Characterization of wetting using topological principles

Hypothesis: Understanding wetting behavior is of great importance for natural systems and technological applications. The traditional concept of contact angle, a purely geometrical measure related to curvature, is often used for characterizing the wetting state of a system. It can be determined from Young's equation by applying equilibrium thermodynamics. However, whether contact angle is a representative measure of wetting for systems with significant complexity is unclear. Herein, we hypothesize that topological principles based on the Gauss-Bonnet theorem could yield a robust measure to characterize wetting. Theory and experiments: We introduce a macroscopic contact angle based on the deficit curvature of the fluid interfaces that are imposed by contacts with other immiscible phases. We perform sessile droplet simulations followed by multiphase experiments for porous sintered glass and Bentheimer sandstone to assess the sensitivity and robustness of the topological approach and compare the results to other traditional approaches. Findings: We show that the presented topological principle is consistent with thermodynamics under the simplest conditions through a variational analysis. Furthermore, we elucidate that at sufficiently high image resolution the proposed topological approach and local contact angle measurements are comparable. While at lower resolutions, the proposed approach provides more accurate results being robust to resolution-based effects. Overall, the presented concepts open new pathways to characterize the wetting state of complex systems and theoretical developments to study multiphase systems.