Curvature expansion of density profiles

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 pro. le 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.