Bubbly liquids occur in a large number of environmental, naval and industrial settings. From a modeling viewpoint, they present a challenging multi-phase flow problem because the highly compressible bubbles behave nonlinearly in response to large-amplitude acoustic waves, or when excited near their resonance. In this thesis, we study nonlinear wave propagation in liquids containing gas bubbles. We focus on the effect relative motion between the phases has on the wave structure.; We begin with a detailed analysis of the fluid mechanics and heat exchange for a single gas bubble. In addition to the standard added-mass and buoyancy-like forces that act on the bubble, our analysis yields the terms which strongly couple its pulsation and translation. We also analyze the heat exchange between the pulsating gas bubble and the surrounding liquid. We exactly invert the Laplace transform solution for the temperature field inside the bubble, and thereby obtain a system of integro-differential equations for the radial oscillations of a bubble. We also present a much simpler but accurate two-point Padé approximation for the thermal damping of a bubble.; We incorporate the results from the single-bubble investigation into a continuum-level description of bubbly liquids. The continuum model consists of the standard conservation laws together with a novel nonlinear equation-of-state (EOS). The EOS relates the instantaneous mixture mass and number densities, and their first two material time derivatives, to the instantaneous pressure field. We use our continuum model to study both linear and nonlinear waves (e.g., shocks) in bubbly media. Among other things, we describe exact nonlinear traveling wave solutions to our system of equations, and develop a numerical method, based upon the conservative Godunov scheme, to study transient wave phenomena in bubbly liquids.
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