A numerical study on horizontal clustering of rising air bubbles

In bubbly flows, the hydrodynamic interactions among bubbles and flow structure result in inhomogeneous distributions of bubbles. We perform direct numerical simulations of air bubbles rising in stagnant water to investigate their clustering mechanism. A bubble interface is tracked by a level-set method, and bubble coalescence is modeled based on a contact time concept in film-drainage theory. Strong and weak horizontal clusterings occur in monodispersed rising bubbles with small (d_eq = 1mm) and large (d_eq = 2mm and 3mm) bubbles, respectively. In all cases, the bubbles at short distances (r_ij <2d_eq) tend to align horizontally. This alignment is caused by vortex-induced interactions as well as by potential interactions. After bubble-to-bubble collision without coalescence, counter-rotating vortex pair occur between the bubbles, and the structures push the bubbles against each other, while maintaining horizontal alignment. Horizontal alignment by the vortex pair occurs more frequently as the deformability of the bubbles decreases.