The impact of pressure oscillations on bubble rising in shear-thinning fluids

We study the rising dynamics of a bubble driven into periodic volumetric oscillations by an external pressure driving within a highly viscous shear-thinning fluid. We perform axisymmetric direct numerical simulations employing the Carreau–Yasuda model to describe the rheological behavior of the fluid and the finite element method to discretize the equations. We carry out a parametric study of the bubble rising dynamics, changing the amplitude and the frequency of the external pressure driving, and the bubble radius. Due to the external pressure oscillations, the bubble undergoes volume changes that strain the liquid at much larger rates than those due to natural rising, causing the surrounding fluid viscosity to thin. The numerical results show that the rising dynamics become highly nonlinear and unsteady due to the interplay of the shear-thinning rheology and the external driving. As a result, the period-averaged rising velocity of the bubble can increase by orders of magnitude compared to its natural rising velocity. These nonlinear effects become progressively more important as the amplitude and the frequency of the pressure driving or the bubble radius are increased. Qualitatively, the simulation model agrees with previous experimental findings in terms of average rising velocity. However, the experiments exhibit terminal velocities that are smaller than those predicted numerically, along with differences in bubble shape during the ascent. These discrepancies may be attributed to modeling the fluid rheology as a generalized Newtonian fluid rather than as a viscoelastic one.