The self-propelled Brownian spinning top: dynamics of a biaxial swimmer at low Reynolds numbers

TL;DR

This paper develops a comprehensive model for the dynamics of biaxial self-propelled particles at low Reynolds numbers, revealing complex trajectories including helices and superhelices, with analytical and numerical insights into their motion.

Contribution

It generalizes the Langevin equation for self-propelled Brownian particles to biaxial shapes, providing new analytical solutions and classifying diverse trajectories.

Findings

Zero-temperature trajectory is a circular helix for orthotropic particles.

Transient irregular motion occurs before settling into periodic motion.

In the absence of external forces, particles follow superhelical trajectories.

Abstract

Recently, the Brownian dynamics of self-propelled (active) rod-like particles was explored to model the motion of colloidal microswimmers, catalytically-driven nanorods, and bacteria. Here, we generalize this description to biaxial particles with arbitrary shape and derive the corresponding Langevin equation for a self-propelled Brownian spinning top. The biaxial swimmer is exposed to a hydrodynamic Stokes friction force at low Reynolds numbers, to fluctuating random forces and torques as well as to an external and an internal (effective) force and torque. The latter quantities control its self-propulsion. Due to biaxiality and hydrodynamic translational-rotational coupling, the Langevin equation can only be solved numerically. In the special case of an orthotropic particle in the absence of external forces and torques, the noise-free (zero-temperature) trajectory is analytically found to be a circular helix. This trajectory is confirmed numerically to be more complex in the general case involving a transient irregular motion before ending up in a simple periodic motion. By contrast, if the external force vanishes, no transient regime is found and the particle moves on a superhelical trajectory. For orthotropic particles, the noise-averaged trajectory is a generalized concho-spiral. We furthermore study the reduction of the model to two spatial dimensions and classify the noise-free trajectories completely finding circles, straight lines with and without transients, as well as cycloids and arbitrary periodic trajectories.