Splash Droplet Size in Drop Impact on Solid Surfaces: Applicability of Classical Fluid Mechanical Instabilities

This study presents a framework for theoretically predicting the average diameter of the secondary droplets using classical fluid mechanical instabilities when a droplet impacts a solid surface. The framework assumes that Rayleigh–Taylor instability triggers the formation of fingers and Rayleigh–Plateau instability triggers the ejection of secondary droplets from the fingers. Using the theoretical framework, it is estimated that the average diameter of the splashed secondary droplets scales as We−1/4 matching the inviscid scaling reported in the literature (We is the Weber number). Two pre-factors, C1 and C2, are introduced in the theoretical formulation to quantitatively match the experimental data reported in the literature. C1 captures a correction factor for the diameter of the finger, whereas C2 implicitly incorporates viscous and wetting effects. The value of the pre-factor C2 increases towards 1 as We increases. The theoretical framework incorporating C1 and C2 reveals that the average diameter of the secondary droplets increases with time for a fixed We. Moreover, at a fixed time instant, it decreases with increasing We. These predictions are consistent with the limited experimental data reported in the literature.