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Crumpled water bells

Published online by Cambridge University Press:  24 January 2012

H. Lhuissier  and
E. Villermaux
H. Lhuissier
Affiliation:
Aix-Marseille Université, IRPHE, 13384 Marseille CEDEX 13, France
E. Villermaux*
Affiliation:
Aix-Marseille Université, IRPHE, 13384 Marseille CEDEX 13, France
*
†Email address for correspondence: villermaux@irphe.univ-mrs.fr
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Abstract

Stationary axi-symmetrical pressurized bells formed by the impact of a liquid jet on a solid disc (so-called Savart water bells) can exhibit uncommon sharp and pointed shapes. They are characterized by two successive inflections of the two-dimensional bell generator profile, corresponding to partially concave bells. We show that this shape is incompatible with the usual assumption that the detail of the flow across the liquid sheet constitutive of the bell is unimportant. We consider the equilibrium of a curved liquid sheet of finite thickness sustaining a pressure difference between both sides, and show that several curvatures of the interface may be a solution under given flow conditions. The inflection of the bell profile is then explained in terms of a spontaneous transition from a ‘negative’ to a ‘positive’ curvature which conserves mass flow, linear and angular momenta. That inflection is also a transition from a super to a subcritical flow (with respect to capillary waves), having the status of a capillary hydraulic jump on a freely suspended sheet, a novel object in fluid mechanics. The azimuthal wrinkles forming at the jump result from the inertial destabilization of the sheet due to the centripetal acceleration fluid particles experience as they flow along the highly curved bell profile in the vicinity of the fold. This finding also explains the singular shape at the edge of freely flapping sheets.

JFM classification

Mathematical Foundations: General fluid mechanics Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 693 , 25 February 2012 , pp. 508 - 540
Copyright
Copyright © Cambridge University Press 2012

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Footnotes

‡

Present address: Also at Institut Universitaire de France.

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