Abstract:
The acoustically forced oscillations of gas bubbles in Newtonian fluids have been studied extensively; however, these oscillations have not been as thoroughly investigated in non-Newtonian fluids. An understanding of the non-Newtonian effects of viscoelasticity on this phenomena is particularly important to medical acoustic applications involving oscillatory bubble behavior in biological tissues and fluids. The stress tensor formalisms for non-Newtonian fluids used in previous works are reviewed and scrutinized. Inconsistencies in the literature and subsequent questions about the trace of the stress tensor are highlighted. As an initial step, a weakly nonlinear perturbation method is used to examine forced single bubble oscillations in a viscoelastic fluid. A novel analytical formulation is employed to make the perturbation approach (method of multiple scales) to the problem more tractable. Furthermore, this new formulation also allows for complementary numerical solutions. The physical limitations and relevance of this work with respect to medical applications are also discussed. [Work support by NIH through Grant No. RO1 CA39374.]