Journal of Fluid Mechanics



Life of a flapping liquid sheet


E. VILLERMAUX a1 and C. CLANET a1
a1 Institut de Recherche sur les Phénomènes Hors Equilibre, Université de Provence, Aix-Marseille I–CNRS, Technopôle de Château-Gombert, 49, rue Frédéric Joliot-Curie, 13384 Marseille Cedex 13, France

Abstract

A round liquid jet with density ρ, surface tension σ and diameter D0 impacting a solid circular surface at normal incidence with velocity U0 takes the form of a radially expanding sheet whose thickness decreases with distance from the impact point. When the sheet develops in a still environment with density ρa = αρ, it destabilizes, provided the impacting Weber number We = ρU20D0/σ is larger than about 40α−1/2, as a result of a shear instability with the surrounding medium, in a sinuous, flag-like motion. We show how the instability properties set both the radial extent of the liquid sheet and the drop formation process at its rim. The shear instability gives the liquid a flag-like motion, ultimately triggering a Rayleigh–Taylor instability at the rim of the sheet which disintegrates, at the radial location R, into disjointed droplets of size d such that

R/D0 [similar] α−2/3 We−1/3 and d/D0 [similar] α−2/3We−1.

The features of the sheet instability, its radius and the droplet sizes are determined experimentally for a broad range of control parameters, using different liquids and ambient-medium densities.

(Received September 19 2000)
(Revised January 14 2002)



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