### 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-fsmodulus 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 tα 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) t4/9 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 laboratorymodel for further studies of fluid-driven cracks, which has important applications such as hydraulic fracturing.

Original language | English (US) |
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Article number | 20150255 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 471 |

Issue number | 2182 |

DOIs | |

Publication status | Published - Oct 8 2015 |

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### Keywords

- Fluid-structure interactions
- Geophysical and geological flows
- Thin films

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

### Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*471*(2182), [20150255]. https://doi.org/10.1098/rspa.2015.0255