Unravelling the existence of asymmetric bubbles in viscoelastic fluids

Abstract

We study the motion and deformation of a single bubble rising inside a cylindrical container filled with a viscoelastic material. We solve numerically the mass and momentum balances along with the constitutive equation for the viscoelastic stresses, without assuming axial symmetry to allow the growth of three-dimensional disturbances. Hence, we may predict the emergence of the notorious knife-edge shape of the bubble, which is a result of a purely elastic instability triggered in the locality of the trailing edge. Our results compare well with existing experiments. We visualize, for the first time to the best of our knowledge, the flow kinematics and dynamics that arise downstream of the bubble. We propose two quantities, one kinematical and one geometrical, for the determination of the onset of the instability. We demonstrate that extension-rate thinning in the constitutive law is necessary for the emergence of the instability. Moreover, our results indicate that increasing (a) the deformability of the bubble and (b) the initial extension rate hardening of the viscoelastic material, prior to thinning, triggers the instability earlier. These novel findings help us formulate and propose a mechanism that controls the onset of the instability and explain why the knife-edge shape is not encountered as frequently.