Simultaneous sedimentation and coalescence of a dilute dispersion of small drops

Macroscopic phase separation and the evolution of the drop size distribution for non-homogeneous dispersions, in which buoyancy-driven settling and coalescence of drops cause spatial as well as temporal variations of the drop size distribution, was analysed by numerical solution of the population dynamics equations. Collision efficiencies based on detailed hydrodynamic interactions of spherical drops with clean interfaces were incorporated in the description of the pairwise drop coalescence rates. A dimensionless parameter that characterizes the relative importance of settling and coalescence was identified. For finite values of this parameter, the phase separation rates and average drop size initially increase owing to coalescence, and then decrease owing to the larger drops settling out of the dispersion.