Hairy fluid mechanics: Dynamic elastocapillarity in deformable beam arrays

Natural surfaces are frequently textured with arrays of slender, filamentous structures that serve vital functions on a wide variety of length scales. Such surfaces often operate at fluid interfaces and are flexible enough to be deformed by surface tension effects. While previous studies have looked at beam bending due to either viscous drag or surface tension independently, the role of a moving contact line through a deformable medium remains relatively unexplored. Interfacial flows past flexible arrays of fibres are highly coupled: when capillary forces of a moving interface are strong enough to deform a surface, that deformation in turn modifies local flow geometry. Here we study this phenomenon by fabricating channels textured with a "hairy" elastoporous media and subsequently displacing an initial layer of fluid with an immiscible invading phase. We first develop a model to describe the deflection of a one-dimensional array of elastic beams by Laplace pressure. Then, we couple the surface tension model with the local fluid dynamics through the porous media. We find that a defending phase can be fully removed from a rigid, undeformed array. However, for flexible surfaces the onset of elastocapillary effects has a profound effect on drainage at quasi-static flow conditions.