Experimental study on penny-shaped fluid-driven cracks in an elastic matrix

Abstract

When a pressurized fluid is injected into an elastic matrix, the fluid generates a fracture that grows along a plane and forms a fluid-filled disc-like shape. We report a laboratory study of such a fluid-driven crack in a gelatin matrix, study the crack shape as a function of time and investigate the influence of different experimental parameters such as the injection flow rate, Young’s modulus of the matrix and fluid viscosity. We choose parameters so that effects of material toughness are small. We find that the crack radius R ( t ) increases with time t according to t α with α =0.48±0.04. The rescaled experimental data at long times for different parameters collapse based on scaling arguments, available in the literature, showing R ( t )∝ t 4/9 from a balance of viscous stresses from flow along the crack and elastic stresses in the surrounding matrix. Also, we measure the time evolution of the crack shape, which has not been studied before. The rescaled crack shapes collapse at longer times and show good agreement with the scaling arguments. The gelatin system provides a useful laboratory model for further studies of fluid-driven cracks, which has important applications such as hydraulic fracturing.