Wetting and Minimal Surfaces

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.

22 pages

References in corpus (9)

• 2-loop Functional Renormalization Group Theory of the Depinning Transition
• Roughness at the depinning threshold for a long-range elastic string
• Width distribution of contact lines on a disordered substrate
• Relaxation of a Moving Contact Line and Landau-Levich Effect
• Roughening Transition in a Moving Contact Line
• Can non-linear elasticity explain contact-line roughness at depinning?
• Relativistic String in a Pulse
• World-sheet duality for D-branes with travelling waves
• High Energy Scattering on Distant Branes

Cited by in corpus (3)

• Elasticity of a contact-line and avalanche-size distribution at depinning
• Roughness and critical force for depinning at 3-loop order
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles