# Interdisciplinary Applied Mathematics

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Figure 11.32. The dashed line shows a scaled grand potential profile. (Courtesy of S. Melchionna.)

TABLE 11.4. Dependence    of    the    full    and empty    states    of    water    on    the

Lennard-Jones interaction parameters.

 Nanotube material Tube Diameter (A) Tube Length О oxygen—wall Fill/Empty (A) (A) States Artificial Membrane (Beckstein et at, 2001) 9.0 8.0 3.42 Both States Carbon nanotube (Waghe et al., 2002) 8.1 27.0 3.27 Full Carbon nanotube (Waghe et al., 2002) 8.1 27.0 3.41 Both States Carbon nanotube (Waghe et al., 2002) 8.1 27.0 3.43 Empty Carbon nanotube (Hummer et al., 2001) 8.1 13.4 3.23 Full Artificial Slab 9.1 15.1 3.49 Both States Silicon Dioxide 10.0 60.0 3.27(Si), 3.16 Full (O)

Summary

In summary, from the various results presented in this chapter, we note that water in confined nanochannels can exhibit very interesting and different physical characteristics compared to that of bulk water. The properties of water in confined nanochannels can depend strongly on the type of surface (hydrophilic versus hydrophobic channel wall structure) and on whether the nanopore surface is charged. It is important to properly understand the merits and limitations of the various water models before they can be used for nanotechnology design.

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### Electroosmotic Flow in Nanochannels

In this chapter we discuss fundamental concepts and simulation of electroosmotic flow in nanochannels. The basic continuum theory was presented in Chapter 7, so here the limitations of the continuum theory for electroosmotic flow in nanochannels are identified by presenting a detailed comparison between continuum and MD simulations. Specifically, the significance of the finite size of the ions and the discrete nature of the solvent molecules is highlighted. A slip boundary condition that can be used in the hydrodynamic theory for nanochannel electroosmotic flows is presented. Finally, the physical mechanisms that lead to charge inversion and corresponding flow reversal phenomena in nanochannel electroosmotic flows are discussed.

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