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

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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
Volume16
Issue number6
DOIs
StatePublished - Dec 2005

Fingerprint

Variational Model
Contact Line
Lubrication
Energy Dissipation
Contact Angle
Energy dissipation
Wetting
Fluid Model
Approximation
Dynamic Equation
Approximation Methods
Galerkin
Fluids
Fluid
Contact angle
Motion
Line
Interaction
Modeling
Context

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Variational models for moving contact lines and the quasi-static approximation. / Glasner, Karl B.

In: European Journal of Applied Mathematics, Vol. 16, No. 6, 12.2005, p. 713-740.

Research output: Contribution to journalArticle

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