Negative wake and velocity of a bubble rising in a viscoelastic fluid

A three-dimensional finite element based numerical method is used to simulate the rise of a bubble in a viscoelastic fluid modeled by the Oldroyd-B model. The rise velocity is studied as a function of the bubble volume on a log-log plot. The dependence of rise velocity on the bubble shape and the viscoelastic properties of the ambient fluid are also investigated. In simulations, rather than a jump in the rise velocity at a critical volume as observed in experiments, we find that there is a steep, but continuous, change in the rise velocity over a very small range of bubble volumes. Interestingly, this steep increase in the rise velocity is exaggerated when a parameter, which is a measure of the polymer concentration, is increased, while keeping the zero-shear viscosity fixed. The wake is 'negative' in the sense that the direction of fluid velocity behind the bubble for this parameter range is the opposite of that for a Newtonian fluid.