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  • Cited by 5
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Fried, Eliot and Jabbour, Michel 2015. Sessile drops: spreading versus evaporation–condensation. Zeitschrift für angewandte Mathematik und Physik, Vol. 66, Issue. 3, p. 1037.

    NOCHETTO, RICARDO H. SALGADO, ABNER J. and WALKER, SHAWN W. 2014. A DIFFUSE INTERFACE MODEL FOR ELECTROWETTING WITH MOVING CONTACT LINES. Mathematical Models and Methods in Applied Sciences, Vol. 24, Issue. 01, p. 67.

    Lawrie, Jane B. 2012. On acoustic propagation in three-dimensional rectangular ducts with flexible walls and porous linings. The Journal of the Acoustical Society of America, Vol. 131, Issue. 3, p. 1890.

    Sibley, David N. Savva, Nikos and Kalliadasis, Serafim 2012. Slip or not slip? A methodical examination of the interface formation model using two-dimensional droplet spreading on a horizontal planar substrate as a prototype system. Physics of Fluids, Vol. 24, Issue. 8, p. 082105.

    Afkhami, S. Zaleski, S. and Bussmann, M. 2009. A mesh-dependent model for applying dynamic contact angles to VOF simulations. Journal of Computational Physics, Vol. 228, Issue. 15, p. 5370.


On a model for the motion of a contact line on a smooth solid surface

  • J. BILLINGHAM (a1)
  • DOI:
  • Published online: 01 July 2006

In this paper we investigate the model for the motion of a contact line over a smooth solid surface developed by Shikhmurzaev, [24]. We show that the formulation is incomplete as it stands, since the mathematical structure of the model indicates that an additional condition is required at the contact line. Recent work by Bedeaux, [4], provides this missing condition, and we examine the consequences of this for the relationship between the contact angle and contact line speed for Stokes flow, using asymptotic methods to investigate the case of small capillary number, and a boundary integral method to find the solution for general capillary number, which allows us to include the effect of viscous bending. We compare the theory with experimental data from a plunging tape experiment with water/glycerol mixtures of varying viscosities [11]. We find that we are able to obtain a reasonable fit using Shikhmurzaev's model, but that it remains unclear whether the linearized surface thermodynamics that underlies the theory provide an adequate description for the motion of a contact line.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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