Dynamics of gas bubbles in viscoelastic fluids. I. Linear viscoelasticity

The nonlinear oscillations of spherical gas bubbles in linear viscoelastic fluids are studied. A novel approach is implemented to derive a governing s ystem of nonlinear ordinary differential equations. The linear Maxwell and Jeffreys models are chosen as the fluid constitutive equations. An advantag e of this new formulation is that, when compared with previous approaches, it facilitates perturbation methods and numerical investigations. Analytica l solutions are obtained using a multiple scale perturbation method and com pared with the Newtonian results for various Deborah numbers. Numerical ana lysis of the full equations supports the perturbation analysis, and further reveals significant differences between the viscoelastic and Newtonian cas es. Differences in the oscillation phase and harmonic structure characteriz e some of the viscoelastic effects. Subharmonic excitations at particular f luid parameters lead to a discrete group modulation of the radial excursion s; this appears to be a unique, previously undiscovered phenomenon. Implica tions for medical ultrasound applications are discussed in light of these c urrent findings. (C) 2000 Acoustical Society of America. [S0001-4966(00)046 06-3].