Interdisciplinary Applied Mathematics

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to e.    In both    runs,    the    average number density    of the    fluid in    the    pore    is

0.8 and the temperature of the fluid is 0.835. Clearly, the layering effect is much more distinct in the first run compared to the second run. This can be explained by the fact that as ewf increases, the attractive force exerted by the wall atoms on the fluid atoms increases, and the tendency of a fluid atom to stay near the wall increases. A similar observation has been made by (Thompson and Robbins, 1990) in their study of Couette flow in a slit channel of width 12.8a.

(Travis and Gubbins, 2000) further investigated the variation of the density profile in a nanochannel when the attractive part of the Lennard-Jones

interaction is turned on and off by shifting the Lennard-Jones potential. Specifically, the Poiseuille flow in a 4.0a-wide slit channel was investigated for three different systems, A, B, and C. In system A, fluid-fluid and fluid-wall interactions are described by the purely repulsive part of the Lennard-Jones, or Weeks-Chandler-Andersen (WCA) potential (see Section 16.1 for details on WCA potential). In system B, the fluid-fluid and fluid-wall interactions are described by the full 12-6 Lennard-Jones (including both the attractive and the repulsive interactions) potential. In system C, the fluid-fluid interactions are described by the WCA potential, and the interactions between    the    fluid and    the    wall    are described    by    the    full    12-6

Lennard-Jones potential. Figure 10.5 (a) shows a comparison of the density profiles for the three different systems. It is observed that the presence of attractive fluid-wall forces (system B and C) leads to the formation of boundary liquid layers of higher density than in the case of repulsive wall-fluid interactions (system A). It is also observed that the density of the layers is higher in system C compared to that of system B. This can be explained by the fact that compared to system B, the fluid atoms in system C have a greater affinity for the wall atoms and less affinity for other fluid atoms. In addition, the number of density peaks (i.e., the number of fluid layers in the channel) is also different for the three systems. These results indicate that the density distribution of fluid atoms in the channel is sensitive to both the fluid-wall and fluid-fluid interactions, and care should be taken in choosing the best potential to depict a particular fluidic system. Figure 10.5 (b) shows the average number density of fluid atoms along the channel length direction. We see that the fluids are highly structured in all three systems. The density oscillates with a wavelength of order a. Clearly, the wall structure has been imposed upon the fluid. Similar behavior has also been observed by (Zhang et al., 2001) in the simulation of n-decane confined between two Au(111) surfaces.

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