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 properties, such as layering near the confining walls, and the flow properties. We show that, under appropriate as- sumptions, 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
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