Capillary and priming pressures control the penetration of yield-stress fluids through non-wetting 2D meshes

Forcing hydrophilic fluids through hydrophobic porous solids is a recurrent industrial challenge. If the penetrating fluid is Newtonian, the imposed pressure has to overcome the capillary pressure at the fluid-air interface in a pore. The presence of a yield-stress, however, makes the pressure transfer and the penetration significantly more complex. In this study, we experimentally investigate the forced penetration of a water based yield-stress fluid through a regular hydrophobic mesh under quasi-static conditions, combining quantitative pressure measurements and direct visualisation of the penetration process. We reveal that the penetration is controlled by a competition between the yield-stress and two distinct pressures: the capillary pressure, which dictates the threshold at which the yield-stress fluid penetrates the hydrophobic mesh, and a priming pressure, which controls how the fluid advances through it. The latter corresponds to a pressure drop ensuing a local capillary instability, never reported before. Our findings shed new light on forced imbibition processes, with direct implications on their fundamental understanding and practical engineering.