Dynamics and interactions of parallel bubbles rising in a viscoelastic fluid under buoyancy

Abstract

Three dimensional interface-resolved numerical simulations are performed to investigate interactions of two buoyancy-driven parallel bubbles rising in an otherwise quiescent viscoelastic fluid for a range of parameters. The flow equations are solved fully coupled with the FENE-P viscoelastic model equation using a front-tracking method and some new features of this complex flow field are reported for the first time. The flow parameters are varied around the baseline case for which a single bubble produces a negative wake. The surface tension, pressure, viscous and viscoelastic forces acting on the bubbles are computed and plotted as a function of time to demonstrate their evolution. The corresponding effects on bubble shapes, terminal velocities, flow field around the bubbles and the evolution of distance between their centers have been examined in detail. Effects of Weissenberg number, Galilei number, Eötvös number and the initial distance between bubbles are investigated. It is found that closely initialized parallel bubbles strongly interact via the negative wakes. Unlike the Newtonian fluid, a reversed flow is observed in between the parallel bubbles rising in a viscoelastic fluid. Long tails form behind the bubbles and they tilt towards each other due to wake interactions. We show that the total viscoelastic force acting on bubbles oscillates with a certain frequency and never attains a steady state value even when the bubbles reach a nearly steady motion. However, amplitude of resulting oscillations in bubble velocity is found to be much smaller. The steady distance between bubbles decreases with the Weissenberg number and the viscosity ratio while it increases with the Galilei number. The polymeric viscosity of the liquid is found to have a significant influence on the magnitude of repelling force acting on the bubbles and the direction of flow in between them. The Eötvös number is found to have a little impact on the distance between the bubbles at their steady-state motion for the range considered here. The normalized terminal velocity of bubbles increases rapidly as the Eötvös number becomes smaller than a critical value.