Are Drop-Impact Phenomena Described by Rayleigh-Taylor or Kelvin-Helmholtz Theory?

Abstract

Drop impact, spreading, fingering, and snap-off are important inmany engineering applications such as spray drying, industrial painting, environmentally friendly combustion, inkjet printing, materials processing, fire suppression, and pharmaceutical coating. Controlling drop-impact instability is crucial to designing optimized systems for the aforementioned applications. Classical Rayleigh-Taylor (RT) theory has been widely used to analyze fingering where instabilities at the leading edge of the toroidal ring form fingers that may ultimately snap off to form small droplets. In this study, we demonstrate the inapplicability of RT theory, in particular because it fails to explain the stable regimes observed under conditions of low air density and the instabilities observed when a drop impacts a pool of equal-density fluid. Specifically, finger instability decreases with decreasing air density, whereas the RT theory suggests that instability should remain unchanged. Moreover, experiments show that fingers form upon impact of a dyed water drop with a water pool, whereas the RT theory predicts noinstability when the densities of the two interacting fluids are equal. Experimental evidence is instead consistent with instability predictions made using the shear-driven Kelvin-Helmholtz theory.