  The structures of dilute electrolyte solutions close to non-uniformly charged
planar substrates are systematically studied within the entire spectrum of
microscopic to macroscopic length scales by means of a unified classical
density functional theory (DFT) approach. This is in contrast to previous
investigations, which are applicable either to short or to long length scales.
It turns out that interactions with microscopic ranges, e.g., due to the hard
cores of the fluid molecules and ions, have negligible influence on the
formation of non-uniform lateral structures of the electrolyte solutions. This
partly justifies the Debye-H\"uckel approximation schemes applied in previous
studies of that system. In general, a coupling between the lateral and the
normal fluid structures leads to the phenomenology that, upon increasing the
distance from the substrate, less details of the lateral non-uniformities
contribute to the fluid structure, such that ultimately only large-scale
surface features remain relevant. It can be expected that this picture also
applies to other fluids characterized by several length scales.
