Interfacial flows past arrays of elastic fibers

At the millimetric scale and below, many systems in nature and industry are soft or deformable, e.g., in biological settings where beds of hair are common. Yet, liquid entrapment over such structures remains virtually unexplored. Here we study the fluid-structure interactions between linear arrays of flexible hairs and a mobile contact line during liquid-liquid displacement in a Hele-Shaw cell. We show that confinement and elastocapillarity together have a dramatic effect on drainage: upon flooding a channel with oil and displacing with an immiscible water phase, the moving contact line evacuates the interstice between beams while simultaneously deforming the fibers due to interfacial forces. When beams contact neighbors, pores become inaccessible and thus the defending phase is trapped within elastocapillary bundles. Unlike the single phase case, in which viscous dissipation is the sole force deforming the beams, here deformation is pronounced due to the presence of an interface even in the limit of vanishing flow rates. We predict the volume of fluid removed past a highly deformable elastic medium, which deviates significantly from the rigid case.