  We study, using Density Functional theory and Monte Carlo simulations,
aqueous electrolyte solutions between charged infinite planar surfaces, in a
contact with a bulk salt reservoir. In agreement with recent experimental
observations [Z. Luo et al., Nat. Comm. 6, 6358 (2015)], we find that the
confined electrolyte lacks local charge neutrality. We show that a Density
Functional Theory (DFT) based on a bulk- HNC expansion properly accounts for
strong electrostatic correlations and allows us to accurately calculate the
ionic density profiles between the charged surfaces, even for electrolytes
containing trivalent counterions. The DFT allows us to explore the degree of
local charge neutrality violation, as a function of plate separation and bulk
electrolyte concentration, and to accurately calculate the interaction force
between the charged surfaces.
