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Bubble dynamics in a viscoelastic medium with nonlinear elasticity

Published online by Cambridge University Press:  30 January 2015

R. Gaudron ,
M. T. Warnez  and
E. Johnsen
R. Gaudron*
Affiliation:
Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48109, USA
M. T. Warnez
Affiliation:
Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48109, USA
E. Johnsen*
Affiliation:
Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48109, USA
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

In a variety of recently developed medical procedures, bubbles are formed directly in soft tissue and may cause damage. While cavitation in Newtonian liquids has received significant attention, bubble dynamics in tissue, a viscoelastic medium, remains poorly understood. To model tissue, most previous studies have focused on Maxwell-based viscoelastic fluids. However, soft tissue generally possesses an original configuration to which it relaxes after deformation. Thus, a Kelvin–Voigt-based viscoelastic model is expected to be a more appropriate representation. Furthermore, large oscillations may occur, thus violating the infinitesimal strain assumption and requiring a nonlinear/finite-strain elasticity description. In this article, we develop a theoretical framework to simulate spherical bubble dynamics in a viscoelastic medium with nonlinear elasticity. Following modern continuum mechanics formalism, we derive the form of the elastic forces acting on a bubble for common strain-energy functions (e.g. neo-Hookean, Mooney–Rivlin) and incorporate them into Rayleigh–Plesset-like equations. The main effects of nonlinear elasticity are to reduce the violence of the collapse and rebound for large departures from the equilibrium radius, and increase the oscillation frequency. The present approach can readily be extended to other strain-energy functions and used to compute the stress/deformation fields in the surrounding medium.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Cavitation Drops and Bubbles: Drops and Bubbles
Type
Papers
Information
Journal of Fluid Mechanics , Volume 766 , 10 March 2015 , pp. 54 - 75
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© 2015 Cambridge University Press 

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