The wobbling motion of single and two inline bubbles rising in quiescent liquid

The wobbling motions of single and two inline bubbles rising in quiescent liquid are investigated via three-dimensional simulations using the volume of fluid method. First, we simulate an 8 mm air bubble rising in quiescent water, yielding the wobbling motion. The bubble wobbling has two roles: (1) the excessive curvature speeds up the separation of the boundary layer and (2) the velocity peaks (high Reynolds number) result in the formation of asymmetrical vortices. The oscillation frequencies (6 Hz, St = 0.22) of the bubble movement, the vorticity accumulated on the bubble surface, the lift force and viscous force are the same while the oscillation frequency of the aspect ratio is twice that of the bubble movement. The volume-averaged liquid velocity presents a linear increase with the bubble rise while the kinetic energy displays a quadratic increase. Finally, two bubbles rising inline are investigated with different initial distances. The central breakup of the trailing bubble is observed at a short distance of 2d (d is the bubble diameter). For a longer distance of 6d, the wake of the leading bubble results in the lateral motion of the trailing bubble, depending on the position of the trailing bubble in the wake and the intensity of the vortices it encounters.