Quantification of sub-surface capillary pressure distribution within unstructured superhydrophobic surfaces

Abstract

We propose a novel methodology for obtaining the sub-surface capillary pressure $\left(P_C\right)$ distribution of unstructured superhydrophobic surfaces (USHS), enabling the quantification of its resistance to Cassie to Wenzel transition (CWT) before any direct testing. The method effectively characterizes USHS with completely random textures utilizing surface texture measurements from profilometry. This approach supersedes the standard practice of using a singular $P_C$ value to characterize such surface microtextures, which is often insufficient to capture the uncertainty associated with the wetting transition in the case of USHS. The proposed method incorporates a resolution adequacy check, thereby making the methodology self-regulating and ensuring the credibility of the raw profilometer data. We propose a morphological approach using FE-SEM images to obtain reasonable $P_C$ estimates in case obtaining high-resolution profilometry data is not possible. We demonstrated that $\mathrm{RSm}$ (mean spacing of profile irregularities) values obtained from the profilometry of USHS help estimate their $P_C$ distribution, offering a scalable route for characterizing USHS. The methodology is validated using elastic non-Newtonian droplets in impact tests on four different types of USHS, showing accurate predictions of $P_C$ distribution. This work addresses a long-standing methodological gap in the characterization of USHS, providing a predictive means to estimate capillary pressure a priori to experimental testing. Furthermore, we demonstrate how reliability analysis can be implemented to quantify uncertainty associated with USHS.