An Analytical Study on the Mechanism of Grouping of Droplets

The condition for the formation of droplet groups in liquid sprays is poorly understood. This study looks at a simplified model system consisting of two iso-propanol droplets of equal diameter, D-d0, in tandem, separated initially by a center-to-center distance, a(20), and moving in the direction of gravity with an initial velocity, V-d0 > V-t, where V-t is the terminal velocity of an isolated droplet from Stokes flow analysis. A theoretical analysis based on Stokes flow around this double-droplet system is presented, including an inertial correction factor in terms of drag coefficient to account for large Reynolds numbers (>> 1). From this analysis, it is observed that the drag force experienced by the leading droplet is higher than that experienced by the trailing droplet. The temporal evolutions of the velocity, V-d(t), of the droplets, as well as their separation distance, a(2)(t), are presented, and the time t(0) at which the droplets come in contact with each other and their approach velocity at this time, Delta V-d0, are calculated. The effects of the droplet diameter, D-d0, the initial droplet velocity, V-d0, and the initial separation, a(20) on t(0) and Delta V-d0 are reported. The agreement between the theoretical predictions and experimental data in the literature is good.