Macrotransport of active particles in periodic channels and fields: rectification and dispersion

TL;DR

This paper develops a theoretical framework using generalized Taylor dispersion theory to analyze the long-time transport and dispersion of active particles in periodic channels, revealing how activity induces rectified motion and effective diffusion.

Contribution

It introduces a continuum macrotransport model for active Brownian particles in structured environments, connecting activity-driven density gradients to rectified transport.

Findings

Active particles exhibit rectified motion due to activity and channel asymmetry.

The effective long-time transport is described by an advection-diffusion equation.

The theory aligns well with Brownian dynamics simulations.

Abstract

Transport and dispersion of active particles in structured environments such as corrugated channels and porous media are important for the understanding of both natural and engineered active systems. Owing to their continuous self-propulsion, active particles exhibit rectified transport under spatially asymmetric confinement. While progress has been made in experiments and particle-based simulations, a theoretical understanding of the effective long-time transport dynamics in spatially periodic geometries remains less developed. In this paper, we apply generalized Taylor dispersion theory (GTDT) to analyze the long-time effective transport dynamics of active Brownian particles (ABPs) in periodic channels and fields. We show that the long-time transport behavior is governed by an effective advection-diffusion equation. The derived macrotransport equations allow us to characterize the average drift and effective dispersion coefficient. For the case of ABPs subject to a no-flux boundary condition at the channel wall, we show that regardless of activity, the average drift is given by the net diffusive flux along the channel. For ABPs, their activity is the driving mechanism that sustains a density gradient, which ultimately leads to rectified motion along the channel. Our continuum theory is validated against direct Brownian dynamics simulations of the Langevin equations governing the motion of each ABP.