Motion of a Taylor bubble in a shear-thinning liquid

This talk will focus on the motion of a gaseous Taylor bubble in a capillary tube. Although the dynamics of a bubble in a Newtonian liquid have been the subject of several studies since the seminal works of Taylor and Bretherton, the case where the fluid exhibits a shear-thinning behaviour is much less understood. To fill this gap, we derive a lubrication model in the film region to identify the scaling laws for the bubble speed and the film thickness as a function of the Ellis number and the degree of shear-thinning. Our model identifies a universal scaling law for the effective viscosity that accounts for the interplay of the zero-shear-rate and shear-thinning effects. After discussing the features of the front and rear menisci, we present an analysis of the recirculation vortexes ahead of the bubble. 

In the final part of the talk, we show the results of recent numerical simulations that validate the proposed theory and suggest a strategy to account for the effect of finite capillary numbers on the scaling law for the film thickness in the case of shear-thinning fluids.