Three-Dimensional Numerical Simulations of a Rising Bubble in a Viscoelastic FENE-CR Model Fluid

Abstract

We present the results of three‐dimensional (3d) numerical simulations of the dynamic motion of a gas bubble rising in a viscoelastic fluid. In our study, viscoelastic fluids are described by the Chilcott‐Rallison model (FENE‐CR) model. The simulations are carried out by a coupled level set/volume‐of‐fluid (CLSVOF) method. Governing equations based on the CLSVOF method for incompressible viscoelastic two‐phase flows are solved through a hydrodynamic scheme with formal second‐order accuracy. In our study, we address bubble motion exhibiting large deformations. It is shown that the shape of a bubble largely depends on the FENE‐CR model parameters: the extensibility parameter L and the characteristic relaxation time λ play a role in emerging viscoelastic effects. The choice of parameters determines whether or not the characteristic cusp forms at the tail of a bubble rising in a viscoelastic liquid.