Growth of sinuous waves on thin liquid sheets: Comparison of predictions with experiments

A recent theory [M. S. Tirumkudulu and M. Paramati, "Stability of a moving radial liquid sheet: Time dependent equations," Phys. Fluids 25(10), 102-107 (2013)] has shown that a radially expanding liquid sheet is unstable to sinuous wave disturbances due to the thinning of the liquid sheet while ignoring the presence of a surrounding gas phase. In this work, we compare the predictions of the aforementioned theory with the measurements of Crapper et al. ["Large amplitude Kelvin-Helmholtz waves on thin liquid sheets," Proc. R. Soc. London, Ser. A 342(1629), 209-224 (1975)] who measured the amplitude and spatial growth rates of sinuous waves induced in radially expanding liquid sheets produced by fan spray nozzles. The predicted growth rates are remarkably close to the measurements over a range of forcing frequencies and amplitudes even though the experiments were performed in the presence of a surrounding gas phase. This is in contrast to large discrepancies observed by Crapper et al. when the same measurements were compared with the predictions of a spatial stability analysis for a moving liquid sheet that accounts for the inertia of the surrounding gas phase but ignores the thickness variation of the sheet. Published by AIP Publishing.