy barriers should play a significant role in the hysteresis of wetting, the liquid-repellent Cassie-Baxter state (CB), and the CB-Wenzel wetting transition on a microtextured surface.     

Reentrant wetting transition on surfactant solution surfaces

The wetting of polydimethylsiloxane oil drops on the surfaces of anionic surfactant sodium dodecylsulfate solutions is studied systematically by changing the bulk surfactant concentration. The wetting state changes from complete wetting to pseudopartial wetting at 0.3 cmc (critical micelle concentration) surfactant concentration and there is a reentrant transition back to complete wetting at 1.4 cmc. The measured free energy is consistent with the prediction of the wetting theory. The interaction potential minimum of the two surfaces of the oil film disappears at the reentrant point, which is speculated to be an effect of micelle formation in the solution.     

Geometry-driven wetting transition

Wetting states are quantitatively described by the number of inflection points on the liquid-vapor interface and by the macroscopic contact angle. The number of inflection points required for complete, partial, and pseudopartial wetting is determined for geometries with positive, zero, and negative capillary pressures. The wetting state of a material system is not always independent of the magnitude of the capillary pressure; for example, the wetting state of a fluid inside a capillary tube may depend on the capillary radius. In particular, a fluid that pseudopartially wets the inside of a tube exhibits a transition to partial wetting (or complete wetting) as the capillary radius is decreased.     

Manipulation of droplets by dynamically controlled wetting gradients

The reversible transportation of droplets was realized by spatiotemporal control of the wetting gradient. The surface wetting was reversibly regulated by using electrochemical reactions of the ferrocenyl (Fc) alkanethiol monolayer, and the wetting gradient was generated by the application of the in-plane bias voltage to the substrate. The back-and-forth motion of the wetting boundary, where the surface changed from wetting to repulsive, sequentially caused a droplet unidirectional spreading and shrinking on the surface. These unidirectional deformations resulted in the net transport of the droplet in an inchwormlike manner. The droplet moved backward when the direction of the in-plane bias voltage was reversed.     

Condensation-induced wetting state and contact angle hysteresis on superhydrophobic lotus leaves

In this paper, we demonstrate how condensed moisture droplets wet classical superhydrophobic lotus leaf surfaces and analyze the mechanism that causes the increase of contact angle hysteresis. Superhydrophobic lotus leaves in nature show amazing self-cleaning property with high water contact angle (>150°) and low contact angle hysteresis (usually <10°), causing droplets to roll off at low inclination angles, in accordance with classical Cassie–Baxter wetting state. However, when superhydrophobic lotus leaves are wetted with condensation, the condensed water droplets are sticky and exhibit higher contact angle hysteresis (40–50°). Compared with a fully wetted sessile droplet (classical Wenzel state) on the lotus leaves, the condensed water droplet still has relatively large contact angle (>145°), suggesting that the wetting state deviates from a fully wetted Wenzel state. When the condensed water droplets are subjected to evaporation at room conditions, a thin water film is observed bridging over the micropillar structures of the lotus leaves. This causes the dew to stick to the surface. This result suggests that the condensed moisture does not uniformly wet the superhydrophobic lotus leaf surfaces. Instead, there occurs a mixed wetting state, between classical Cassie–Baxter and Wenzel states that causes a distinct increase of contact angle hysteresis. It is also observed that the mixed Cassie–Baxter/Wenzel state can be restored to the original Cassie–Baxter state by applying ultrasonic vibration which supplies energy to overcome the energy barrier for the wetting transition. In contrast, when the surface is fully wetted (classical Wenzel state), such restoration is not observed with ultrasonic vibration. The results reveal that although the superhydrophobic lotus leaves are susceptible to being wetted by condensing moisture, the configured wetting state is intermediate between the classical Cassie–Baxter and Wenzel states.     

Comparison of monodisperse droplet generation in flow-focusing devices with hydrophilic and hydrophobic surfaces

A thin flow-focusing microfluidic channel is evaluated for generating monodisperse liquid droplets. The microfluidic device is used in its native state, which is hydrophilic, or treated with OTS to make it hydrophobic. Having both hydrophilic and hydrophobic surfaces allows for creation of both oil-in-water and water-in-oil emulsions, facilitating a large parameter study of viscosity ratios (droplet fluid/continuous fluid) ranging from 0.05 to 96 and flow rate ratios (droplet fluid/continuous fluid) ranging from 0.01 to 2 in one geometry. The hydrophilic chip provides a partially-wetting surface (contact angle less than 90°) for the inner fluid. This surface, combined with the unusually thin channel height, promotes a flow regime where the inner fluid wets the top and bottom of the channel in the orifice and a stable jet is formed. Through confocal microscopy, this fluid stabilization is shown to be highly influenced by the contact angle of the liquids in the channel. Non-wetting jets undergo breakup and produce drops when the jet is comparable to or smaller than the channel thickness. In contrast, partially-wetting jets undergo breakup only when they are much smaller than the channel thickness. Drop sizes are found to scale with a modified capillary number based on the total flow rate regardless of wetting behavior.     

