Dynamics of a Taylor bubble through a shear-thinning fluid up to finite capillary numbers

Although the motion of confined Taylor bubbles through non-Newtonian fluids is typical of many engineering and biological systems, a fundamental understanding of the problem is still an open problem. In this work, we investigate the dynamics of Taylor bubbles which move in an inelastic shear-thinning fluid that obeys the Carreau-Yasuda viscosity model by means of numerical simulations. We focus on regimes where inertia and buoyancy are negligible to assess the effect of the fluid rheology on bubble characteristics up to finite capillary numbers. First, we validate the recent lubrication theory by Picchi et al. (2021) by analysis of the trends of the film thickness and bubble speed in the small capillary number limit. Then, we show the existence of a general scaling that embeds for both zero-shear-rate and shear-thinning effects and holds up to finite capillary numbers. Interestingly, the shape of the Taylor bubble is strongly influenced by fluid rheology, which competes with the capillary number. Finally, the analysis of the viscosity fields shows an interplay between the zero-shear rate and shear thinning effects in different regions of the bubble, including the presence of recirculating vortexes that form ahead and behind the bubble.