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

Ernst A. Van Nierop; Benoit Scheid; Howard A. Stone

doi:10.1017/S0022112008000955

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

Ernst A. Van Nierop, Benoit Scheid, Howard A. Stone

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

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 U^2/3 and U².

Original language	English (US)
Pages (from-to)	119-127
Number of pages	9
Journal	Journal of Fluid Mechanics
Volume	602
DOIs	https://doi.org/10.1017/S0022112008000955
State	Published - May 2008

All Science Journal Classification (ASJC) codes

Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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title = "On the thickness of soap films: An alternative to Frankel's law",

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.",

author = "{Van Nierop}, {Ernst A.} and Benoit Scheid and Stone, {Howard A.}",

note = "Funding Information: We thank the Harvard MRSEC DMR-0213805, and Unilever Research for support of this research. We thank Peter Howell for helpful conversations about thin films.",

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T2 - An alternative to Frankel's law

AU - Van Nierop, Ernst A.

AU - Scheid, Benoit

AU - Stone, Howard A.

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AB - 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.

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

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