Confinement and Interaction Effects on the Diffusion of Passive Particles - Selected Topics of Computational and Experimental Fluid Mechanics - page 376

cavity shape but for the three analyzed potentials (CLJ, SLJ and HLJ). As already
discussed, the triangular cavity has the longest available distance, that for a very
diluted system generates the highest MSD for all the interaction potentials studied
(see Fig. 6 , first row). For ˁ ∗ 75 we see that the MSD for CLJ particles is

slightly higher than the MSD for HLJ particles for all cavities. A system made of
hard spheres has also repulsion at the walls, so that the particles stay away from the
walls and migrate to the center, with their impacts generating a high pressure that
reduce diffusion. In contrast, CLJ has attraction and therefore particles attach to the
walls originating free space at the center of the cavity and hence increasing diffusion.
The case of SLJ with a MSD even smaller than CLJ and HLJ (Fig. 6 , third row, for
all shapes) can be understood easily since for this case the system presents order thus
decreasing its MSD. When order appears the argument of hard collisions decreasing
the speed of spheres (case ˁ ∗

= 0 .

5) is not longer valid since the system is not
liquid-like, but rather crystal-like and hence entropy plays an important role. The
effect of confinement for an ordered system, as in the case of particles interacting by
means of a SLJ potential, can be seen in the third row of Fig. 6 . Here, as one moves
to the right, the MSD decreases in the following shape sequence: circular, square
and triangular. This is a plausible result since geometrically and for high densities,
the triangular cavity constrains more the particles. Note that for a diluted system the
cavity shape effect on theMSD has the opposite sequence, that is, theMSD decreases
in the following shape sequence: triangular, square and circular, since the longest

= 0 .

1.5k

1.0k

CLJ
SLJ
HLJ

0.5k

=0.10

=0.10 =0.10

0

1.5k

=0.50 =0.50 =0.50

1.0k

0.5k

0

0.6k

=0.75 =0.75

=0.75

0.4k

0.2k

0

1k 2k 3k 1k 2k 3k 1k 2k 3k

time time time

Fig. 6 (Color online) Interaction effects on the mean-square displacement (MSD). Rows shows
three representative densities ( ˁ ∗ = 0 . 1 , 0 . 5and0 . 75). Columns show the studied cavity shapes