Interaction between two spherical bubbles rising in a liquid

The main goal of the present study is to provide a complete description of the interaction between two bubbles for moderate bubble Reynolds number (20 $\le $ Re $\le $ 500, Re being based on the bubble diameter) and for positions described by the distance S (2.5 $\le $ S $\le $ 8, S being the ratio between the distance of centre and the bubble diameter) and (0\r{ } $\le \quad \theta \quad \le $ 90\r{ }) the angle formed between the line of centre and the horizontal. The value $\theta $=0\r{ } corresponds to the situation of two bubbles moving side by side (Legendre, Magnaudet and Mougin 2003 JFM, 497,133-166) and $\theta $=90\r{ } to the axis-symmetric situation of two bubbles moving in line (Yuan {\&} Prosperetti 1994 JFM, 278, 325-349). The three-dimensional flow around two spherical bubbles moving in a viscous fluid is studied numerically by solving the full Navier-Stokes equations. The bubble surface is assumed to be clean so that the outer flow obeys a zero-shear-stress condition and does not induce any rotation of the bubbles. The nature of the interaction is studied and the wake of the leading bubble is found to play a significant role in the attraction/repulsion mechanism. A general model for pair interaction is proposed.