We carry out Brownian dynamics simulations and study the ordering of particles under a uniform external force in a narrow system. In our previous studies [M. Sato et al., Phys. Rev. E 87, 032403 (2013); J. Phys. Soc. Jpn. 82, 084804 (2013)], we showed that the ordering of particles depends on the direction of the external force. In the studies, however, the system size and the number of particles are small, so the behaviors we observed corresponds to the motions in the initial stage of crystallization. In this paper, using a longer container and more particles, we investigate how solidification in a narrow system proceeds. We also study the effect of the shape of simulation box on the ordering of particles. When we use a rhomboid as a simulation box, the ratio of the particles with the face-centered cubic structure to those with the hexagonal close-packed structure is larger than that in a cuboid system.

Keeping formation of a colloidal crystal by a centrifugal force in mind, we carry out Brownian dynamics simulations in thin systems and study ordering of particles induced by an external force. During solidification, the two-dimensional ordering along walls initially occurs. Then, the ordered particles on the walls act as substrates, and crystallization proceeds into bulk. When the external force is weak, the close-packed face of the crystal structure is parallel to the bottom wall. The direction of the close-packed face depends on the strength of the external force: The close-packed face becomes parallel to the side walls with a strong external force.