Linear Waves in Bubbly Liquids via the Kramers-Kronig Relations

[+] Author and Article Information
N. Brauner

School of Engineering, Department of Fluid Mechanics and Heat Transfer, Tel Aviv University, Ramat Aviv 69978, Israel

A. I. Beltzer

Holon Institute for Technological Education, affiliated with Tel-Aviv University, P.O. Box 305, Holon 58102, Israel

J. Vib. Acoust 113(3), 417-419 (Jul 01, 1991) (3 pages) doi:10.1115/1.2930201 History: Received April 01, 1990; Online June 17, 2008


A simple closed form analytic solution, as well as numerical solutions, are derived for acoustic waves of an arbitrary frequency, propagating in dilute bubbly liquids. The applied method treats the effective wave as a causal response of a linear system. The results are compared with the prediction of Foldy’s theory, which in this particular case is shown to be consistent with the Kramers-Kronig relations. These results thus complement recently reported investigations concerning the causal approach as well as the validity of Foldy’s theory.

Copyright © 1991 by The American Society of Mechanical Engineers
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