The Dynamics of Freely Oscillating Gas-Vapor Bubbles

This dissertation describes experimental and theoretical studies of the dynamics of freely oscillating gas-vapor bubbles. Longuet-Higgins has predicted that bubble surface modes can produce, through nonlinear coupling, monopole sound radiation. The first part of this dissertation is devoted to an experimental investigation of this phenomenon. A hydrophone and needle were submerged in water in a small sealed cell that was connected to a regulated evacuation system. The sound produced by releasing a bubble from the needle was monitored by a hydrophone and displayed on an oscilloscope. Two high speed video cameras simultaneously recorded the bubble motion and the displayed sound trace. At pressures of a few cm-Hg, it was seen that after the bubble -generation sound died out, there followed a sound of the same frequency but lower magnitude. Because this sound amplitude increased as the ambient pressure decreased and had its maximum value at resonance, it appeared that this sound was evidence for a surface-mode induced volume-mode. Careful data analysis shows that there exists a mutual interaction between these surface and volume modes. The second half of the dissertation contains the development of a theory, in which the resonance frequency omega_{x} and damping constant omega_{y} for free volume oscillations of a spherical bubble in an infinite medium are derived from the linearized, fundamental equations of fluid dynamics. There are three possible wave propagation modes that satisfy the governing equations for the gas-vapor mixture inside the bubble. Outside it, only two modes need be considered because gas diffusion across the bubble surface into the liquid appears negligible for free oscillations. Two parameters omega _{x} and omega_ {y} are values such that the boundary conditions can be satisfied. The dependence of omega_{x} and omega _{y} on many physical parameters is examined. For a bubble containing mostly gas, the values of omega_{x} and omega_{y} agree with previous theories. For a bubble containing mostly vapor, significant additional damping occurs from the effects of vapor evaporation-condensation. We also find that there exists only one resonance frequency for free oscillations, in contrast to the predictions of Finch and Neppiras who suggested that two resonances are possible.