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

•A model for tracking a fluid interface in a bank of parallel dissimilar cylinders.•Algorithm is based on balance of applied pressure and capillary forces on menisci.•Instantaneous interface shape and fluid saturation are obtained and reported.•Algorithm can handle systems with fibers of multiple wettabilities.•Proposed an equation to expand utility of results beyond the current simulations.

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.

Graphical abstractA novel interface tracking algorithm is presented which determines the location and shape of the fluid interface(s) over varying applied pressures for structures comprised of randomly placed parallel fibers or cylinders. Fibers of different hydrophilicities can exist within the same structure.Figure optionsDownload full-size imageDownload as PowerPoint slide