Journal of Engineering Mathematics

, Volume 50, Issue 2–3, pp 157–175 | Cite as

Surfactant-driven motion and splitting of droplets on a substrate

  • L. W. Schwartz
  • R. V. Roy
  • R. R. Eley
  • H. M. Princen


A theoretical and computational model is presented to predict the motion of a small sessile liquid droplet, lying on a solid substrate including surfactant effects. The model, as formulated, consists of coupled partial differential equations in space and time, and several auxilliary relationships. The validity of the long-wave, or ‘lubrication’ approximation is assumed. It is shown that there are circumstances where surfactant injection or production will cause the droplet to split into two daughter droplets. It is conjectured that the results are relevant to basic mechanisms involved in biological cell division (cytokinesis). It is also demonstrated that motion of a droplet, analogous to the motility of a cell, can be produced by surfactant addition. Computed examples are given here, in both two and three space dimensions. Approximate energy requirements are also calculated for these processes. These are found to be suitably small.

Key words

cell division coupled partial differential equations lubrication approximation numerical model surfactant theory 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • L. W. Schwartz
    • 3
  • R. V. Roy
    • 1
  • R. R. Eley
    • 1
  • H. M. Princen
    • 2
  1. 1.ICI Paints Research CenterStrongsvilleU.S.A.
  2. 2.Surfaces & ColloidsFlemingtonU.S.A.
  3. 3.Department of Mechanical EngineeringUniversity of DelawareNewarkU.S.A.

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