Dynamics and deformation of a three-dimensional bubble rising in viscoelastic fluids

Abstract

The rise of a deforming air bubble of fixed volume surrounded by viscoelastic liquids is investigated by an adaptive direct numerical technique coupled with the volume-of-fluid method. The effects of the Weissenberg number (characterizing the strength of elasticity in the flow) and the viscosity ratio on the three-dimensional bubble dynamics have been studied and identified in a wide range of Galilei (Ga) and Eötvös (Eo) numbers, which measure gravitational force over viscous and surface tension forces, respectively. Our results demonstrate that the deformed bubble shape is not a strong predictor of the jump in the rise velocity in different flow regimes; and we verify that in highly elastic flows, the negative wake is mainly responsible for the rising velocity jump, consistent with previous experimental findings. The viscoelasticity induces a cusp shape at large Eo, while the increase in the rising velocity diminishes with a fattened bubble shape. By probing the polymeric conformational state and stresses, it is further indicated that the strain in the fluid is associated with the shear induced by the rising bubble, which produces the release of the elastic stress, giving rise to a fluid downward motion to form the negative wake. Interestingly, we first observe that when Ga is large enough the bubble undergoes a pulsating rising velocity in highly elastic flows due to the vortex shedding in the distant wake region. Moreover, since the development of viscoelastic stresses is closely correlated with the shear-strain response, a larger polymer deformation is seen to be formed at the bubble trailing edge for modest surface tension, which affects the balance between the extensional flow and the shear stresses on the tail interface, leading to the bubble breakup to form a satellite tail.