Apparent Contact Angles on Lubricant-Impregnated Surfaces/SLIPS: From Superhydrophobicity to Electrowetting

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.

Bidirectional motion of droplets on gradient liquid infused surfaces

“…On liquid-infused surfaces, the apparent contact angle of a droplet depends on the surface tensions and the intrinsic contact angles of all fluids involved in the system [24][25][26] . This rich interplay makes it much less trivial to predict the direction of droplet motion when there is a topographical gradient.…”

“…To determine the direction of droplet motion, we can introduce the droplet-air effective interfacial tension 26 γ eff γ oa þ γ ow ; if S > 0ð lubricant encapsulation Þ; γ wa ; otherwise ; & and the following definitions of apparent contact angles cos θ eff wajs…”

“…Alternatively, we can determine cos θ eff wajs and cos θ eff wajo using a graphical method as follows. In the vanishing meniscus approximation, the droplet apparent contact angle on the composite solid-lubricant surface can be expressed as 24,26 cos θ app ¼ γ ðs;oÞa À γ ðs;oÞw…”

Electrical bearing failures in electric vehicles

“…The contact angle of a droplet on a surface can be regulated by a voltage between the electrodes, which is called the electrowetting effect [110]. This electromechanical mechanism dominates the microfluidic behavior by modifying the interfacial tension [111]. More relevant to the bearing working conditions, it is observed that the nonpolar dielectric lubricant in the contact area of a steel ball and a metallic layer will spread along the surface under the action of an electric field [112].…”

Factors controlling the pinning force of liquid droplets on liquid infused surfaces

“…When the lubricant encapsulates the droplet, the effective droplet-gas surface tension becomes g eff dg = g lg + g ld . 32 3…”