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

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 timeand 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 µm, 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.

Bursting of Dilute Emulsion-Based Liquid Sheets Driven by a Marangoni Effect

“…The plot shows the continuity of h out at the pre-hole to hole transition, and that all over the process, the thickness is proportional to d0 3 u0rt , with a proportionality constant α = (0.094 ± 0.018). This thickness field corresponds quantitatively to that of an expanding plain water sheet (without holes) as measured [14] and predicted [13]. The theoretical proportional constant α = 1/12 = 0.083 [13], is in very good agreement with the experimental one.…”

“…But, to the best of our knowledge, those conditions have never been confronted to robust experimental facts. To unambiguously clarify the physical mechanisms at play, rationale experiments on individual perforation events are therefore required.In this Letter, we investigate the perforation mechanisms of an emulsion-based free liquid sheet issued from a single-drop experiment; resulting from the impact of one drop of fluid onto a small target [12][13][14]. During the sheet expansion, holes nucleate and grow.…”

“…Emulsions are prepared by mechanical stirring, yielding a volume median diameter of the oil droplets of (20 ± 4) µm, as determined by granulometry. Details of the experimental set-up are given in [14]. In brief, free radially expanding liquid sheets are formed by the impact of a small drop of emulsion (diameter d 0 =3.7 mm) on a target (chemically treated to avoid dewetting) of diameter 6 mm with an impact velocity u 0 = 4.0 m/s.…”

“…The sheet formation and destabilization are recorded from the top with a fast camera (Phantom V7.3) run at an acquisition rate of 10 kHz. The thickness field of the sheet loaded with dye is determined (range of measurable thicknesses (5 − 450) µm with an uncertainty of 5 µm) thanks to a time-and space-resolved measurement of the adsorbance of the sheet [14,19]. Figure 1(a) displays the destabilization process of a dyed emulsion-based liquid sheet (see movies in the Supplemental Material [20]).…”

Interplay between viscosity and elasticity in freely expanding liquid sheets

“…Upon impact the drop freely expands in air, reaches a maximal extension and then retracts due to surface tension [18][19][20][21][22]. Hence, the dissipation processes occurring at the fluid/surface interface are reduced, if not suppressed, possibly facilitating their modeling and/or experimental investigations.…”