Influence of atomistic physics on electro-osmotic flow: An analysis based on density functional theory

Abstract

Molecular density profiles and charge distributions determined by density functional theory (DFT) are used in conjunction with the continuum Navier-Stokes equations to compute electro-osmotic flows in nanoscale channels. The ion species of the electrolyte are represented as centrally charged hard spheres, and the solvent is treated as a dense fluid of neutral hard spheres having a uniform dielectric constant. The model explicitly accounts for Lennard-Jones interactions among fluid and wall molecules, hard sphere repulsions, and short range electrical interactions, as well as long range Coulombic interactions. Only the last of these interactions is included in classical Poisson-Boltzmann (PB) modeling of the electric field. Although the proposed DFT approach is quite general, the sample calculations presented here are limited to symmetric monovalent electrolytes. For a prescribed surface charge, this DFT model predicts larger counterion concentrations near charged channel walls, relative to classical PB modeling, and hence smaller concentrations in the channel center. This shifting of counterions toward the walls reduces the effective thickness of the Debye layer and reduces electro-osmotic velocities as compared to classical PB modeling. Zeta potentials and fluid speeds computed by the DFT model are as much as two or three times smaller than corresponding PB results. This disparity generally increases with increasing electrolyte concentration, increasing surface charge density and decreasing channel width. The DFT results are found to be comparable to those obtained by molecular dynamics simulation, but require considerably less computing time.