Hydrodynamic interactions between two bubbles placed in tandem

The three-dimensional flow around two bubbles placed in tandem in a viscous fluid is studied by direct numerical simulations. The effect of parameters including the Reynolds number of the bubble $Re∈[50,200]$⁠, the center-to-center distance of two bubbles $S∈[1.25,6]$⁠, and the aspect ratios of the bubbles $χ∈[1,2.5]$ on the flow fields, the drag forces, and the equilibrium separation distances is analyzed. The results show that no obvious flow vortex appears behind the spherical bubble opposite to the sphere, indicating that the disturbance to the flow field is much weaker than that of the sphere. This difference can be mainly attributed to the free-slip boundary of the bubble surface. The increase in Reynolds number and the decrease in the separation distance mainly affect the pressure drag of the bubbles, rather than the viscous drag. An equilibrium distance exists between the two bubbles depending on the competition of the attraction effect of the wake and the repulsion effect of the potential flow, due to the fact that the drag force of the downstream bubble may larger than that of a single bubble at a short distance caused by the latter effect. When the bubble becomes non-spherical due to deformation, the increase in the bubble aspect ratio can significantly enhance the wake effect, while almost keep the potential flow effect almost unchanging. This reduces the drag of the downstream bubbles, thereby shortening the equilibrium distance between the bubbles. These findings provide an important theoretical basis for understanding the interactions between bubbles and the collective dynamics of bubbly flows.