The main purpose of the present work is to investigate the nonlinear motion of a single oscillating bubble immersed in a non-Newtonian fluid, subjected to an acoustic pressure field. The fluid is characterized as a suspension of additives (long Â¯bers or few ppm of macromolecules), combining an extensional viscosity and elastic effects. While the extensional viscosity is related to the strong anisotropy produced in the flow by the stretched macromolecule, the elastic part of the model represents the relaxation of the additives, resulting in a modified version of the classical Rayleigh-Plesset equation of bubble dynamics that might be integrated by using a Â¯fth order Runge-Kutta scheme with appropriated time steps. Constitutive equations for an anisotropic model, linear viscoelastic and nonlinear Maxwell-Oldroyd models are developed and different solutions are presented. A scale analysis of the relevant parameters in the bubble dynamics is made, with the purpose to investigate the importance of anisotropic and elastic con- tributions on the bubble movement stabilization. The influence of several physical parameters in the bubble response are investigated, e.g., the Reynolds number, Re, Deborah number, De, the particle volume fraction, and many others. An additive orientation function is developed, which describes the radial bubble motion coupling with the additives orientation using a probability density function to represent the mean orientation of the additives in the host fluid. The interaction bubble-additives is considered for an influence radius or a boundary layer thickness of probability, Â±, which varies accordingly with the bubble oscillation and an initial random orientation condition. Analytical solutions for the bubble minimum radius of collapse, for the convolution integral in the linear viscoelastic model and for the thickness Â± are presented. The bubble dynamics in the frequence spectrum is also analyzed |