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The deflation of a hydraulic fracture subject to fluid withdrawal through a narrow conduit: the influence of material toughness

Published online by Cambridge University Press:  18 March 2025

Zhong Zheng Open the ORCID record for Zhong Zheng [Opens in a new window]
Zhong Zheng*
Affiliation:
State Key Laboratory of Ocean Engineering, School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China MOE Key Laboratory of Hydrodynamics, School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
*
Corresponding author: Zhong Zheng, [email protected], [email protected]
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Abstract

We study the dynamic deflation of a hydraulic fracture subject to fluid withdrawal through a narrow conduit located at the centre of the fracture. Recent work revealed a self-similar dipole-flow regime, when the influence of material toughness is negligibly small. The focus of the current work is on the influence of material toughness, which leads to an additional self-similar regime of fracture deflation with fixed frontal locations in the toughness-dominated regime. The two limiting regimes can be distinguished by a dimensionless material toughness $\Pi _k$, defined based on a comparison with the influence of the viscous thin film flow within the fracture: $\Pi _k \to 0$ indicates the dipole-flow regime, while $\Pi _k \to \infty$ indicates the fixed-length regime. For intermediate $\Pi _k$, the fracture’s front continues to propagate during an initial period of deflation before it remains pinned at a fixed location thereafter. A regime diagram is then derived, with key scaling behaviours for the frontal dynamics, pressure and volume evolution summarised in a table for the self-similar stage. A comparison is also attempted between theoretical predictions and available experimental observations of viscous backflows from transparent solid gelatins.

JFM classification

Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1007 , 10 April 2025 , A71
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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