Journal of Engineering Mathematics

, Volume 94, Issue 1, pp 19–41 | Cite as

A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading

  • David N. Sibley
  • Andreas Nold
  • Nikos Savva
  • Serafim Kalliadasis


The motion of a contact line is examined, and comparisons drawn, for a variety of models proposed in the literature. Pressure and stress behaviours at the contact line are examined in the prototype system of quasistatic spreading of a thin two-dimensional droplet on a planar substrate. The models analysed include three disjoining pressure models based on van der Waals interactions, a model introduced for polar fluids, and a liquid–gas diffuse-interface model; Navier-slip and two non-linear slip models are investigated, with three microscopic contact angle boundary conditions imposed (two of these contact angle conditions having a contact line velocity dependence); and the interface formation model is also considered. In certain parameter regimes it is shown that all of the models predict the same quasistatic droplet spreading behaviour.


Contact line Diffuse interface Disjoining pressure Interface formation Precursor film Slip 



We are grateful to the editor and all anonymous referees for the many useful comments and suggestions. We acknowledge financial support from ERC Advanced Grant No. 247031, and Imperial College London through a DTG International Studentship.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • David N. Sibley
    • 1
  • Andreas Nold
    • 1
  • Nikos Savva
    • 2
  • Serafim Kalliadasis
    • 1
  1. 1.Department of Chemical EngineeringImperial College LondonLondonUK
  2. 2.School of MathematicsCardiff UniversityCardiffUK

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