Apparent contact angle of drops on liquid infused surfaces: geometric interpretation

Wetting on silicone surfaces

Silicone is frequently used as a model system to investigate and tune wetting on soft materials. Silicone is biocompatible and shows excellent thermal, chemical, and UV stability. Moreover, the mechanical properties of the surface can be easily varied by several orders of magnitude in a controlled manner. Polydimethylsiloxane (PDMS) is a popular choice for coating applications such as lubrication, self-cleaning, and drag reduction, facilitated by low surface energy. Aiming to understand the underlying interactions and forces, motivated numerous and detailed investigations of the static and dynamic wetting behavior of drops on PDMS-based surfaces. Here, we recognize the three most prevalent PDMS surface variants, namely liquid-infused (SLIPS/LIS), elastomeric, and liquid-like (SOCAL) surfaces. To understand, optimize, and tune the wetting properties of these PDMS surfaces, we review and compare their similarities and differences by discussing (i) the chemical and molecular structure, and (ii) the static and dynamic wetting behavior. We also provide (iii) an overview of methods and techniques to characterize PDMS-based surfaces and their wetting behavior. The static and dynamic wetting ridge is given particular attention, as it dominates energy dissipation, adhesion, and friction of sliding drops and influences the durability of the surfaces. We also discuss special features such as cloaking and wetting-induced phase separation. Key challenges and opportunities of these three surface variants are outlined.

Understanding the role of infusing lubricant composition in the interfacial interactions and properties of slippery surface

Liquid-infused surfaces (LISs) have attracted tremendous attention in recent years owing to their excellent surface properties, such as self-cleaning and anti-fouling. Understanding the effect of lubricant composition on LIS performance is of vital importance, which will help establish the criteria to choose suitable infusing lubricants for specific applications. In this work, the role of chemical composition of lubricant in the properties of LISs was investigated. The apparent water contact angle θapp was dependent on the temperature and beeswax/silicone oil ratio. Nevertheless, the trend of moving velocity of water drop on the tilted LISs did not follow that of θapp at 20 °C and 37 °C, which was attributed to the increased lubricant viscosity with beeswax/silicone oil ratio. At 60 °C, the drop velocity and θapp shared the similar variation trend with beeswax/silicone oil ratio, highlighting the significant role of chemistry of the components in beeswax. The alkanes and fatty acids promoted the drop movement, while the fatty acid esters impeded the movement. The interaction forces between water drop and lubricant surfaces were measured using atomic force microscopy. It was demonstrated that the interaction between water drop and lubricant was not the only factor to control the drop movement, while the interaction between lubricant and substrate as well as of lubricant itself also determined the movement. When the adhesions of water-lubricant and lubricant-substrate were similar for different lubricants, the influence of cohesion of lubricant became significant. This work provides useful insights into the fundamental understanding of the interfacial interactions of test drop, infusing lubricant and solid substrate of LISs, and the effect of infusing lubricant composition on the LIS performance.

Visualization and Experimental Characterization of Wrapping Layer Using Planar Laser-Induced Fluorescence

Droplets on nanotextured oil-impregnated surfaces have high mobility due to record-low contact angle hysteresis (∼1-3°), attributed to the absence of solid-liquid contact. Past studies have utilized the ultralow droplet adhesion on these surfaces to improve condensation, reduce hydrodynamic drag, and inhibit biofouling. Despite their promising utility, oil-impregnated surfaces are not fully embraced by industry because of the concern for lubricant depletion, the source of which has not been adequately studied. Here, we use planar laser-induced fluorescence (PLIF) to not only visualize the oil layer encapsulating the droplet (aka wrapping layer) but also measure its thickness since the wrapping layer contributes to lubricant depletion. Our PLIF visualization and experiments show that (a) due to the imbalance of interfacial forces at the three-phase contact line, silicone oil forms a wrapping layer on the outer surface of water droplets, (b) the thickness of the wrapping layer is nonuniform both in space and time, and (c) the time-average thickness of the wrapping layer is ∼50 ± 10 nm, a result that compares favorably with our scaling analysis (∼50 nm), which balances the curvature-induced capillary force with the intermolecular van der Waals forces. Our experiments show that, unlike silicone oil, mineral oil does not form a wrapping layer, an observation that can be exploited to mitigate oil depletion of nanotextured oil-impregnated surfaces. Besides advancing our mechanistic understanding of the wrapping oil layer dynamics, the insights gained from this work can be used to quantify the lubricant depletion rate by pendant droplets in dropwise condensation and water harvesting.

