Growth of gas bubbles by rectified diffusion at high supersaturation levels

There is continued interest in possible effects of under‐water sound on the growth of gas bubbles in capillaries of marine mammals and humans. [Houser et al., J. Theor. Biol. 213, 183 (2001)] showed that following a series of dives, gas supersaturation in capillaries of marine mammals can reach 300%. For such high supersaturation levels, standard mathematical models of both static and rectified diffusion 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 heat conditions in the bubble. The Rayleigh‐Plesset equation is used to describe the bubble dynamics. 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 equilibrium state for a bubble of constant 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 concentration gradient at the bubble wall, and therefore a growth rate in excess of predictions based on quasistatic gas concentrations. [Work supported by ONR.]