Sedimentation and polar order of active bottom-heavy particles

TL;DR

This paper studies how bottom-heavy self-propelled particles behave under gravity, revealing effects on sedimentation length and orientation, with new analytical expressions and simulation validation for these phenomena.

Contribution

It introduces a multipole expansion approach to analyze sedimentation and orientation of bottom-heavy active particles, providing new analytical expressions and simulation comparisons.

Findings

Sedimentation length increases with activity for bottom-heavy particles.

Particles exhibit maximal orientational order at intermediate swimming speeds.

High activity levels reduce orientational order to zero in both bottom-heavy and non-bottom-heavy particles.

Abstract

Self-propelled particles in an external gravitational field have been shown to display both an increased sedimentation length and polar order even without particle interactions. Here, we investigate self-propelled particles which additionally are bottom-heavy, that is they feel a torque aligning them to swim against the gravitational field. For bottom-heavy particles the gravitational field has the two opposite effects of i) sedimentation and ii) upward alignment of the particles' swimming direction. We perform a multipole expansion of the one-particle distribution with respect to orientation and derive expressions for sedimentation length and mean particle orientation which we check against Brownian Dynamics simulations. For large strength of gravity or small particle speeds and aligning torque, we observe sedimentation with increased sedimentation length compared with passive colloids but also active colloids without bottom-heaviness. Increasing, for example, swimming speed the sedimentation profile is inverted and the particles swim towards the top wall of the enclosing box. We find maximal orientational order at intermediate swimming speeds for both cases of particles with bottom-heaviness and those without. Ordering unsurprisingly is increased for the bottom-heavy particles, but this difference disappears at higher levels of activity and for very high activities ordering goes to zero in both cases.