Numerical investigation of the stability of bubble train flow in a square minichannel

The stability of a train of equally sized and variably spaced gas bubbles that move within a continuous wetting liquid phase through a straight square minichannel is investigated numerically by a volume-of-fluid method. The flow is laminar and cocurrent upward and driven by a pressure gradient and buoyancy. The simulations start from fluid at rest with two identical bubbles placed on the axis of the computational domain, the size of the bubbles being comparable to that of the channel. In vertical direction, periodic boundary conditions are used. These result in two liquid slugs of variable length, depending on the initial bubble-to-bubble distance. The time evolution of the length of both liquid slugs during the simulation indicates if the bubble train flow is stable (equal terminal length of both liquid slugs) or unstable (contact of both bubbles). Several cases are considered, which differ with respect to bubble size, domain size, initial bubble shape, and separation. All cases lead to axisymmetric bubbles with the capillary number in the range of 0.11-0.23. The results show that a recirculation pattern develops in the liquid slug when its length exceeds a critical value that is about 10%-20% of the channel width. If a recirculation pattern exists in both liquid slugs, then the bubble train flow is stable. When there is a recirculation pattern in one liquid slug and a bypass flow in the other, the bubble train flow may be stable or not depending on the local flow field in the liquid slugs close to the channel centerline. These results suggest that a general criterion for the stability of bubble train flow cannot be formulated in terms of the capillary and Reynolds number only, but must take into account the length of the liquid slug.