Motion of a bubble ring in a viscous fluid

In this paper, lattice Boltzmann method was undertaken to study the dynamics of a vortex ring bubble (or bubble ring) in a viscous incompressible fluid. The study is motivated partly by our desire to assess whether a bubble ring keeps increasing its radius and decreasing its rise velocity as it rises through fluid as was predicted by Turner [“Buoyant vortex rings,” Proc. R. Soc. London, Ser. A 239, 61 (1957)]10.1098/rspa.1957.0022 and Pedley [“The toroidal bubble,” J. Fluid Mech. 32, 97 (1968)]10.1017/S0022112068000601, or does the ring like a rising bubble, eventually reaches a steady state where its radius and velocity remain constant as was predicted by Joseph et al. [Potential Flows of Viscous and Viscoelastic Fluids (Cambridge University Press, 2008)]. The parameters investigated included ring circulation, Reynolds number, density ratio and Bond number. Our numerical results show that a rising bubble ring increases its radius and decreases its velocity, but the process is interrupted by ring instability that eventually causes it to break up into smaller bubbles. This finding is consistent with the stability analysis by Pedley, who predicted that a bubble ring has a finite lifespan and is ultimately destroyed by surface tension instability. Furthermore, it is found that increasing initial circulation has a stabilizing effect on a bubble ring while increasing Reynolds number or Bond number hastens ring instability, resulting in an earlier break up into smaller bubbles; the number of bubbles depends on the wavenumber of the perturbation.