Taylor bubble through a Carreau fluid up to finite capillary numbers

The motion of confined Taylor bubbles through non-Newtonian fluids is characteristic of numerous engineering and biological systems, yet a comprehensive understanding of this phenomenon remains elusive. This study explores the dynamics of Taylor bubbles moving in an inelastic shear-thinning fluid, which follows the Carreau-Yasuda viscosity model, through numerical simulations. Our focus is on regimes where inertia and buoyancy are negligible, allowing us to examine the impact of fluid rheology on bubble characteristics at finite capillary numbers. Initially, we validate the recent lubrication theory by Picchi et al. (2021) by analyzing trends in film thickness and bubble speed at small capillary numbers. We then demonstrate the existence of a general scaling that incorporates both zero-shear-rate and shear-thinning effects, applicable up to finite capillary numbers. Notably, the shape of the Taylor bubble is significantly affected by fluid rheology, which interacts with the capillary number. Lastly, our analysis of viscosity fields reveals an interplay between zero-shear-rate and shear-thinning effects in various regions of the bubble, including the formation of recirculating vortices ahead of and behind the bubble.