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

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 θ₀. 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, θ₀, 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.