Numerical prediction of axisymmetric bubbles rising in viscoelastic fluids around critical volumes using a conservative level-set method.

At certain critical volumes, bubbles rising in a viscoelastic fluid can exhibit phenomenological behaviour that is still not completely understood. The rise velocity as a function of bubble volume exhibits a discontinuity that is not present for Newtonian bubbles. Developing a full understanding of this behaviour has many applications in industrial and biological situations that deal with rheologically complex fluids. We present a novel axisymmetric formulation of the viscoelastic constitutive equation with a novel conservative level-set multiphase framework for simulating these phenomena accurately and efficiently. The log-conformation formulation is utilised to enhance stability so that approximations can be obtained for large values of the Weissenberg number. We present numerical predictions that are in quantitative agreement with experimental studies, an analysis of the so-called 'negative wake' velocity field and polymeric stress visualisations around the circumference of the bubble.