Fluid-Driven Fractures in Elastic Hydrogels: Propagation and Coalescence
In this thesis we focus on a novel experimental exploration of fluid-driven fractures in a brittle hydrogel matrix. Fluid-driven fracturing is a procedure by which a fracture is initiated and propagates due to pressure applied by a fluid introduced inside the fracture. We describe how to construct the experimental setup utilised in this research, including how to synthesise polyacrylamide hydrogels to study the processes linked with fluid-driven fracturing. These transparent, linearly elastic and brittle gels permit fracturing at low pressures and speeds allowing accurate measurements to be obtained. The broad range of modulus and fracture energy values attainable from this medium allow the exploration of particular regimes of importance. Fracturing within these hydrogels also creates beautiful spiral patterns on the plastically deformed surfaces. We analyse these patterns and discuss their formation, while also commenting on their fractal-like nature. Initially, we study single fractures that are driven by an incompressible Newtonian fluid, injected at a constant rate into an elastic matrix. The injected fluid creates a radial fracture that propagates along a plane. We investigate this type of fracture theoretically and then verify the scaling predictions experimentally. We examine the rate of radial crack growth, fracture aperture, shape of the crack tip and internal fluid flow field. We exhibit the existence of two distinct fracturing regimes, and the transition between these, in which propagation is either dominated by viscous flow within the fracture or the material toughness. Particle image velocimetry measurements also strikingly show that the flow in the fracture can alter from an expected radial symmetry to circulation cells, dependent on the regime of propagation. We then expand our research to the problem of two coplanar fluid-driven radial fractures. This was chosen to focus on the physical mechanisms that are key to fracture network formation, related to many geophysical and industrial practices. Initially, the two fractures propagate independently of each other. At a critical separation they begin to interact, with non-uniform growth occurring along the fracture edges due to the evolving stress state in the gel matrix. When the radial extents of the fractures become sufficiently large, they coalesce and form a bridge between them. Following initial contact, a large increase in flow is seen into the newly created bridge and most of the growth is localised along this, perpendicular to the line connecting the injection sources. From experimental measurements, we observe a universal dynamic behaviour for the growth of this bridge. We model this universal behaviour theoretically and construct scalings related to the growth after coalescence, which again identifies both a viscous and toughness regime. The toughness regime is verified experimentally for the bridge growth and the universal shape of the thickness profile along the bridge. The coalesced fractures then transition into a single fracture at late times. Finally, we discuss a number of other interesting scenarios that may occur such as, non-coalescing fractures, asymmetric coalescence and ridge formation.
Hydraulic fracturing, Coalescence, Geophysics, Hydrogel, Fluids
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