Displacement Flow in Penny-Shaped Cracks

We revisit the classical displacement flow problem in a growing penny-shaped fracture. When a single fluid is injected into a brittle material, the viscous dissipation in the fracking fluid and fracture energy required at the crack tip resist the propagation. Experimental studies have demonstrated the existence of two asymptotes of propagation. If viscous dissipation dominates the crack dynamics, the propagation is in the viscous regime. If the fracture toughness is the limiting process, the propagation is in the toughness regime. Here, we report an experimental study of injection in an oil-filled fracture in gelatine, a model material to study fractures in elastic-brittle materials. The initial oil-filled crack is penny-shaped, and upon injection of an immiscible liquid, the crack further expands by pushing the oil. We investigate the propagation of the fracture and the displacement of the oil/water interface in both the viscous and toughness regimes. Our experiments show that the propagation dynamics in this displacement configuration differ from the single-fluid injection. We explain the experimental results, compare the behavior in the two regimes, and provide insights into the underlying physics with scaling arguments.