Curvature expansion of density profiles

¹ Max-Planck-Institut für Metallforschung - Heisenbergstrasse 3 70569 Stuttgart, Germany
² Institut für Theoretische und Angewandte Physik, Universität Stuttgart Pfaffenwaldring 57, 70569 Stuttgart, Germany
³ Department for the Modeling of Physico-Chemical Processes Maria Curie-Skłodowska University, 20-031 Lublin, Poland
⁴ Institut fuer Theoretische Physik, Universität Erlangen-Nürnberg Staudtstrasse 7, 91058 Erlangen, Germany

Received: 28 October 2004
Accepted: 23 December 2004

Abstract

We present a technique to calculate density profiles of a fluid close to a hard convex wall by arguing that its equilibrium density distribution depends only on the local curvatures of the wall. We perform a systematic expansion of the profile in powers of the curvatures and apply it to a hard-sphere fluid within the framework of density-functional theory (DFT). For large distances from the wall, the curvature expansion can be done analytically. Our approach can be generalized to systems with short-ranged fluid-fluid and wall-fluid interaction potentials, as long as intrinsic length scales remain small.