Interdisciplinary Applied Mathematics

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1. The velocity profile is flat in the central portion of the channel,

2. A significant velocity slip is observed near the channel wall, and

3. The velocity for a negatively charged surface is very small, indicating that the bulk transport is negligible in this case.

Figure 13.20 (a) shows the typical trajectory of 8 Cl_ ions during a 60 ps period. Note that the starting z-position of all 8 ions is shifted to z = 0 nm. We observe that the contact adsorbed Cl_ ions are not immobilized, since the Cl_ charged surface atom interactions are not very strong. Figure 13.20 (b) shows the typical trajectory of 8 Na+ ions during a 120 ps period. We observe that the contact adsorbed Na+ ions are immobilized because of the stronger Na+ charged surface atom interactions. Since the movement of Na+ ions is negligible, the driving force on the fluid is negligible. Thus,

(a)

Along channel length (nm)

(b)

Along channel length (nm)

FIGURE 13.20. (a) Typical trajectory of Cl~ ions for a positively charged surface during a time period of 60 ps. (b) Typical trajectory of Na+ ions for a negatively charged surface during a time period of 120 ps. The starting г—position of all ions are shifted to г = 0 nm.

the bulk fluid velocity for a negatively charged surface is much smaller than that observed for a positively charged surface.

The observed dependence of electroosmotic transport on the surface charge is significantly different from the results obtained using the conventional continuum theories, which predict that the electroosmotic transport will simply reverse its direction if the surface charge density is flipped. This anomalous dependence of electroosmotic transport on the surface charge is mainly caused by the different adsorption behavior of the counterions, which depends on the size of the counterion, the local electrostatic interactions between ion-water and ion-charged surface atoms, and on the external electric field.

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