Variational models for moving contact lines and the quasi-static approximation

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9 Scopus citations


This paper proposes the use of a variational framework to model fluid wetting dynamics. The central problem of infinite energy dissipation for a moving contact line is dealt with explicitly rather than by introducing a specific microscopic mechanism which removes it. We analyze this modelling approach in the context of the quasi-steady limit, where contact line motion is slower than bulk relaxation. We find that global effects enter into Tanner-type laws which relate line velocity to apparent contact angle through the role that energy dissipation plays in the bulk of the fluid. A comparison is made to the dynamics of lubrication equations that include attractive and repulsive intermolecular interactions. A Galerkin-type approximation method is introduced which leads to reduced-dimensional dynamical descriptions. Computations are conducted using these low-dimensional approximations, and a substantial connection to lubrication equation dynamics is found.

Original languageEnglish (US)
Pages (from-to)713-740
Number of pages28
JournalEuropean Journal of Applied Mathematics
Issue number6
StatePublished - Dec 2005

ASJC Scopus subject areas

  • Applied Mathematics


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