On peculiar behaviours at critical volumes of a three-dimensional bubble rising in viscoelastic fluids

Abstract

In this paper, we carried out an investigation of the dynamics of an air bubble rising in viscoelastic liquids with increasing volumes via volume-of-fluid based direct numerical simulations (DNS) with local adaptive mesh refinement techniques. The exponential Phan-Thien Tanner (EPTT) model is adopted for describing the rheological behaviours of the shear-thinning viscoelastic fluid. The well-known jump discontinuity in the terminal rise velocity at a critical bubble volume is captured, which agrees qualitatively with the experimental observation in the literature. On this basis, the numerical simulations have been performed for different rheological properties in wider flow regimes, providing new insights into the local flow field and the stress distribution around the deformable rising bubbles. A characteristic dimensionless regime map has also been proposed to distinguish the peculiar behaviours of a bubble rising in viscoelastic fluids at different Galilei (Ga) and Eötvös (Eo) numbers. We found that at low Ga and low Eo numbers, the large elastic stresses concentrate in the small region near the bubble’s trailing end, leading to the formation of bubble cusp. The appearance of the negative wake is the main reason for the velocity jump to occur. However, for higher Ga of 10, the viscous forces become less dominating. The fluctuations of the polymeric stresses are substantially intensified with increasing bubble volume, and large bubbles experience a pulsating rising velocity with oscillation shapes. On the other hand, at intermediate Ga and high Eo of 10, the modest surface tension induces a cap with a thin skirt trailing the bubble main body at early times. Due to the polymer stretching, the strong extensional flow behind the small bubble eventually forces the bubble tail to break up. The above analyses on the bubble dynamics at constant Morton (Mo) numbers facilitate the extrapolation of the volume effects at different flow regimes and, therefore, will guide the applications in the future.