AbstractThe 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 high-speed camera. This method enables a precise measurement of the thickness in the range $10{-}450~{\rm\mu}\text{m}$, 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 by Rozhkov et al. (Proc. R. Soc. Lond. A, vol. 460, 2004, pp. 2681–2704) for the short-time regime and Villermaux and Bossa (J. Fluid Mech., vol. 668, 2011, pp. 412–435) for the long-time regime, but never experimentally measured before. Interestingly, our experimental data also provide evidence for the existence of a maximum of the film thickness $h_{max}(r)$ at a radial position $r_{h_{max}}(t)$ corresponding to the cross-over 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 provide evidence of an azimuthal thickness modulation of the liquid sheets.
Short-time existence of the second order renormalization group flow in dimension three
