Dynamics of fluid-driven fractures in the viscous-dominated regime

Hydraulic fracturing is a natural and industrial process that creates tensile fractures in rock using

pressurized liquids. In its simplest form, the tensile fracture is a single penny-shaped crack. The

propagation dynamics of a crack depend on the viscosity and flow rate of the injected fluid and the

material properties of the brittle solid. During the injection, the fracture’s growth can be controlled

by viscous dissipation in the liquid (the so-called viscous regime) or the fracture energy (the so-called

toughness regime). We report an experimental study on the fracture dynamics during and after the

injection of a viscous fluid in a block of hydrogel. Our experiments show that the fracture radius

increases even after the injection stops. We measure the radius and thickness of the fracture over

time. We evidence three regimes of propagation: (1) a constant-flow rate viscous regime, (2) a

constant-volume viscous regime, and (3) toughness-limited saturation. Scaling arguments are

provided to explain the experimental results and provide insights into the underlying physics.