Nonlinear dynamics of gas bubbles in viscoelastic media Nonlinear dynamics of gas bubbles in viscoelastic
media
Xinmai Yang and Charles C. Church
National Center for Physical Acoustics, The University of Mississippi, University, Mississippi 38677
xmyang@olemiss.edu
Abstract: Understanding the behavior of cavitation bubbles driven by ultrasonic
fields is an important problem in bioMedical acoustics. The Keller–
Miksis equation for nonlinear bubble dynamics is combined with the Voigt
model for viscoelastic media. Using experimentally determined values, the
effects of elasticity on bubble oscillations are studied. Inertial cavitation
thresholds are determined using Rmax /R052, and subharmonic emissions are
also estimated. The elasticity increases the threshold pressure for inertial
cavitation, and subharmonic signals are significant only in a certain region of
radii and driving pressures at a given frequency. These results should prove
useful in cavitation detection and bubble-enhanced imaging work.
© 2005 Acoustical Society of America
PACS numbers: 43.35.Wa, 43.80.Sh, 43.35.Ei
Date Received: December 15, 2004 Date Accepted: April 11, 2005
1. Introduction Polytechnic
Bubble dynamics models are well established for bubbles in water or simple Newtonian fluids.
With the development of new Materials and new techniques, the study of bubble dynamics in
viscoelastic media becomes necessary. The increasing importance of cavitation studies is partly
due to applications in Medical ultrasound. For example, the use of bubble-based contrast agents
in diagnostic ultrasound has significantly increased the quality of imaging. In these situations,
the media often exhibit non-Newtonian behavior. Recently, this issue has become more
important due to the development of high-intensity focused ultrasound for therapeutic medicine.
High-intensity sound may induce cavitation in soft tissue, and these microbubbles can have a
huge impact on the distribution of the ultrasound energy. Understanding the behavior of this
cavitation can provide a powerful tool for improving the quality of results of medical ultrasound
in clinics.
The study of these microbubbles involves bubble oscillations in viscoelastic media.
Many researchers have extended the study of bubble dynamics in Newtonian fluids to
viscoelastic fluids.1–7 For the purpose of diagnostic ultrasound, relatively low-intensity sound is
used. At these levels, essentially no cavitation occurs in soft tissue directly,8 and the only source
of microbubbles is by injection of bubble-based contrast agents. However, the use of highintensity
ultrasound will cause cavitation in soft tissue directly. These bubbles differ from
contrast agent bubbles in that they (1) are free bubbles; and (2) may oscillate nonlinearly
because of the high intensity of the sound field.