Effect of container shape and walls on solidification of Brownian particles in a narrow system

Abstract

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.

Crystallization of Brownian particles in thin systems constrained by walls

“…We controlled the direction of the external force and succeeded in forming large grains with the fcc structure. The results in our previous simulations [6][7][8][9] qualitatively agreed with the experiment [5], but the external forces were much stronger than those used in other studies [10][11][12]. Thus, in this paper, we set the external force in the direction perpendicular to the bottom walls and study how the process of ordering of particles is affected by the strength of the external force.…”

“…Keeping the experiment [5] in mind, we carried out Brownian dynamics simulations and studied how crystallization of particles with a short range repulsion proceeds under a uniform external force [6][7][8][9]. In our simulations, two-dimensional ordering of particles on walls occurred initially.…”

Crystallization of Brownian Particles in a Pyramidal Pit by a Uniform External Force

“…In our previous studies, [8][9][10][11][12] in which the container was cuboid or rhomboid, the two-dimensional ordering along the walls of the container first occurred. Then, the crystallization in bulk pro- container shape is different from those in the previous studies, but the crystallization process is the same.…”

“…[8][9][10][11][12] We assume that particles move while receiving a uniform external force and resistance, which is proportional to their velocity. If the resistance is strong, the velocity of the ith particle is given…”

Dependence of crystallization of Brownian particles by sedimentation on the force direction

“…The local structure around the ith particle is regarded as the fcc structure if −0.18 < w 4 (i) < −0.01 and 0.175 < Q 4 (i) < 0.2, and as the hcp structure if 0.02 < w 4 (i) < 0.15 and 0.06 < Q 4 (i) < 0.15. The criteria are the same as those used in our previous studies [14][15][16]20) and consistent with those used in previous studies by other groups. [26][27][28][29][30] …”