Effect of Surface Mobility on Collision of Spherical Drops

The collision of two spherical liquid drops is considered which allows the effect of coalescence on the formation and stability of dispersions to be studied. An analytical solution is derived for the variation in the hydrodynamic force with the approach velocity and the separation thickness during the impact in terms of the drop diameter, allowing for the effect of induced flow inside the drops. Setting this force equal to the rate of change of momentum of the drops enables the variation with time in the separation between the drops to be obtained in terms of the initial approach velocity, drop diameter, and viscosity ratio. The analysis also yields the time variation in the force and approach velocity. For a given impact velocity, the separation thickness decreases with time until a minimum value is reached, which decreases as the impact velocity and the viscosity ratio of the continuous and dispersed phases increase. Previous authors have only obtained the variation in the approach velocity with the unknown variable force and separation thickness during the impact and therefore could not obtain the variation in the separation thickness with time. Knowing this variation enables the possibility of coalescence during impact to be investigated. Coalescence is influenced by the minimum separation thickness attained at low impact velocities and by drop deformation and inertial drainage at high velocities.