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Capillary retraction of the edge of a stretched viscous sheet

Published online by Cambridge University Press:  03 April 2018

James P. Munro Open the ORCID record for James P. Munro [Opens in a new window]  and
John R. Lister
James P. Munro*
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA, UK
John R. Lister
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

Surface tension causes the edge of a fluid sheet to retract. If the sheet is also stretched along its edge then the flow and the rate of retraction are modified. A universal similarity solution for the Stokes flow in a stretched edge shows that the scaled shape of the edge is independent of the stretching rate, and that it decays exponentially to its far-field thickness. This solution justifies the use of a stress boundary condition in long-wavelength models of stretched viscous sheets, and gives the detailed shape of the edge of such a sheet, resolving the position of the sheet edge to the order of the thickness.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Low-Reynolds-number flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , R1
Copyright
© 2018 Cambridge University Press 

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