Relaxation of a fluid-filled blister on a porous substrate

The relaxation dynamics of a fluid-filled blister between an elastic sheet and a porous substrate are controlled by the deformation of the elastic sheet, the viscous stresses in the pores, and the capillary pressure at the liquid-air interface due to imbibition. We develop a mathematical model to study the effects of varying the permeability of the porous substrate, the bending stiffness of the elastic sheet, and the blister size on the relaxation dynamics. Experiments are conducted by injecting a finite volume of viscous fluid between a porous substrate and an elastic sheet, where fluid first invades the pores, and subsequently, as the pressure in the fluid increases, the elastic sheet is peeled and uplifted from the substrate to form a fluid-filled blister. After injection is stopped, the fracture front is static, and the elastic stresses in the overlying sheet and the capillary pressure at the liquid-air interface drive the drainage of the blister into the pores. We identify two regimes of drainage. For thick sheets and more permeable substrates, drainage is primarily due to the stresses in the deformed elastic sheet. For thin sheets and less permeable substrates, drainage is driven by the imbibition of the liquid into the pore space. Our model and experiments are relevant to the drainage of fluid-driven fractures in porous media.