Contact line moving on a solid
Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
a e-mail: firstname.lastname@example.org
Revised: 15 June 2011
Published online: 30 August 2011
The moving contact line problem can be summarized as follows: consider the triple line where a solid, a liquid and its vapor meet. This contact line may be the perimeter of a liquid droplet standing on a solid. Suppose now that, because of gravity for instance, the droplet and so its perimeter slides on the solid surface. The boundary conditions for viscous fluids impose that the flow velocity on an immobile solid is zero. If one assumes that the liquid/vapor surface is a material surface, i.e. that it is convected by the fluid, the contact line cannot move with respect to the solid, contrary to what is observed. Over the years many suggestions have been made to solve this problem. I show that solutions relying on the introduction of microscopic length scales are not consistent within the general framework of continuum mechanics. To get consistent solutions, one needs to introduce evaporation/condensation near the moving line, in agreement with experimental findings.
© EDP Sciences, Springer-Verlag, 2011