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.