Life of a flapping liquid sheet

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 ρ_a = 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 ∼ α^−2/3We^−1/3 and d/D₀ ∼ 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.