Interdisciplinary Applied Mathematics

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12.1 The Need for Atomistic Simulation

A fundamental issue that needs to be addressed is whether continuum theories based on the Poisson-Boltzmann and the Navier-Stokes equations— which have been popularly used to understand electroosmotic flow in micron-scale channels—can be used to describe electroosmotic flow in nanometerwide channels. For example, in the derivation of the classical Poisson-Boltzmann equation, the ions are assumed to be infinitesimal; the interactions between the ions, ion-water, and ion-wall are all considered in a mean-field fashion, and the molecular aspects of these interactions are neglected. Similarly, the continuum flow theory based on Stokes or Navier-Stokes equations assumes that the state variables (e.g., density) do not

♦ IxPBS Model    И0.1х PBS Model    A0.01 x PBS Model

01 x PBS Experiment    □ 0.1 x PBS Experiment Д 0.01 x PBS Experiment

1.6 —



1 1 | 0.8





2 . ▲

LL 02 0




0    5    10    15    20    25    30

Height (nm)

FIGURE 12.1. Comparison of the theoretical flowrates with experimental results. 1 x PBS, 0.1 x PBS and 0.01 x PBS refer to original PBS, 10-fold diluted PBS, and 100-fold diluted PBS, respectively. (Courtesy of A.T. Conlisk.)

vary significantly over intermolecular distances and that the shear stress can be    related    to    the    local    strain    rate    by    a    linear    constitutive    relation

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