Interaction of two cylindrical bubbles embedded in a corotating vortex pair

Abstract

Cylindrical bubbles are frequently accompanied by vortical flows. However, there is a lack of knowledge concerning cylindrical bubble pairs, the simplest interaction unit, compared to the understanding of the interactions between two spherical bubbles or two single-phase vortices. Here, we propose a theoretical model to describe the interaction process of two cylindrical bubbles embedded in two corotating vortices. The dynamic equations of surface modes for two cylindrical bubbles are formulated based on a rotating frame of reference whose angular velocity is determined by the distributions of circulations. The Coriolis force is thereby added to the momentum equation and contributes to the displacements and deformations of the bubbles. Our model recovers the universally accepted unitary criterion for two single-phase vortices. A striking finding is that the merging of two cylindrical bubbles in vortical flows can display two kinds of criteria depending on the relative weights of the surface tension and vortex force.