Relationship between self-propelled velocity and Brownian motion for spherical and ellipsoid particles

In this study, the Brownian motion of spherical and ellipsoidal self-propelled particles is simulated without considering the effect of inertia and using the Langevin equation and the diffusion coefficient of ellipsoidal particles derived by Perrin. The Péclet number ( Pe ) is introduced to measure the relative strengths of self-propelled and Brownian motions. We found that the motion state of spherical and ellipsoid self-propelled particles changed significantly under the influence of Brownian motion. For spherical particles, there were three primary states of motion: 1) when Pe ＜ 30, the particles were still significantly affected by Brownian motion; 2) when Pe > 30, the self-propelled velocities of the particles were increasing; and 3) when Pe > 100, the particles were completely controlled by the self-propelled velocities and the Brownian motion was suppressed. In the simulation of the ellipsoidal self-propelled particles, we found that the larger the aspect ratio of the particle, the more susceptible they were to the influence of Brownian motion. In addition, the value interval of Pe depended on the aspect ratio. Finally, we found that the directional motion ability of the ellipsoidal self-propelled particles was much weaker than that of the spherical self-propelled particles.