Fluid density variation across a narrow slit. Density of molecular centers is greatest in layers adjacent to planar walls. Peaks are spaced one molecular diameter apart.
Density distributions computed by DFT (solid lines) compare well with Monte Carlo (MC) and molecular dynamics (MD) simulations (symbols) by others. Both slits have hard planar walls. The wide slit has no Lennard-Jones interactions.
Distributions of counterions, coions, and solvent molecules near a charged surface. Present DFT calculations (solid lines) are in close agreement with comparative DFT results from Tang et al. (Ref. 23) for and .
Comparison of molecular density profiles computed by DFT (solid lines) with corresponding Poisson-Boltzmann (PB) predictions (dotted) for , , and . DFT has fewer counterions in the channel center, relative to PB, suggesting higher concentrations near the surface.
Cumulative charge distributions computed by DFT (solid lines) and by Poisson-Boltzmann (dotted) models. Both models have remarkably similar counterion charges between surface and no-slip plane. Beyond this plane, DFT tends to shift counterions away from the center toward the walls.
Electro-osmotic speeds computed by DFT (solid line) are considerably smaller than classical PB predictions (upper dotted line) partly because counterions are shifted from the center toward the surface. The modified Poisson-Boltzmann (MPB) model uses the classical PB ion distribution but applies no-slip boundary condition molecular diameter off the surface, as also applied in DFT modeling and observed in prior MD simulations.
The influence of ambient ion concentration on electro-osmotic velocity profiles is relatively weak for . At larger concentrations electro-osmotic speeds are substantially reduced, ultimately resulting in flow reversal in the channel center for the DFT calculation for .
Variation of mean electro-osmotic speed with normalized surface charge density for several choices of the ambient ion concentration. Poisson-Boltzmann predictions substantially exceed DFT predictions, particularly for large surface charges and ion concentrations.
The MPB model is in better agreement with DFT than classical PB modeling of Fig. 8, particularly when surface charge and ion concentrations are moderate.
DFT predicts a nonmonotonic variation of normalized zeta potential with surface charge density similar in form to DFT predictions of electro-osmotic speed in Figs. 8 and 9. In contrast, the PB model predicts monotonic variation of both zeta potential and speed.
Normalized mean speeds scaled by zeta potential are quite similar for DFT (solid), PB (dotted), and MPB (dashed). However, knowledge of this ratio alone is insufficient, since it is still necessary to compute the zeta potential by DFT or MD in order to make predictions of electro-osmotic speed.
Predictions of normalized potential at charged surface (bare wall potential) are quite similar for DFT and PB, particularly for moderate surface charge densities of greatest practical interest. Vertical scale is expanded by 60% relative to Fig. 10, since surface potentials are sometimes that much greater than zeta potentials.
Variation of mean electro-osmotic speed with normalized channel width. Disparity between DFT and classical PB predictions grows larger, in a fractional sense, as channel width decreases. Increased surface charge also increases disparity. Steric effects become more pronounced with decreasing channel width.
The modified Poisson-Boltzmann model provides improved agreement with DFT predictions of mean channel speeds, as compared with classical PB results shown earlier in Fig. 13. Improvement is particularly great at very small channel widths, since fractional disparity between DFT and MPB now decreases rather than increases with decreasing channel width.
Comparison of counterion density profiles computed by present DFT (solid lines) and by MD modeling of Qiao and Aluru (solid symbols) (Ref. 16). Peaks for DFT and MD are about twice as great as comparative Poisson-Boltzmann calculations (dotted and open symbols).
DFT model predicts electro-osmotic speeds (solid line) somewhat greater than MD (symbols). Chapman-Enskog modeling of viscosity in the DFT model (chain-dotted line) brings results into better agreement. The classical PB model overpredicts speeds by about a factor of 2.
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