Probing Effective Wetting in Subsurface Systems

Wetting phenomena are of central importance for many natural and technological processes in subsurface geosciences. Surface roughness, chemical heterogeneity, and dynamic effects cause the microscopic contact angle to vary widely in subsurface multiphase systems. These effects must be characterized in a fundamental and transparent way to determine the overall state of wetting. Here, we apply the Gauss-Bonnet theorem to establish a direct link between the contact angle and bulk fluid topology based on a newly defined term, deficit curvature. The resulting macroscopic measure is able to capture the average effects of complex microscopic variations in contact angle based on intrinsic geometric constraints that are imposed on the curvature of the contact line as a consequence of fluid topology. We show that deficit curvature is able to capture the effects of contact angle hysteresis and describe wetting in multiphase systems where geometrically complex contact lines are present along with surface heterogeneity.