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

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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 or 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 ≪ R , it is possible to evaluate the condition to a high degree of accuracy, and for R a = 0.84 μm it is found to be α4/3 RV 1.69 > 7.4, where α is the eccentricity of the drop at the moment of impact. Deceleration of the drop apex does not commence until > 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 10 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.

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