Free radially expanding liquid sheet in air: time- and space-resolved measurement of the thickness field

TL;DR

This study introduces a precise, time- and space-resolved method to measure the thickness of radially expanding liquid sheets, confirming theoretical scalings and revealing a maximum thickness point and azimuthal modulations.

Contribution

It provides the first experimental validation of theoretical thickness scalings in expanding liquid sheets and uncovers new features like the maximum thickness location and azimuthal variations.

Findings

Confirmed asymptotic scalings for sheet thickness in short- and long-time regimes.

Identified a maximum thickness point moving with impact velocity.

Discovered azimuthal thickness modulation in the liquid sheets.

Abstract

The collision of a liquid drop against a small target results in the formation of a thin liquid sheet that extends radially until it reaches a maximum diameter. The subsequent retraction is due to the air-liquid surface tension. We have used a time- and space-resolved technique to measure the thickness field of this class of liquid sheet, based on the grey level measurement of the image of a dyed liquid sheet recorded using a fast camera. This method enables a precise measurement of the thickness in the range $(10-450) \, \mathrm{\mu m}$, with a temporal resolution equal to that of the camera. We have measured the evolution with time since impact, $t$, and radial position, $r$, of the thickness, $h(r,t)$, for various drop volumes and impact velocities. Two asymptotic regimes for the expansion of the sheet are evidenced. The scalings of the thickness with $t$ and $r$ measured in the two regimes are those that were predicted in \citet{Rozhkov2004} fort the short-time regime and \citet{Villermaux2011} for the long time regime, but never experimentally measured before. Interestingly, our experimental data also evidence the existence of a maximum of the film thickness $h_{\rm{max}}(r)$ at a radial position $r_{\rm{h_{max}}}(t)$ corresponding to the crossover of these two asymptotic regimes. The maximum moves with a constant velocity of the order of the drop impact velocity, as expected theoretically. Thanks to our visualization technique, we also evidence an azimuthal thickness modulation of the liquid sheets.