# Interdisciplinary Applied Mathematics

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Another emerging application in which nanoflows are gaining importance is that of molecular gates (Kuo et al., 2003a; Kuo et al., 2003b). Nanoporous membranes can be used to interface vertically separated microfluidic channels to create a truly three-dimensional fluidic architecture, as shown in Figure 1.27. Such hybrid three-dimensional architectures can be used for gateable transfer of selected solution components between vertically separated microfluidic channels. For example, by adjusting the voltages applied at    the    terminals, and    by    controlling    the    polarity    and density    of the    sur

face charges of the nanopores, vertical transport of analyte through the nanopores can be controlled precisely. Integration of such fluidic circuits into a single chip can thus enable very complicated fluidic and chemical manipulations. Bohn and colleagues (Kuo et al., 2003b) have also shown that even when operated in a passive mode, without external manipulation, the nanochannels can separate solutions in different layers and inhibit mixing while the fluidic manipulations are performed in each of the microchannels. The    diameter    of    the    cylindrical    pores is    usually    on    the    order

of 10 to 100 nm. In nanopores, flow occurs in structures of the same size as

physical parameters that govern the flow. For example, in molecular gates, the Debye length (see Figure 1.27), which characterizes the length scale of ionic interactions in a solution, can be comparable to the diameter of the pore    (Kuo    et    al.,    2001).    In    microflows,    the    Debye    length is negligible

compared to the channel diameter. As a result, the flow characteristics in nanochannels can be different compared to the flows in microchannels; see Chapter 12.

Even though we have discussed only three examples in which nanoflows play an important role in determining the characteristics of the system, there are a number of other applications such as fuel cell devices, drug delivery systems, chemical and biological sensing and energy conversion devices, and a number of other nanodevices in which nanoflows are important and need to be understood in great detail. With advances in nanofabrication techniques, it is now possible to fabricate devices with diameters ranging from a few angstroms to few hundred nanometers. Such advances make it possible to understand fundamental physical mechanisms in nanoflows through a detailed comparison between experimental and theoretical studies.

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