Chain oscillations in liquid jets

A circular jet breaks up into droplets via the Rayleigh-Plateau instability, retaining a circular cross section throughout. If, however, the nozzle from which the jet issues is elongated, the circular symmetry is broken, and the jet forms a chainlike structure with neighboring links separated by 90∘. The cause of this structure is two-dimensional capillary-inertial oscillation of jet cross sections in their own plane. We perform an experimental study of chain oscillations as a function of flow rate using careful prelaminarization and 12 elliptical nozzles with different areas and eccentricities. The oscillation frequencies inferred from the observed chain-link structure do not agree with those predicted by Rayleigh's infinitesimal theory [L. Rayleigh, Proc. R. Soc. London 29A, 71 (1879)]. However, they do agree with an extended nonlinear theory of Bohr [N. Bohr, Philos. Trans. R. Soc. A 209, 281 (1909)10.1098/rsta.1909.0012] that accounts for finite-amplitude effects. This agreement shows that our fluid chains are nonlinear oscillations whose frequency decreases with increasing amplitude. We perform direct numerical simulations of chain oscillations using a volume-of-fluid method and find good agreement with the predictions of Bohr's theory. Finally, we generalize Bohr's theory to the case of two interacting modes with quadrupolar and octapolar azimuthal dependencies. The resulting solution explains qualitatively the "dimpled"shape of the jet's surface observed in the experiments.