An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surface

Abstract

The flow of fluid associated with the impact of water drops of radius R at a speed V onto unyielding dry metal surfaces of known roughness R$_a$ is described. Spatial dimensions of the deforming drop are normalized by transformations of the kind x' = x/R, and time scales are normalized according to t' = tV/R, to permit comparison of events where R or V differ. It is shown that the primary influence of the surface roughness parameter R$_a$ is the determination of the condition for the ejection of secondary droplets by the excitation of an instability in the developing watersheet; provided R$_a \simeq$ R, it is possible to evaluate the condition to a high degree of accuracy, and for R$_a$ = 0.84 $\mu m$ it is found to be $\alpha^{\frac{4}{3}}RV^{1.69}$ > 7.4, where $\alpha$ is the eccentricity of the drop at the moment of impact. Deceleration of the drop apex does not commence until t' > 0.6, contrary to the prediction of Engel (1955) but in good agreement with that of Savic & Boult (1957). Close examination of the very early stages of impact suggests strongly that the so-called watersheet originates at a moment t' = 0.01 after first contact, regardless of the absolute values of R, V or R$_a$; the initial normalized watersheet velocity is of order 5. Where there is ejected material, its normalized velocity at the moment of ejection is of the order of 20% greater than that of the watersheet substrate. Simple calculations also suggest that initial fluid velocities greater than 10V are required immediately before the initiation of the watersheet (t' < 0.01). Impacts at speeds considerably greater than the appropriate terminal fall speed in air show no deviations in character from those investigated at much lower speeds. A simple subsidiary experiment also suggests that greater impact velocities are required to produce splashing on inclined targets.