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Frequency selection in a gravitationally stretched capillary jet in the jetting regime

Published online by Cambridge University Press:  29 April 2020

Isha Shukla Open the ORCID record for Isha Shukla [Opens in a new window]  and
François Gallaire Open the ORCID record for François Gallaire [Opens in a new window]
Isha Shukla
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne,1015Lausanne, Switzerland
François Gallaire*
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne,1015Lausanne, Switzerland
*
† Email address for correspondence: francois.gallaire@epfl.ch
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Abstract

A capillary jet falling under the effect of gravity continuously stretches while thinning downstream. We report here the effect of external periodic forcing on such a spatially varying jet in the jetting regime. Surprisingly, the optimal forcing frequency producing the most unstable jet is found to be highly dependent on the forcing amplitude. Taking benefit of the one-dimensional Eggers & Dupont (J. Fluid Mech., vol. 262, 1994, pp. 205–221) equations, we investigate the case through nonlinear simulations and linear stability analysis. In the local framework, the WKBJ (Wentzel–Kramers–Brillouin–Jeffreys) formalism, established for weakly non-parallel flows, fails to capture the nonlinear simulation results quantitatively. However, in the global framework, the resolvent analysis, supplemented by a simple approximation of the required response norm inducing breakup, is shown to correctly predict the optimal forcing frequency at a given forcing amplitude and the resulting jet breakup length. The results of the resolvent analysis are found to be in good agreement with those of the nonlinear simulations.

JFM classification

Interfacial Flows (free surface): Capillary flows Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 894 , 10 July 2020 , A6
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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