Symmetry breaking and the emergence of the knife-edge shape of a bubble rising in viscoelastic solutions*

The peculiar dynamics of rising bubbles in viscoelastic solutions has stirred a lot of interest in the scientific community. The three phenomena that have been identified over the ongoing 60 years of research are: (a) the velocity jump discontinuity [1,2], (b) the negative wake structure [2], and (c) the knife-edge bubble shape [3]. The first two have been thoroughly investigated. However, the notorious knife edge shape has not been reproduced numerically. Thus, we undertake a novel, fully 3D computational study to examine the buoyancy-driven rise of a bubble in a viscoelastic solution because we are interested in finding solutions that do not exhibit azimuthal symmetry. The governing equations are solved numerically using PEGAFEM-V [5]. For the first time, we capture numerically the so-called knife-edge shape obtaining excellent agreement with experiments. By varying the rheological properties of the material, we propose the physical mechanism that leads to the breakdown of axial symmetry and the appearance of the asymmetric bubble shape.  

[1] Astarita and Apuzzo, A.I.Ch.E. 11 (1965)

[2] Pilz and Brenn, J. Non-Newtonian Fluid Mech. 145 (2007)

[3] Liu et al., JFM 304 (1995)

[4] Fraggedakis et al. J. Fluid Mech. 789 (2016)

[5] Varchanis et al. J. Non-Newtonian Fluid Mech., 284 (2020)