  We introduce a theoretical and numerical method to investigate the flow of
charged fluid mixtures under extreme confinement. We model the electrolyte
solution as a ternary mixture, comprising two ionic species of opposite charge
and a third uncharged component. The microscopic approach is based on kinetic
theory and is fully self-consistent. It allows to determine configurational
prop- erties, such as layering near the confining walls, and the flow
properties. We show that, under appropriate assumptions, the approach
reproduces the phenomenological equations used to describe electrokinetic
phenomena, without requiring the introduction of constitutive equations to
determine the fluxes. Moreover, we model channels of arbitrary shape and
nanometric roughness, features that have important repercussions on the
transport properties of these systems. Numerical simulations are obtained by
solving the evolution dynamics of the one-particle phase- space distributions
of each species by means of a Lattice Boltzmann method for flows in straight
and wedged channels. Results are presented for the microscopic density, the
velocity profiles and for the volumetric and charge flow-rates. Strong
departures from electroneutrality are shown to appear at molecular level.