Droplet Self-Propulsion on Slippery Liquid-Infused Surfaces with Dual-Lubricant Wedge-Shaped Wettability Patterns

Young's equation is fundamental to the concept of the wettability of a solid surface. It defines the contact angle for a droplet on a solid surface through a local equilibrium at the three-phase contact line. Recently, the concept of a liquid Young's law contact angle has been developed to describe the wettability of slippery liquid-infused porous surfaces (SLIPS) by droplets of an immiscible liquid. In this work, we present a new method to fabricate biphilic SLIP surfaces and show how the wettability of the composite SLIPS can be exploited with a macroscopic wedge-shaped pattern of two distinct lubricant liquids. In particular, we report the development of composite liquid surfaces on silicon substrates based on lithographically patterning a Teflon AF1600 coating and a superhydrophobic coating (Glaco Mirror Coat Zero), where the latter selectively dewets from the former. This creates a patterned base surface with preferential wetting to matched liquids: the fluoropolymer PTFE with a perfluorinated oil Krytox and the hydrophobic silica-based GLACO with olive oil (or other mineral oils or silicone oil). This allows us to successively imbibe our patterned solid substrates with two distinct oils and produce a composite liquid lubricant surface with the oils segregated as thin films into separate domains defined by the patterning. We illustrate that macroscopic wedge-shaped patterned SLIP surfaces enable low-friction droplet self-propulsion. Finally, we formulate an analytical model that captures the dependence of the droplet motion as a function of the wettability of the two liquid lubricant domains and the opening angle of the wedge. This allows us to derive scaling relationships between various physical and geometrical parameters. This work introduces a new approach to creating patterned liquid lubricant surfaces, demonstrates long-distance droplet self-propulsion on such surfaces, and sheds light on the interactions between liquid droplets and liquid surfaces.

Water Drop Evaporation on Slippery Liquid-Infused Porous Surfaces (SLIPS): Effect of Lubricant Thickness, Viscosity, Ridge Height, and Pattern Geometry

Sessile drop evaporation and condensation on slippery liquid-infused porous surfaces (SLIPS) is crucial for many applications. However, its modeling is complex since the infused lubricant forms a wetting ridge around the drop close to the contact line, which partially blocks the free surface area and decreases the drop evaporation rate. Although a good model was available after 2015, the effects of initial lubricant heights (h_oil)_i above the pattern, and the corresponding initial ridge heights (h_r)_i, lubricant viscosity, and solid pattern type were not well studied. This work fills this gap where water drop evaporations from SLIPS, which are obtained by infusing silicone oils (20 and 350 cSt) onto hydrophobized Si wafer micropatterns having both cylindrical and square prism pillars, are investigated under constant relative humidity and temperature conditions. With the increase of (h_oil)_i, the corresponding (h_r)_i increased almost linearly on lower parts of the drops for all SLIPS samples, resulting in slower drop evaporation rates. A novel diffusion-limited evaporation equation from SLIPS is derived depending on the available free liquid-air interfacial area, A_LV, which represents the unblocked part of the total drop surface. The calculation of the diffusion constant, D, of water vapor in air from (dA_LV/dt) values obtained by drop evaporation was successful up to a threshold value of (h_oil)_i = 8 μm within ±7%, and large deviations (13-27%) were obtained when (h_oil)_i > 8 μm, possibly due to the formation of thin silicone oil cloaking layers on drop surfaces, which partially blocked evaporation. The increase of infused silicone oil viscosity caused only a slight increase (12-17%) in drop lifetimes. The effects of the geometry and size of the pillars on the drop evaporation rates were minimal. These findings may help optimize the lubricant oil layer thickness and viscosity used for SLIPS to achieve low operational costs in the future.

