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Static and dynamic fluid-driven fracturing of adhered elastica

Banff International Research Station for Mathematical Innovation and Discovery

The geometry and propagation of fluid-driven fractures is determined by a competition between the flow of viscous fluid, the elastic deformation of the solid, and the energy required to create new surfaces through fracturing. To date, much research has focused on the formation of idealised penny-shaped cracks in elastic media [1]. However, the dynamics of fluid-driven fracturing of thin adhered elastica remain unexplored and unobserved, and provide an experimentally accessible and theoretically simpler setting in which to assess the underlying physical processes. We present a theoretical and experimental approach to model a â fractureâ produced when fluid is injected from a point source between a solid horizontal plane and an elastic sheet, which is adhered to the plane. Divergence of viscous stresses necessitates the formation of a vapour tip between the fluid front and fracture front. This results in two dynamical regimes of spreading: viscosity dominant spreading controlled by the flow of viscous fluid into the vapour tip, and adhesion dominant spreading controlled by the energy required to fracture the two layers. Constant flux experiments using clear elastic sheets (PDMS) enable new, direct measurements of the vapour tip and confirm the existence of spreading regimes controlled by viscosity and adhesion. We extend this work to consider the possibility of turbulent flow within the body of the fracture and assess the scale of the laminar tip at the fracture front. This analysis identifies the transition from turbulent to laminar control of the spreading, or equivalently the transition from bulk to tip control. These processes primarily feature industrially in the hydraulic fracturing of shale [2], but are also commonplace in nature, from magmatic intrusions in the Earthâ s crust [3, 4], to the propagation of cracks at the base of glaciers [5]. [1] D. I. Garagash and E. Detournay, â The Tip region of a Fluid-Driven fracture in an Elastic Medium,â J. Appl. Mech. 67, 183-192 (1999) [2] E. Detournay, â Mechanics of Hydraulic Fractures,â Annu. Rev. Fluid Mech. 48, 311-339 (2016) [3] C. Michaut, â Dynamics of Magmatic Intrusions in the Upper Crust: Theory and Applications to Laccoliths on Earth and the Moon,â J. Geophys. Res. 116, 1-19 (2011) [4] A. M. Rubin, â Propagation of Magma Filled Cracks,â Annu. Rev. Earth Planet. Sci. 23, 287-336 (1995) [5] V. C. Tsai and J. R. Rice, â A Model for Turbulent Hydraulic Fracture and Application to Crack Propagation at Glacier Beds,â J. Geophys. Res. Earth Surf. 115, 1-18 (2010)

Mathematics; Mechanics of deformable solids; Fluid mechanics

video/mp4

Author affiliation: Cambridge University

2019-03-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68889

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/