Simple-to-Apply Wetting Model to Predict Thermodynamically Stable and Metastable Contact Angles on Textured/Rough/Patterned Surfaces

Abstract

Rough/patterned/textured surfaces with nano/microcavities that broaden below the surfaceknown as "re-entrants"can be omniphobic (macroscopic contact angle greater than 90°for both water and oils). The existing theoretical models that explain the effects of texture on wetting are complex and do not provide a simple procedure for predicting the thermodynamically stable and metastable states and their corresponding contact angles (for example, wetting states that involve partially filled cavities). Here, we develop a simple-to-apply wetting model that allows for (1) predicting a priori the wetting state (partially or fully filled) of the cavities both under and outside the liquid droplet and the corresponding macroscopic contact angles on any type of textured surface; (2) determining the conditions under which metastable states exist; and (3) engineering specific nano/microtextures that yield any desired macroscopic contact angle, θ t , for a given intrinsic contact angle θ 0. Subsequently, we experimentally demonstrate how one can use the model to predict the metastable and the thermodynamically stable contact angles on nondeformable textured surfaces consisting of arrays of axisymmetric cavities/protrusions. In this model, we do not consider the effects of gravitational forces, Laplace pressure of the droplet, line tension, droplet impact velocity, and quantitative aspects of contact angle hysteresis. Nonetheless, the model is suitable for accurately predicting the contact angles of macroscopic droplets (droplet volume ∼1 μL and base diameters <2 mm), which is of immense relevance in engineering. In the experimental section we also discuss the suitability of the model to be extended in order to include the effects of contact angle hysteresis on the macroscopic apparent contact angle on textured surfaces. Controlling these macroscopic contact angles, whether higher or lower than the intrinsic angle, θ 0 , is desirable for many applications including nonwetting, self-cleaning, and antifouling surfaces and for completely wetting/spreading applications, such as creams, cosmetics, and lubricant fluids.

Assessing omniphobicity by immersion

“…Below we explain the mechanisms underlying the contrasting behaviors of silica surfaces with DRPs and DRCs on immersion. It has been demonstrated that doubly reentrant features, pillars or cavities, can stabilize sessile drops due to their geometry, such that if the drops were pushed into the microtexture the curvature at the solid-liquid-vapor interface resisted penetration (Figure 4 inset) [20,24,27,28]. In fact, the concave curvature of the liquid meniscus gave rise to capillary pressure, also known as the 'Laplace pressure', that prevented the imbibition and has the following general expression , where is the surface tension of the liquid, θ o is the intrinsic contact angle at the solid-liquid-vapor interface at thermodynamic Omniphobic Omniphobic equilibrium, and is the mean curvature of liquid-vapor interface, and R 1, R 2 the two mutually orthogonal radii of curvatures of the liquid-vapor interface [33].…”

“…Thus, the thermodynamically stable fully-filled (Wenzel) state could be delayed [27] . The same liquid, however, infiltrates the microtexture from the boundary, a surrogate for localized defects (right corner).…”

“…Functionally, when coating-based omniphobic surfaces come into contact with liquids-sessile or pendant drops, or on immersion-the microtexture entraps air leading to Cassie states [11-13, 15, 27]. Those Cassie-states transition to the Wenzel state gradually through a variety of mechanisms, including capillary condensation and gas dissolution [19,[27][28][29][30][31]. Thus, contact angles present a reliable and simple criterion for assessing omniphobicity [12,25,26,[32][33][34].…”

Proof-of-Concept for Gas-Entrapping Membranes Derived from Water-Loving SiO₂/Si/SiO₂ Wafers for Green Desalination

“…On the other hand, if the inlets and outlets of the pores have reentrant profiles (e.g., "T"-shaped), they may prevent the wetting liquid from penetrating the pore and entrap air inside, leading to Cassie states 33 ( Figure 1C,D). Once the air is trapped inside the pore, it will further prevent liquid intrusion due to its compressibility and low solubility in water over time 34,35 .…”

“…Such a system will slowly transition from Cassie to Wenzel state, and the kinetics of this process can be tuned by the pore's shape, size, and profile, vapor pressure of the liquid, and solubility of the trapped air in the liquid 29,34,36 . Researchers have been able to realize GEMs using silicon wafers and polymethylmethacrylate sheets as the test substrates, and proof-of-concept applications for DCMD in a cross-flow configuration have been demonstrated 37 .…”