Bubble coalescence in pure liquids

Solutions of the flow and deformation during the approach of two bubbles along their centre line are presented for the low Weber number case. When viscosity is absent, Weber number and radius ratio disappear from the equations under suitable transformations of the variables and a universal solution is obtained. This solution indicates the formation of a dimple, after which the thinning rate of the film between the bubbles tends to a constant high value. When liquid viscosity is included the Reynolds number, Re, enters the equations. A retardation of the coalescence process is found for Re <100, while for Re 1 dimple formation is suppressed. The influence of gas properties is considered briefly. An extrapolation of the inviscid results to Weber numbers of order unity suggests that the bubbles will bounce apart before coalescence is achieved.