A model of coalescence between two equal-sized spherical drops or bubbles

Abstract

When two spherical drops or bubbles (or two spherical menisci) approach each other, a thin liquid film is trapped and forms a dimple between them. A model is developed for the dynamics of an axisymmetric, dimpled thinning film which includes the effects of London-van der Waals and electric double-layer forces. The model describes the film profile evolution between two equal-sized drops, and predicts the film stability, time scale, and film thickness, given only the radius of the drops and the required physical properties of the fluids and surfaces. The competing effects of these two forces on film are clearly shown: the van der Waals disjoining pressure destabilizes the film, whereas the electric double layer stabilizes it. Depending on the strength of these two components of disjoining pressure, the dimpled thinning film either forms a flat film or ruptures at the rim. Predictions on the film stability and its thickness are in excellent agreement with experimental results of D. Platikanov and E. Manev (in “Proceedings, 4th International Conference of Surface Active Substances,” Vol. 2, p. 1189, 1964). The predicted rupture time and equilibrium time are also presented. In the absence of the electric double-layer forces, an equation is derived for the rupture time.