Chapter 15
Nanofluidics: fluid and current flow in molecular-scale and thick-double-layer systems

To this point, we have considered flow in channels whose dimension was large as compared to the Debye length or the size of any molecules or particles suspended in the flow. When we employ channels with shallow (e.g., nanoscale) depths d, we cannot separate the electrical double layer from the bulk fluid using boundary-layer theory, and instead we must account for the presence of net charge density in the bulk flowfield. Even if the double layers remain thin, the perturbative effects of double layers (for example, surface conductance) are more significant as the channel becomes small. Since these phenomena typically coincide with transport through nanoscale channels, the term nanofluidics is often used to refer to flows with small d^* or flows with molecules or particles comparable to the size of the channel, though the scale need not be nanoscopic for these phenomena to be important, and these phenomena are unimportant in some nanoscale flows. Other sources use the termnanofluidics to refer specifically to flows in nanoscale channels with no reference to molecular size or λ_D. Since our interest is the interplay of electrokinetic effects with channels and molecular-scale confinement, our focus is on channels with molecular scale or of a size comparable to λ_D, and we pay only cursory attention to the absolute dimension of the channel.

For unidirectional flow in infinitelylong, uniform cross-section channels, thick double layer effects are observed only through changes in the off-diagonal elements of the electrokinetic coupling matrix. In this case, the absence of gradients in the direction of flow keeps the system analytically straightforward, but system properties normal to the wall must be integrated to determine a cross-section-averaged channel property. These systems exhibit only one-way coupling (the double layer affects the flow but not the other way around). Real engineering systems have added complexity since they include cross-sectional variations and/or interfaces between regions with different dimensions. In these cases, the flow and the double layer exhibit two-way coupling, meaning that the bulk fluid flow affects the electrical double layer and vice versa. This leads to phenomena such as concentration polarization and ion-current rectification. Interfaces also provide obstacles for macromolecules such as DNA and proteins, and the transport properties of these macromolecules is dependent on the geometry.

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