# Interdisciplinary Applied Mathematics

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in Figure 10.10 (a) shows that the wall registry (characterized by the wall registry index a) also affects the diffusivity significantly in narrow pores. This is    likely to be    caused    by    the    changed fluid    structure    when    the    wall

structure is varied. The wall registry is a measure of the variation in surface roughness of the wall (Somers and Davis, 1992). When the axial coordinate of the surface    atoms    on    both    the    walls    (i.e.,    the    upper    wall    and    the    lower

wall of    the    slit)    are    the    same, then    the    wall    registry index    a is 0. However,

when the upper wall atoms and the lower wall atoms are seperated by a certain distance, then the wall registry index is nonzero.

As mentioned above, the diffusivity normal to the channel wall cannot be defined using equation (10.2) or (10.3). However, it is possible to characterize the diffusion process normal to the channel wall by a mean-square displacement Az2(t) that can be calculated for a short time. Figure 10.11 shows the comparison of the mean-square displacement in the direction normal (z-direction) and parallel to the channel wall (x- and y-directions) for channel widths of 3.0a and 4.0a. Figure 10.11 indicates that:

1. After 2.0 ps, the diffusion process in the z-direction can be characterized by a mean-square displacement.

2. The diffusion process in the z-direction is faster in the larger channel (h = 4a) compared to the smaller channel (h = 3a).

3.    For    h =    4a,    the diffusion    in    the    x- and    y-directions    is    much faster

compared to the diffusion in the z-direction.

These results are not surprising, since the movement of the fluid atoms is more confined in the direction normal to the channel wall compared to the movement of the fluid in the direction parallel to the channel wall.

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