Electro-osmotic flow of a model electrolyte

Electro-osmotic flow is studied by nonequilibrium molecular dynamics simulations in a model system chosen to elucidate various factors affecting the velocity profile and facilitate comparison with existing continuum theories. The model system consists of spherical ions and solvent, with stationary, uniformly charged walls that make a channel with a height of 20 particle diameters. We find that hydrodynamic theory adequately describes simple pressure-driven (Poiseuille) flow in this model. However, Poisson-Boltzmann theory fails to describe the ion distribution in important situations, and therefore continuum fluid dynamics based on the Poisson-Boltzmann ion distribution disagrees with simulation results in those situations. The failure of Poisson-Boltzmann theory is traced to the exclusion of ions near the channel walls resulting from reduced solvation of the ions in that region. When a corrected ion distribution is used as input for hydrodynamic theory, agreement with numerical simulations is restored. An analytic theory is presented that demonstrates that repulsion of the ions from the channel walls increases the flow rate, and attraction to the walls has the opposite effect. A recent numerical study of electro-osmotic flow is reanalyzed in the light of our findings, and the results conform well to our conclusions for the model system.