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On the cusps bordering liquid sheets

Published online by Cambridge University Press:  30 July 2014

J. M. Gordillo ,
H. Lhuissier  and
E. Villermaux
J. M. Gordillo
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingenería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Avenida de los Descubrimientos s/n 41092, Sevilla, Spain
H. Lhuissier
Affiliation:
Université Paris Diderot, CNRS, Matière et Systèmes Complexes UMR 7057, 75205 Paris, France
E. Villermaux*
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384 Marseille, France
*
†Institut Universitaire de France, Paris, France. Email address for correspondence: villermaux@irphe.univ-mrs.fr
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Abstract

The edge of a stationary radially expanding liquid sheet and the receding rim bordering a plane sheet are naturally indented. It presents a collection of cusps at the extremity of which the liquid concentrates and is expelled. An experimental description of these cusps for a stationary flat inviscid Savart sheet is given. We identify the stable node–jet structure responsible for the deflection of the incoming flow at the rim and demonstrate how these cusps are the structures that accommodate for both mass and momentum conservation at the sheet edge. Their shape, their number around the sheet, and the residual momentum carried by the ejected liquid are computed.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 754 , 10 September 2014 , R1
Copyright
© 2014 Cambridge University Press 

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