Contact condition for the density profiles in spherical and cylindrical double layers

Exact sum rules involving the contact values of the density profiles and bulk osmotic pressure in spherical and cylindrical electric double layers are formulated. When the radius of curvature in these systems tends to infinity, the contact conditions reduce to the well-known contact condition in planar double layer due to Henderson, Blum, and Lebowitz (1979). However, unlike the latter relation, the contact conditions in the non-planar geometries are non-local, and require for their implementation full knowledge of the electrode–ion singlet distribution functions.