Nonlinear oscillations of gas bubbles in viscous and viscoelastic fluids

The nonlinear oscillations of gas bubbles in viscous and viscoelastic fluids are examined. The primary motivation is to better understand acoustically forced bubble behavior in tissues and biological fluids. As a preliminary step, pressure thresholds for inertial cavitation are calculated for biological media modeled as a viscous fluid. There is a trend toward increasing pressure thresholds with increasing frequency and/or viscosity. The "nonlinear resonance radius" provides a descriptor of the initial bubble sizes most likely to undergo inertial cavitation.;In order to more accurately account for the physical characteristics of biological materials, a description of bubble behavior in viscoelastic fluids is sought. A novel approach is implemented in which a new set of equations for bubble dynamics in linear viscoelastic fluids is developed. This set of equations is examined using the method of multiple scales perturbation technique and also numerically. The analysis reveals an increased oscillation amplitude compared to the corresponding Newtonian case. This effect has a pressure threshold dependence and increases with increasing Deborah number. Increasing the retardation time in the linear Jeffereys model damps the oscillatory elastic effects. New viscoelastic effects are revealed for resonance and nonresonance forcing cases.;Questions about the trace of the stress tensor are addressed. Numerical solutions are obtained for bubble dynamics equations coupled with the Upper Convective Maxwell (UCM) and Phan-Thien constitutive equation models. These results document how the radial and theta components contribute to the bubble collapse and growth. The UCM model solutions are compared with those from the linear Maxwell formulation. Excellent agreement is found in the limit of small amplitude oscillations; however, the linear Maxwell eventually over-predicts the bubble growth for increasing deformation. Potential implications for medical ultrasound applications are discussed.