Modeling rectified diffusion, with application to potential bubble growth in marine mammals



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In this thesis, research by Crum and Mao [J. Acoust. Soc. Am. 99, 2898--2907 (1996)] and Houser, Howard, and Ridgway [J. Theor. Biol. 213, 183--195 (2001)] is extended by numerically investigating bubble growth (initial radius of 10 microns) during rectified diffusion for gas supersaturations up to 300% by using the Fyrillas-Szeri equation [J. Fluid Mech. 277, 381--407 (1994)]. Bubble growth is simulated for a range of frequencies (100 Hz to 10 kHz), sound pressure levels (205 dB to 215 dB re 1 micropascal), and gas supersaturations (150% to 300%). Simulations are presented for continuous and monofrequency excitation, repeated tone bursts, and pulsed frequency-modulated waveforms. The potential for bubble growth to occur in marine mammals is also considered. For the parameters considered, static diffusion becomes the dominant growth mechanism as supersaturation is increased, bubble growth is frequency independent away from bubble resonance, and bubble growth due to duty-cycle excitation can be modeled as an effective continuous source with a reduced sound pressure level. A more accurate model of in vivo marine mammal tissue is required to determine if rectified diffusion can trigger bubble growth at the levels predicted in this thesis.