THE COLLISION RATE OF SMALL DROPS IN LINEAR FLOW-FIELDS

A dilute dispersion containing small, force-free drops of one fluid di spersed in a second, immiscible fluid in a linear flow field is consid ered for small Reynolds numbers and large Peclet numbers under isother mal conditions. The emphasis of our analysis is on the effects of pair wise drop interactions on their collision rate, as described by the co llision efficiency, using a trajectory analysis. Simple shear flow and uniaxial extensional or compressional flow are considered. For both f lows, the collision efficiency decreases with increasing drop viscosit y due to the effects of hydrodynamic interactions. It also decreases a s the ratio of the smaller drop radius to the larger radius decreases. For uniaxial flow, finite collision rates are predicted in the absenc e of interdroplet forces for all finite values of the drop size ratio and the ratio of the viscosities of the drop and suspending medium. In contrast, several kinds of relative trajectories exist for a pair of drops in simple shear flow, including open trajectories, collision tra jectories, and closed and semi-closed trajectories, in the absence of interdroplet forces. When the ratio of small to large drop diameters i s smaller than a critical value, which increases with increasing drop viscosity, all of the relative trajectories that start with the two dr ops far apart remain open (no collisions), unless in the presence of a ttractive forces. Attractive van der Waals forces are shown to increas e the collision rates.