A method to account for acoustic microstreaming when predicting bubble growth rates produced by rectified diffusion

A reinterpretation of existing theory for rectified diffusion, the process by which bubbles in a sound field may grow in radius, is presented in order to quantitate the effect of acoustic microstreaming on bubble growth rates. The 1/t term in the growth rate equation is defined as the "decay term" and t as the "decay time," the time required for the gas concentration in the liquid contacting the bubble to rise (or fall) from its initial to its final value. In the absence of microstreaming, t is the duration of sonification. In the presence of microstreaming, t may be calculated from the streaming velocity and the bubble radius. A comparison between theory and the experimental results of Eller [A. Eller, J. Acoust. Soc. Am. 46, 1246-1250 (1969)] and of Gould [R.K. Gould, J. Acoust. Soc. Am. 56, 1740-1746 (1974)] shows reasonable agreement in the low kHz range. Theoretical results in the frequency range of 1-10 MHz at 1 and 4 bar are also presented.