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, a₂₀, 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, a₂ (t), are presented, and the time t_o at which the droplets come in contact with each other and their approach velocity at this time, ∆V_d0, are calculated. The effects of the droplet diameter, D_d0, the initial droplet velocity, V_d0, and the initial separation, a₂₀ on t_o and ∆V_d0 are reported. The agreement between the theoretical predictions and experimental data in the literature is good.