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On the thickness of soap films: an alternative to Frankel's law

Published online by Cambridge University Press:  25 April 2008

ERNST A. VAN NIEROP ,
BENOIT SCHEID  and
HOWARD A. STONE
ERNST A. VAN NIEROP
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
BENOIT SCHEID
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
HOWARD A. STONE
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
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Abstract

The formation of soap films by vertical withdrawal from a bath is typically described by Frankel's law, which assumes rigid film ‘walls’ and shear-like dynamics. Since most soap films have interfaces that are not rigid, and as the flow in the withdrawal of thin free films is typically extensional, we reconsider the theory of soap film formation. By assuming extensional flow dominated by surface viscous stresses we find that the film thickness scales as the two-thirds power of the withdrawal speed U. This speed dependence is also predicted by Frankel's law; the difference lies in the origin of the viscous resistance which sets the pre-factor. When bulk viscous stresses are important the speed dependence can vary between U2/3 and U2.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 602 , 10 May 2008 , pp. 119 - 127
Copyright
Copyright © Cambridge University Press 2008

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