Interdisciplinary Applied Mathematics

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The study of nanoflows has attracted significant attention in recent years, since the fundamental issues encountered in nanoflows can be different from those of microflows and macroflows for of the following reasons:

1. The surface-to-volume ratio is very high in nanofluidic systems.

2. The critical channel dimension in nanoflows can be comparable to the size of the fluid molecules under investigation.

3. Density fluctuations over interatomic distances can be important in nanoflows, while they can be largely neglected at larger scales.

4. Transport properties such as the diffusion coefficient and viscosity can be different in confined nanoflows.

5. The interaction of the fluid with the surface (e.g., hydrophilic versus hydrophobic) can have a profound influence on the flow characteristics in nanochannels.

6.    The validity of the continuum theory can be questionable for confined nanoflows.

7.    The issue of boundary conditions at solid-liquid interfaces at nanoscales is not very well understood.

8. Anomalous behavior has been observed in nanoflows.

In this book, we discuss a number of fundamental issues encountered in nanoflows. Much of the new physics encountered in nanoflows can be understood by studying simple fluids (such as Lennard-Jones liquids) in confined

nanochannels. In Chapter 10, we discuss simple fluids in nanochannels. In Chapter 11, we discuss the static and dynamic properties of water confined in nanochannels. Finally, in Chapter 12, we discuss electroosmotic flow in confined nanochannels.

1.6 Numerical Simulation at All Scales

While the first part (Chapters 2-6) and second part (Chapters 7-13) address physical modeling issues of gas flows and liquid flows, respectively, at all scales, the third part of the book is devoted to descriptions of different numerical methods. A summary of possible simulation approaches at the atomistic and continuum levels for both gas and liquid microflows is shown in Figure 1.28. In this book we present in some detail the atomistic approaches (DSMC, MD, DPD, Lattice Boltzmann) and representative discretizations for the continuum approaches (spectral elements and meshless methods). Specifically, Chapter 14 describes continuum-based approaches, while Chapters 15 and 16 describe atomistic-based approaches.

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