Skip to main content Accessibility help

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



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.



Hide All
Adelizzi, E. A. & Troian, S. M. 2004 Interfacial slip in entrained soap films containing associating hydrosoluble polymer. Langmuir 20, 74827492.
Berg, S., Adelizzi, E. A. & Troian, S. M. 2005 Experimental study of entrainment and drainage flows in microscale soap films. Langmuir 21, 38673876.
Braun, R. J. & King-Smith, P. E. 2007 Model problems for the tear film in a blink cycle: single-equation models. J. Fluid Mech. 586, 465490.
Breward, C. J. W. 1999 The mathematics of foam. PhD thesis, Oxford University.
Breward, C. J. W. & Howell, P. D. 2002 The drainage of a foam lamella. J. Fluid Mech. 458, 379406.
Bruinsma, R., di Meglio, J. M., Quéré, D. & Cohen-Addad, S. 1992 Formation of soap films from polymer solutions. Langmuir 8, 31613167.
Cohen-Addad, S. & di Meglio, J.-M. 1994 Stabilization of aqueous foam by hydrosoluble polymers 2. Role of polymer/surfactant interactions. Langmuir 10, 773778.
Durand, M. & Stone, H. A. 2006 Relaxation time of the topological T1 process in a two-dimensional foam. Phys. Rev. Lett. 97, 226101.
Edwards, D. A., Brenner, H. & Wasan, D. T. 1991 Interfacial Transport Processes and Rheology. Butterworth-Heinemann.
Fruhner, H., Wantke, K.-D. & Lunkenheimer, K. 1999 Relationship between surface dilational properties and foam stability. Colloids Surfaces A 162, 193202.
de Gennes, P. G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer.
Lal, J. & di Meglio, J.-M. 1994 Formation of soap films from insoluble surfactants. J. Colloid Interface Sci. 164, 506509.
Lionti-Addad, S. & di Meglio, J.-M. 1992 Stabilization of aqueous foam by hydrosoluble polymers 1. Sodium dodecyl sulfate–poly(ethylene oxide) system. Langmuir 8, 324327.
Liu, X. & Duncan, J. H. 2006 An experimental study of surfactant effects on spilling breakers. J. Fluid Mech. 567, 433455.
Martin, B. & Wu, X.-I. 1995 Shear flow in a two-dimensional Couette cell: A technique for measuring the viscosity of free-standing liquid films. Rev. Sci. Instrum. 66, 56035608.
Mysels, K. J. & Cox, M. C. 1962 An experimental test of Frankel's law of film thickness. J. Colloid Sci. 17, 136145.
Mysels, K. J., Shinoda, K. & Frankel, S. 1959 Soap Films: Studies of Their Thinning. Pergamon.
Naire, S., Braun, R. J. & Snow, S. A. 2001 An insoluble surfactant model for a vertical draining free film with variable surface viscosity. Phys. Fluids 13, 24922502.
Schwartz, L. W. & Roy, R. V. 1999 Modeling draining flow in mobile and immobile soap films. J. Colloid Interface Sci. 218, 309323.
Scriven, L. E. 1960 Dynamics of a fluid interface: Equation of motion for Newtonian surface fluids. Chem. Engng Sci. 12, 98108.
Shen, A. Q., Gleason, B., McKinley, G. H. & Stone, H. A. 2002 Fiber coating with surfactant solutions. Phys. Fluids 14, 4055.
MathJax is a JavaScript display engine for mathematics. For more information see

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



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed