Interdisciplinary Applied Mathematics

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TABLE 10.1. Units for various quantities in Lennard-Jones fluids.


Length


a


Velocity


(e/m)1/2


Mass


m


Shear rate


(e/ma2)1/2


Energy


e


Stress


e/a3


Time


(та2/с)1/2


Viscosity


(me)1/2/a2


Number density


a-3


Diffusivity


a(e/m)1/2


Temperature


e/kB

FIGURE 10.2. Density profile of a Lennard-Jones fluid. Simulations are performed in an 11-fluid-atomic-diameter channel.


significant results that have been observed when LJ liquids are confined in nanochannels are summarized below.

10.2 Density Distribution


The strong density oscillations of fluid atoms near the fluid/solid interface is a universal phenomenon, and it has been observed in almost all MD simulations of nanofluidic flows and been verified experimentally (Chan and Horn, 1985; Zhu and Granick, 2002; Zhu and Granick, 2001). Figure 10.2 shows the density profile of Lennard-Jones fluid atoms in a 11-fluid-diameter-wide channel (see also Figure 1.7, which shows density fluctuations of an LJ liquid in a larger channel). Density fluctuations near a channel wall can be explained using the concept of a radial distribution function (RDF). A radial distribution function (or the pair correlation function), typically denoted

measures the probability density of finding a particle at a distance r from a given particle (r = 0 corresponds to the position of the given particle).


by g(r), is a basic measure of the structure of a liquid. RDF measures the probability density of finding a particle at a distance r from a given particle position. Figure 10.3 is a sketch of a typical radial distribution function. At a short distance from the given particle position, g(r) is essentially zero because of the strong repulsion between the particles; i.e., particles cannot get too close to each other. As r increases, g(r) shows a first peak, which is mainly caused by the attractive interactions between the particles. At a short distance from the first peak, a depletion of the particles is observed because of repulsive forces, and this gives rise to a minimum in g(r). The combination of the attractive and the repulsive forces between the particles leads to    the    various    peaks and    valleys    observed    in    the    radial    distribution

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