Interdisciplinary Applied Mathematics

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ship. However, as discussed in Chapter 10, significant fluctuations in fluid density have been observed close to the surface in molecular dynamics simulations (Travis and Gubbins, 2000) as well as in experiments (Cheng et al.,    2001).    Hence,    it    is important    to    understand in    detail    the    validity

of continuum theory for electroosmotic flow in nanochannels. Conlisk and coworkers (Zheng et al., 2003) presented a comparison between experimental and theoretical flow rates for electroosmotic flow in nanochannels with critical dimension (typically the width or the height) varying from 4 nm to 27 nm. This comparison is shown in Figure 12.1. The ionic solution considered is phosphate-buffered saline (PBS), which consists of Na+, Cl_, K+, H2POJ, and    HPO;)~.    The    pH    value    of    PBS is 7.4.    The    theoretical    results

are obtained using the classical continuum theory for electroosomotic flow. The experimental and the theoretical flow rates agree very well except for the 4-nm case. While it is difficult to exactly pin-point the reason for the discrepancy, noncontinuum effects, such as the finite size of the ions, can be a big part of the discrepancy, since they play an important role when the critical channel dimension is just a few molecular diameters.

To understand the limitations and the various assumptions built into the continuum theory, we present detailed comparisons between continuum and MD simulations. Continuum modeling of electroosmotic flow is discussed in detail in Chapter 7. In this section, however, a simplified form of the equations presented in Chapter 7 is used to explain electroosmotic flow in nanochannels. Specifically, we focus on electroosmotic transport in straight flat channels; the channel width is in the z-direction, and the flow is along the x-direction; see Figure 12.2. The assumptions are:

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