# Interdisciplinary Applied Mathematics

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function shown in Figure 10.3. At a distance farther away from the given particle position, the distribution of particles is no longer influenced by the given particle, and g(r) approaches a constant. The fluid layering near the channel wall is mainly induced by the structure of the fluid radial distribution function    and the    structure    of    the    solid    wall.    Here    the    position    of

the solid    wall    is similar to    the    position    of the    given    particle    in the    radial

distribution function, and the fluid density oscillations are similar to the oscillations in the radial distribution function.

Simple fluids in nanochannels are inhomogeneous because of the strong layering of fluid atoms near the channel wall. Classical fluid transport theories do not account for the inhomogeneity of the fluid, and transport parameters such as diffusivity and viscosity are strongly influenced by the fluid layering in nanochannels (Thompson and Troian, 1997). Fluid lay-

FIGURE 10.4. Density (upper panel) and velocity (lower panel) profiles in a 5.0a-radius cylindrical pore for two separate runs with different wall-fluid interactions. In the first run, ewf is 3.5 times larger than e, and in the second run, ewf is equal to e. (Courtesy of J. Fischer.)

ering can be influenced by various parameters such as the wall structure, fluid-wall interactions, and channel width, and these issues are discussed below.

The interaction between a fluid atom and a wall atom is usually modeled by the Lennard-Jones potential. The Lennard-Jones parameters for fluid-fluid and fluid-wall interactions are denoted by (e, a) and (ewf,awf), respectively. A higher ewf corresponds to a stronger interaction between the fluid and the wall atoms. (Heinbuch and Fischer, 1989) found that the fluid layering becomes stronger when ewf increases. Figure 10.4 shows the number density and velocity profiles for two separate runs with different fluid-wall interaction parameters in a 5.0-a radius cylindrical pore. In the first run,    ewf    is 3.5 times larger than e,    and in    the    second    run,    ewf    is    equal

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