Journal of Engineering Mathematics

, Volume 94, Issue 1, pp 63–79 | Cite as

Surfactant spreading on a thin liquid film: reconciling models and experiments

  • Ellen R. SwansonEmail author
  • Stephen L. Strickland
  • Michael Shearer
  • Karen E. Daniels


The spreading dynamics of surfactant molecules on a thin fluid layer is of both fundamental and practical interest. A mathematical model formulated by Gaver and Grotberg [J Fluid Mech 235:399–414, 1992] describing the spreading of a single layer of insoluble surfactant has become widely accepted, and several experiments on axisymmetric spreading have confirmed its predictions for both the height profile of the free surface and the spreading exponent (the radius of the circular area covered by surfactant grows as \(t^{1/4}\)). However, these prior experiments utilized primarily surfactant quantities exceeding (sometimes far exceeding) a monolayer. In this paper, we report that this regime is characterized by a mismatch between the timescales of the experiment and model and, additionally, find that the spatial distribution of surfactant molecules differs substantially from the model prediction. For experiments performed in the monolayer regime for which the model was developed, the surfactant layer is observed to have a spreading exponent of less than \(1/10\), far below the predicted value, and the surfactant distribution is also in disagreement. These findings suggest that the model is inadequate for describing the spreading of insoluble surfactants on thin fluid layers.


Experiment Model Surfactant Thin liquid film  



We are grateful for support from the National Science Foundation under Grant DMS-0968258, DMS-0604047, DMS-0636590 RTG, and Research Corporations. In addition, we wish to thank Rachel Levy for valuable conversations concerning surfactant spreading.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Ellen R. Swanson
    • 1
    Email author
  • Stephen L. Strickland
    • 2
  • Michael Shearer
    • 3
  • Karen E. Daniels
    • 2
  1. 1.Department of MathematicsCentre CollegeDanvilleUSA
  2. 2.Department of PhysicsNorth Carolina State UniversityRaleighUSA
  3. 3.Department of MathematicsNorth Carolina State UniversityRaleighUSA

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