Electro-osmotic flows under nanoconfinement: A self-consistent approach

We introduce a theoretical and numerical method to investigate the properties of electro-osmotic flows under conditions of extreme confinement. The present approach, aiming to provide a simple modeling of electrolyte solutions described as ternary mixtures, which comprises two ionic species and a third uncharged component, is an extension of our recent work on binary neutral mixtures. The approach, which combines elements of kinetic theory, density functional theory with Lattice-Boltzmann algorithms, is microscopic and self-consistent and does not require the use of constitutive equations to determine the fluxes. Numerical solutions are obtained by solving the resulting coupled equations for the one-particle phase-space distributions of the species by means of a Lattice-Boltzmann discretization procedure. Results are given for the microscopic density and velocity profiles and for the volumetric and charge flow.