Polarization-Density Patterns of Active Particles in Motility Gradients

TL;DR

This paper derives analytical expressions for the density and polarization patterns of active particles near activity gradients, providing insights into their emergent behaviors and potential applications in detecting microscopic activity.

Contribution

It introduces a precise analytical framework for understanding density and polarization profiles of active particles in activity gradients, validated against experimental data.

Findings

Analytical expressions match experimental measurements of microswimmers.

Density and polarization co-localize near activity steps.

Framework applicable to complex active matter phenomena.

Abstract

The co-localization of density modulations and particle polarization is a characteristic emergent feature of motile active matter in activity gradients. It can therefore play the role of a smoking gun for the mesoscale detection of intrinsic microscopic activity. We employ the active-Brownian-particle (ABP) model to derive precise analytical expressions for the density and polarization profiles of a single Janus-type swimmer in the vicinity of an abrupt activity step, including situations with an orientation-dependent propulsion speed. Our results agree well with measurement data for a hot microswimmer presented in the companion paper [1] and can serve as a template for more complex applications, e.g., to motility-induced phase separation or studies of physical boundaries. The essential physics behind our formal results is robustly captured and elucidated by a schematic two-species ``run-and-tumble'' model.