Advanced Mathematical Modeling of Sonar-Induced Bubble Growth and Coalescence in Humans and Marine Mammals
Final rept. Feb 2005-Jul 2008
TEXAS UNIV AT AUSTIN APPLIED RESEARCH LABS
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For high gas supersaturation levels in liquids, on the order of 300 as predicted in capillaries of marine mammals following a series of dives, standard mathematical models of both static and rectified diffusion are found to underestimate the rate of bubble growth by 10-20. The discrepancy is demonstrated by comparing predictions based on existing mathematical models with direct numerical solutions of the differential equations for gas diffusion in the liquid and thermal conditions in the bubble. Underestimation of bubble growth by existing mathematical models is due to the underlying assumption that the gas concentration in the liquid is given by its value for a bubble of constant equilibrium radius. This assumption is violated when high supersaturation causes the bubble to grow too fast in relation to the time scale associated with diffusion. Rapid bubble growth results in an increased gas concentration gradient at the bubble wall, and therefore a growth rate in excess of predictions based on constant equilibrium bubble radius. The effect of gas supersaturation level, excitation frequency, duty cycle and sound pressure level on bubble growth were also studied.
- Numerical Mathematics