The combined effect of electric forces and confinement ratio on the bubble rising

Highlights: • The electric forces act on the interface of the bubble directing from the surrounding fluid towards the bubble. • In any confined domain, there is a corresponding electric force magnitude which assists the formation of a toroidal bubble. • After the formation of the toroidal bubble, a secondary transient stage is observed to begin. • After the formation of the toroidal bubble, a pair of vortices begin to develop at the sides of the bubble ring. • The electric forces are influential on the terminal Reynolds number before the formation of the toroidal bubble. - Abstract: In this work, the combined effect of electrohydrodynamic forces and domain confinement on the formation of a toroidal bubble is numerically studied. The numerical scheme is the Volume of Fluid (VOF) method and the surface tension and electric forces are implemented using the Continuum Surface Force (CSF) and leaky dielectric models, respectively. It is found that both domain confinement and electric forces are influential on the formation of a toroidal bubble. For smaller confinement ratios, larger electric forces are required to pierce the bubble. Moreover, the influence of both electric forces and confinement ratio are presented and discussed for bubble vertical velocity, terminal Reynolds number, velocity streamlines and side-wall shear stress.