Fluid-Structure Interactions for Energy and the Environment

Abstract

This thesis explores a range of problems involving the interplay between fluid flow and deformable interfaces, with applications in energy and the environment. In particular, we study the fracturing of elastic material driven by fluid intrusion, the flow of compressible aqueous foam in a deformable fracture, and the interfacial dynamics of a bursting bubble.

Inspired by hydraulic fracturing, where pressurized water is used to fracture shale formations, we design a laboratory experiment using gelatin to mimic the brittle and elastic rock. Liquid is injected to crack the elastic matrix. We vary the Young's modulus of the solid, the liquid viscosity and the injection flow rate to vary the relative importance of the viscous stresses along the flow to the stresses required to extend the crack surfaces. The experimental results exhibit good agreement with the scaling arguments of fracture dynamics in both the viscous regime (viscous effects dominant) and the toughness regime (stresses related to crack opening dominant). Next, we study the fluid flow in a closing crack driven by the elastic relaxation of the solid. A balance between the elastic stresses of the deformed matrix and the viscous stresses in the fluid flow predicts that the volume of fluid in the crack decays with time according to a -1/3 power law, which agrees well with our experiments.

In addition to incompressible liquids, we investigate the injection of compressible aqueous foam to crack a solid. Foams have been employed in industry to reduce the water use in hydraulic fracturing. For a sufficiently fast injection rate, the compressibility of the foam results in unexpected flow dynamics. We developed a scaling argument for the dynamics of foam-driven fracture, which exhibits excellent agreement with our experiments. Our work provides new insights into the physics of compressible foam flow in narrow channels.

Finally, we discuss the dynamics of bursting bubbles. After a bubble bursts, a jet forms and small daughter bubbles are entrained into the liquid. We present a scaling law for the jet dynamics as a function of the liquid properties and the initial size of the bubble, which agrees with our numerical simulations.