Dynamics of sedimenting active Brownian particles

TL;DR

This paper provides an analytical and simulation-based study of the three-dimensional sedimenting active Brownian particles under gravity, revealing their dynamics, steady states, and collective behavior with experimental validation.

Contribution

It offers the first analytical solution to the Fokker-Planck equation for 3D active Brownian particles under gravity, linking theory, simulation, and experiment.

Findings

Analytical solution describes particle dynamics in 3D

Simulations confirm the impact of activity on collective motion

Results align well with experimental data

Abstract

We investigate the stochastic dynamics of one sedimenting active Brownian particle in three dimensions under the influence of gravity and passive fluctuations in the translational and rotational motion. We present an analytical solution of the Fokker--Planck equation for the stochastic process which allows us to describe the dynamics of the active Brownian particle in three dimensions. We address the time evolution of the monopole, the polarization, and the steady-state solution. We also perform Brownian dynamics simulations and study the effect of the activity of the particles on their collective motion. These results qualitatively agree with our model. Finally, we compare our results with experiments [J. Palacci \emph{et al.}, Phys. Rev. Lett. \textbf{105}, 088304 (2010)] and find very good agreement.