# Interdisciplinary Applied Mathematics

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1.0    2.0    3.0    4.0

Distance from the channel center (nm)

FIGURE 16.7. (a) CD ion concentration across the channel for case 4 (W = 2.22 nm, as = +0.120 C/m2). (b) The electrochemical potential correction term extracted from the ion distribution shown in (a). (c) Comparison of CD ion concentration across the    channel    for case    1    (W    = 3.49    nm,    as    = +0.120    C/m2)    as pre

dicted by the MD simulation and modified P-B equation. (d) Comparison of CD ion concentration across the channel for case 6 (W = 10.0 nm, as = +0.124 C/m2) as predicted by the MD simulation and modified Poisson-Boltzmann (P-B) equation.

which the velocity near the wall, obtained from the fine-scale simulation, is used in the continuum modeling of a coarse-scale channel. This approach is described below.

Figure 16.8 presents details on the simulation of electroosmotic flow in a large channel using the velocity obtained from MD simulation of electroosmotic flow in a small channel. For any position within S’ from the no-slip plane, the velocity in the large channel is obtained by embedding the MD velocity obtained for the electroosmotic flow in a small channel. Once the velocity at z = S’ is obtained, it is used as the boundary condition for the continuum flow modeling in the central portion of the large channel using a constant viscosity. To embed the small channel MD velocity u within S’ from the    no-slip    plane    into    the    simulation    of    flow in a    large channel,    we

first integrate the momentum equation from the channel center (c» is the center of the small channel and c’ is the center of the large channel) to a

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