Interdisciplinary Applied Mathematics

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Embed MD    Continuum Modeling


velocity    using constant viscosity


u











FIGURE 16.8. Continuum simulation of electroosmotic flow in a large channel using the velocity embedding technique. The channel is partitioned into two regions: a near wall region and a channel center region. The velocity near the wall is computed by embedding the velocity obtained from MD simulation of electroosmotic flow in a smaller channel. The velocity in the channel center region is computed using the continuum flow theory based on a constant viscosity.


position z:



(16.28)


(16.29)


where u, c, and Eext are the velocity, the ion concentration, and the external electric field at any position z in the small channel, respectively. Furthermore, U, c, and Eext are the velocity, the ion concentration, and the external electric field at any position z in the big channel, respectively. Using the symmetry of the velocity profile with respect to the channel center,






where F(z) is defined by









p,zs =Sc’ -zqc(s)Eext ds Гс» -zqc(s)Eext ds


Integrating equation (16.31) from the no-slip plane (i.e., z = 0) to any position z, and using the fact that the velocity is zero at the no-slip plane, we obtain

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