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.