Abstract
A fundamental limitation of liquids on many surfaces is their contact line pinning. This limitation can be overcome by infusing a nonvolatile and immiscible liquid or lubricant into the texture or roughness created in or applied onto the solid substrate so that the liquid of interest no longer directly contacts the underlying surface. Such slippery liquid-infused porous surfaces (SLIPS), also known as lubricant-impregnated surfaces, completely remove contact line pinning and contact angle hysteresis. However, although a sessile droplet may rest on such a surface, its contact angle can be only an apparent contact angle because its contact is now with a second liquid and not a solid. Close to the solid, the droplet has a wetting ridge with a force balance of the liquid-liquid and liquid-vapor interfacial tensions described by Neumann's triangle rather than Young's law. Here, we show how, provided the lubricant coating is thin and the wetting ridge is small, a surface free energy approach can be used to obtain an apparent contact angle equation analogous to Young's law using interfacial tensions for the lubricant-vapor and liquid-lubricant and an effective interfacial tension for the combined liquid-lubricant-vapor interfaces. This effective interfacial tension is the sum of the liquid-lubricant and the lubricant-vapor interfacial tensions or the liquid-vapor interfacial tension for a positive and negative spreading power of the lubricant on the liquid, respectively. Using this approach, we then show how Cassie-Baxter, Wenzel, hemiwicking, and other equations for rough, textured or complex geometry surfaces and for electrowetting and dielectrowetting can be used with the Young's law contact angle replaced by the apparent contact angle from the equivalent smooth lubricant-impregnated surface. The resulting equations are consistent with the literature data. These results enable equilibrium contact angle theory for sessile droplets on surfaces to be used widely for surfaces that retain a thin and conformal SLIPS coating.
Highlights
A fundamental underpinning concept when dealing with droplets on surfaces is the Young’s law contact angle defined by cos θY =(γSV − γSL) γLV (1)where the γIJ represents the interfacial tensions for the solid− vapor, solid−liquid, and liquid−vapor interfaces.[1]
We have considered theoretically how apparent contact angles can be predicted in the thin-layer limit of liquidinfused or lubricant-impregnated surfaces defined by a small wetting ridge
We have argued that equilibrium can be defined for a wide variety of situations by using small surface free energy changes dominated by changes in the lubricant− droplet, lubricant−vapor, and droplet−vapor interfacial areas and that changes in the wetting ridges cause higher-order corrections
Summary
A fundamental underpinning concept when dealing with droplets on surfaces is the Young’s law contact angle (θY) defined by cos θY. We show how a surface free energy approach can be used to derive the apparent equilibrium contact angle for droplets on SLIP surfaces with thin conformal lubricant films. We show how this argument can be applied to topographically structured surfaces, such as those used in superhydrophobicity, roughness-induced wetting, and hemiwicking, to surfaces with complex geometry or shape, and to electrowetting and dielectrowetting. Our work provides a conceptual framework for apparent equilibrium contact angles for droplets and contact lines, which is widely applicable to surfaces with thin conformal SLIPS, lubricantimpregnated coatings, or lubricant coatings
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