Negative Wake and Velocity of a Bubble Rising in a Viscoelastic Fluid

Abstract

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 zeroshear 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.