Coalescence of two initially spherical bubbles: Dual effect of liquid viscosity

The coalescence and interaction of two inline bubbles in viscous ambient liquids are explored using axisymmetric computations. The incompressible Navier-Stokes equations for gas-liquid flow are solved numerically through a tree-based finite volume method. Starting from spherical shape, the deformation and evolution of bubbles are simulated by a volume-of-fluid (VOF) method that combines a balanced surface tension force calculation and a height function curvature estimation. High mesh resolution is achieved by dynamic, adaptive mesh refinement to finely resolve the local topological evolutions during coalescence. The influence of liquid viscosity, for which Galilei number Ga ranges from 1 to 150, is studied under different Eötvös numbers Eo. It is discovered that the outcome of coalescence is determined by the competition between the two liquid circulations (vortex rings) around bubbles. We find that the inter-bubble interaction is always enhanced by reducing liquid viscosity. However, the effect of liquid viscosity on bubble coalescence is dual and the minimum coalescence time is obtained at a moderate Ga with other parameters fixed. A comprehensive map of coalescence regime is provided, where four distinct coalescence regimes are identified and three critical Galilei numbers are defined. The motion of bubbles in different coalescence regimes are also analyzed and compared. Our work contributes to a further understanding of the coalescence and interaction of bubbles.