Rectified diffusion at megahertz frequencies

Abstract

Rectified diffusion studies have in the past been generally confined to kilohertz frequency ranges where experimental confirmation of theoretical predictions can be made. However, since most of the ultrasonic devices used in medicine operate in the megahertz frequency range, it is important to extend these studies of the growth of bubbles by ultrasound to the higher range. We have modified and extended the equations associated with rectified diffusion to apply at megahertz frequencies, and have numerically solved these equations for a variety of conditions such as dissolved gas concentration, distribution of nuclei, and the frequency and intensity of the ultrasound. We have also obtained solutions for both the continuous and pulsed modes of operation. Our results indicate that bubbles can be made to grow at typical levels of exposure used in medical applications. Furthermore, at higher intensities, such as those used in studies on bean roots by Morris and Coakley [to be published in Ultrasound Med. Biol.], the times required for growth to resonance size are on the same order of magnitude as the periods associated with acoustic emissions from the root during insonification. [Work partially supported by the Office of Naval Research and the National Science Foundation.]