Dynamics of gas bubbles in viscoelastic fluids. II. Nonlinear viscoelasticity

The nonlinear oscillations of a spherical, acoustically forced gas bubble i n nonlinear viscoelastic media are examined. The constitutive equation [Upp er-Convective Maxwell (UCM)] used for the fluid is suitable for study of la rge-amplitude excursions of the bubble, in contrast to the previous work of the authors which focused on the smaller amplitude oscillations within a l inear viscoelastic fluid [J. S. Alien and R. A. Roy, J. Acoust. Soc. Am. 10 7, 3167-3178 (2000)]. Assumptions concerning the trace of the stress tensor are addressed in light of the incorporation of viscoelastic constitutive e quations into bubble dynamics equations. The numerical method used to solve the governing system of equations (one integrodifferential equation and tw o partial differential equations) is outlined. An energy balance relation i s used to monitor the accuracy of the calculations and the formulation is c ompared with the previously developed linear viscoelastic model. Results ar e found to agree in the Limit of small deformations; however, significant d ivergence for larger radial oscillations is noted. Furthermore, the inheren t limitations of the linear viscoelastic approach are explored in light of the more complete nonlinear formulation. The relevance and importance of th is approach to biomedical ultrasound applications are highlighted. Prelimin ary results indicate that tissue viscoelasticity may be an important consid eration for the risk assessment of potential cavitation bioeffects. (C) 200 0 Acoustical Society of America. [S0001-4966(00)01210-8].