Droplet Memory on Liquid-Infused Surfaces

The knowledge of droplet friction on liquid-infused surfaces (LIS) is of paramount importance for applications involving liquid manipulation. While the possible dissipation mechanisms are well-understood, the effect of surface texture has thus far been mainly investigated on LIS with highly regular solid topographies. In this work, we aim to address this experimental gap by studying the friction experienced by water droplets on LIS based on both random and regular polysilsesquioxane nanostructures. We show that the available models apply to the tested surfaces, but we observe a previously unreported droplet memory effect: as consecutive droplets travel along the same path, their velocity increases up to a plateau value before returning to the original state after a sufficiently long time. We study the features of this phenomenon by evaluating the motion of droplets when they cross the path of a previous sequence of droplets, discovering that moving droplets create a low-friction trace in their wake, whose size matches their base diameter. Finally, we attribute this to the temporary smoothing out of an initially conformal lubricant layer by means of a Landau-Levich-Derjaguin liquid film deposition behind the moving droplet. The proposed mechanism might apply to any LIS with a conformal lubricant layer.

Numerical and experimental investigation of static wetting morphologies of aqueous drops on lubricated slippery surfaces using a quasi-static approach

The static wetting behavior of drops on surfaces with thin lubricating films is very different compared to solid surfaces. Due to the slow dynamics of the wetting ridge, it is challenging to predict the apparent contact angles of such drops. It is hypothesized that for a sinking drop on a lubricated surface, quasi-static wetting morphology can be numerically computed from the knowledge of interfacial energies, lubricant thickness, and drop volume. In this study, we use Surface Evolver to numerically compute the static wetting morphology for the four-phase system using a quasi-static approach with a sinking time similar to the early-intermediate times, and the results agree well with the corresponding experiments. We find that the apparent contact angles depend significantly on the lubricant thickness and substrate wettability compared to other parameters.

The Liquid Young's Law on SLIPS: Liquid-Liquid Interfacial Tensions and Zisman Plots

Slippery liquid-infused porous surfaces (SLIPS) are an innovation that reduces droplet-solid contact line pinning and interfacial friction. Recently, it has been shown that a liquid analogue of Young's law can be deduced for the apparent contact angle of a sessile droplet on SLIPS despite there never being contact by the droplet with the underlying solid. Since contact angles on solids are used to characterize solid-liquid interfacial interactions and the wetting of a solid by a liquid, it is our hypothesis that liquid-liquid interactions and the wetting of a liquid surface by a liquid can be characterized by apparent contact angles on SLIPS. Here, we first present a theory for deducing liquid-liquid interfacial tensions from apparent contact angles. This theory is valid irrespective of whether or not a film of the infusing liquid cloaks the droplet-vapor interface. We show experimentally that liquid-liquid interfacial tensions deduced from apparent contact angles of droplets on SLIPS are in excellent agreement with values from the traditional pendant drop technique. We then consider whether the Zisman method for characterizing the wettability of a solid surface can be applied to liquid surfaces created using SLIPS. We report apparent contact angles for a homologous series of alkanes on Krytox-infused SLIPS and for water-IPA mixtures on both the Krytox-infused SLIPS and a silicone oil-infused SLIPS. The alkanes on the Krytox-infused SLIPS follow a linear relationship in the liquid form of the Zisman plot provided that the effective droplet-vapor interfacial tension is used. All three systems follow a linear relationship on a modified Zisman plot. We interpret these results using the concept of the critical surface tension (CST) for the wettability of a solid surface introduced by Zisman. In our liquid surface case, the obtained critical surface tensions were found to be lower than the infusing liquid-vapor surface tensions.