Viscosity solutions for a model of contact line motion

Karl Glasner, Inwon C. Kim

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

This paper considers a free boundary problem that describes the motion of contact lines of a liquid droplet on a flat surface. The elliptic nature of the equation for droplet shape and the monotonic dependence of contact line velocity on contact angle allows us to introduce a notion of "viscosity" solutions for this problem. Unlike similar free boundary problems, a comparison principle is only available for a modified short-time approximation because of the constraint that conserves volume. We use this modified problem to construct viscosity solutions to the original problem under a weak geometric restriction on the free boundary shape. We also prove uniqueness provided there is an upper bound on front velocity.

Original languageEnglish (US)
Pages (from-to)37-60
Number of pages24
JournalInterfaces and Free Boundaries
Volume11
Issue number1
DOIs
StatePublished - 2009

ASJC Scopus subject areas

  • Surfaces and Interfaces

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