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Ultrasound Beam Radiated From Circular Piston in Bubbly Liquids: Nonlinear Analysis for Envelope of Short Waves With Diffraction Effect

[+] Author Affiliations
Junya Kawahara, Tetsuya Kanagawa, Kazumichi Kobayashi, Masao Watanabe, Shigeo Fujikawa

Hokkaido University, Sapporo, Japan

Takeru Yano

Osaka University, Suita, Japan

Paper No. AJK2011-33019, pp. 251-256; 6 pages
  • ASME-JSME-KSME 2011 Joint Fluids Engineering Conference
  • ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 2, Fora
  • Hamamatsu, Japan, July 24–29, 2011
  • Conference Sponsors: Fluids Engineering Division
  • ISBN: 978-0-7918-4441-0
  • Copyright © 2011 by JSME


A weakly diffracted ultrasound beam radiated from a circular piston placed in a bubbly liquid is formulated in terms of a wave equation based on scaling relations of physical parameters [1]: typical propagation speed, period, wavelength, and diameter of beam. We derive a nonlinear evolution equation for the modulation of quasi-monochromatic waves for the case of a short wavelength with a moderately high frequency from a set of basic equations for bubbly flows: conservation equations of mass and momentum for gas and liquid in a two-fluid model, Keller’s equation for bubble wall motion, state equations for gas and liquid, and so on. The compressibility of liquid is taken into account, and thus the waves are attenuated due to bubble oscillations. The viscosity of gas, heat conduction in gas and liquid, and phase change across bubble wall are ignored. As a result, the nonlinear Schrödinger equation for the envelope of the beam with diffraction effect is derived from the basic equations. For plane waves the diffraction term does not appear, and hence our equation is reduced to the original nonlinear Schrödinger equation [1].

Copyright © 2011 by JSME



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