Modeling air–water interface in disordered fibrous media with heterogeneous wettabilities

Considering the balance of mechanical forces across a meniscus anchored to two circular objects, we developed a CPU-friendly semi-analytical algorithm for tracking the instantaneous shape and position of the air–water interface inside microstructures that resemble a collection of disordered parallel cylinders, e.g., a bundle of fibers in a fiber-reinforced composite or microfabricated posts in a microfluidic system. In the context of fluid transport in fibrous media, in particular, the methodology presented in this paper provides a means for producing a relationship between capillary pressure and fluid saturation in media with heterogeneous wettabilities – often needed to predict the rate of fluid transport. In addition, we developed a conversion formulation that allows a capillary pressure–saturation relationship obtained for one combination of contact angles to be used to construct such a relationship for media with different combinations of contact angles, eliminating the need for additional simulations.