Water wetting transition parameters of perfluorinated substrates with periodically distributed flat-top microscale obstacles

Superhydrophobicity is obtained on photolithographically structured silicon surfaces consisting of flat-top pillars after a perfluorosilanization treatment. Systematic static contact angle measurements were carried out on these surfaces as a function of pillar parameters that geometrically determine the surface roughness, including pillar height, diameter, top perimeter, overall filling factor, and disposition. In line with thermodynamics models, two regimes of static contact angles are observed varying each parameter independently: the "Cassie" regime, in which the water drop sits suspended on top of the pillars (referred to as composite), corresponding to experimental contact angles greater than 140-150 degrees, and the "Wenzel" regime, in which water completely wets the asperities (referred to as wetted), corresponding to lower experimental contact angles. A transition between the Cassie and Wenzel regimes corresponds to a set of well-defined parameters. By smoothly depositing water drops on the surfaces, this transition is observed for surface parameter values far from the calculated ones for the thermodynamic transition, therefore offering evidence for the existence of metastable composite states. For all studied parameters, the position of the experimental transition correlates well with a rough estimation of the energy barrier to be overcome from a composite metastable state in order to reach the thermodynamically favored Wenzel state. This energy barrier is estimated as the surface energy variation between the Cassie state and the hypothetical composite state with complete filling of the surface asperities by water, keeping the contact angle constant.     

Wetting transitions

When a liquid droplet is put onto a surface, two situations distinguishable by the contact angle may result. If the contact angle is zero, the droplet spreads across the surface, a situation referred to as complete wetting. If the contact angle is between zero and 180°, the droplet does not spread, a situation called partial wetting. A wetting transition is a surface phase transition from partial to complete wetting. The wetting transition is generally first-order (discontinuous), implying a discontinuity in the first derivative of the surface free energy. As a consequence, at the transition a discontinuous jump in film thickness occurs from a molecularly thin to a thick film. We show here that the first-order nature of the transition can lead to the observation of metastable surface states and an accompanying hysteresis. The second part of this review deals with the exceptions to the first-order nature of the wetting transition. Two different types of continuous or critical wetting transitions have been reported, for which a discontinuity in a higher derivative of the surface free energy occurs. This consequently leads to a continuous divergence of the film thickness. The first type is long-range critical wetting, due to the long-range van der Waals forces. We show that this transition is preceded by the usual first-order wetting transition, which, however, is not achieved completely. This leads to the existence of a new intermediate wetting state, in which droplets coexist with a mesoscopic film: frustrated complete wetting. The film thickness diverges continuously from this mesoscopic film to a thick film. The second type of continuous transition is short-range critical wetting, for which the layer thickness diverges continuously all the way from a microscopic to a macroscopically thick film. This transition is interesting, as renormalization-group studies predict non-universal behaviour for the critical exponents characterizing the wetting transition. The experimental results, however, show mean field behaviour, the reason for which remains unclear.     

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

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

Wetting and dewetting transitions on hierarchical superhydrophobic surfaces

Many natural superhydrophobic structures have hierarchical two-tier roughness which is empirically known to promote robust superhydrophobicity. We report the wetting and dewetting properties of two-tier roughness as a function of the wettability of the working fluid, where the surface tension of water/ethanol drops is tuned by the mixing ratio, and compare the results to one-tier roughness. When the ethanol concentration of deposited drops is gradually increased on one-tier control samples, the impalement of the microtier-only surface occurs at a lower ethanol concentration compared to the nanotier-only surface. The corresponding two-tier surface exhibits a two-stage wetting transition, first for the impalement of the microscale texture and then for the nanoscale one. The impaled drops are subsequently subjected to vibration-induced dewetting. Drops impaling one-tier surfaces could not be dewetted; neither could drops impaling both tiers of the two-tier roughness. However, on the two-tier surface, drops impaling only the microscale roughness exhibited a full dewetting transition upon vibration. Our work suggests that two-tier roughness is essential for preventing catastrophic, irreversible wetting of superhydrophobic surfaces.     

Lattice model for the wetting transition of alkanes on aqueous surfactant solutions

Droplets of alkanes on aqueous solutions of the cationic surfactants C(n)TAB (CH3(CH2)(n-1)N+ (CH3)3Br-) exhibit a first-order wetting transition as the concentration of the surfactant is increased. A theoretical model is presented in which the surface free energy is broken down into a long-range dispersion interaction and a short-range interaction described by a 2D lattice gas, taking into account the interaction between oil and surfactant molecules. The model provides quantitative agreement with the observed wetting transitions and the variation in composition of the wetting film with bulk surfactant concentration. The behavior of oil drops on large reservoirs of dilute surfactant is discussed.     

Control over wettability of polyethylene glycol surfaces using capillary lithography

We demonstrate that wettability of poly(ethylene glycol) (PEG) surfaces can be controlled using nanostructures with various geometrical features. Capillary lithography was used to fabricate PEG nanostructures using a new ultraviolet (UV) curable mold consisting of functionalized polyurethane with acrylate group (MINS101m, Minuta Tech.). Two distinct wetting states were observed depending of the height of nanostructures. At relatively lower heights (< 300 nm for 150 nm pillars with 500 nm spacing), the initial contact angle of water was less than 80 degrees and the water droplet easily invaded into the surface grooves, leading to a reduced contact angle at equilibrium (Wenzel state). At relatively higher heights (> 400 nm for 150 nm pillars with 500 nm spacing), on the other hand, the nanostructured PEG surface showed hydrophobic nature and no significant change in contact angle was observed with time (Cassie state). The presence of two wetting states was also confirmed by dynamic wetting properties and contact-angle hysteresis. The wetting transition from hydrophilic (bare PEG surface) to hydrophobic (PEG nanostructures) was described by the Cassie-Baxter equation assuming that enhanced hydrophobicity is due to the heterogeneous wetting mediated by an air pocket on the surface. The measured contact angles in the Cassie state were increased with increasing air fraction, in agreement with the theoretical prediction.