On the effect of the approach velocity on the coalescence of fluid particles

Abstract

The effect of the constant relative approach velocity of two Newtonian fluid particles on their coalescence is investigated via a film drainage model. The interfaces are deformable and allowed to have any degree of mobility. The thinning equation is derived based on the lubrication theory, and the tangential velocity of the interface is determined via the Boundary Integral Method (BIM). The details for the treatment of the inherent singularity in BIM are provided. As the approach velocity increases, regardless of the strength of the van der Waals forces and the value of the viscosity ratio (or the degree of the interfacial mobility), three types of behavior of the coalescence time are identified: the linear slow, the dimpled and the multiple-rim drainage regimes. In the first two regions the coalescence time decreases with the approach velocity, eventually passes through a minimum and starts to increase in the third region. The slope in the linear region and the critical velocities separating the regimes are used to quantify the behavior, and given as functions of the Hamaker constant and the viscosity ratio. The results are shown to be in good agreement with several recent experimental studies in the literature.