Wetting and Minimal Surfaces

Constantin Bachas1,2, Pierre Le Doussal1, Kay Jörg Wiese1
1CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
2 Institut für theoretische Physik, ETH Zürich, 8093 Zürich, Switzerland.

Abstract

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple diagrammatic rules to calculate the non-linear corrections to the Joanny-de Gennes energy. We argue that perturbation theory is quasi-local, i.e. that all geometric length scales of the fluid container decouple from the short-wavelength deformations of the contact line. This is illustrated by a calculation of the linearized interaction between contact lines on two opposite parallel walls. We present a simple algorithm to compute the minimal surface and its energy based on these ideas. We also point out the intriguing singularities that arise in the Legendre transformation from the pure Dirichlet to the mixed Dirichlet-Neumann problem.


hep-th/0606247 [pdf]
Phys. Rev. E 75 (2007) 031601 [pdf]


Copyright (C) by Kay Wiese. Last edited March 17, 2008.