Taylor$\unicode{x2013}$Aris dispersion of active particles in oscillatory channel flow

TL;DR

This paper investigates how active particles disperse in oscillatory flows between parallel plates, revealing frequency-dependent diffusivity and the effects of flow unsteadiness on particle accumulation and drift.

Contribution

It extends Taylor–Aris dispersion theory to active particles in oscillatory flows, incorporating phase-dependent effects and analyzing the impact of flow unsteadiness on particle dispersion.

Findings

Active particles can have higher or lower diffusivity than passive solutes depending on oscillation frequency.

Flow unsteadiness reduces the prominence of accumulation mechanisms like gyrotaxis and elongation.

Gyrotactic swimmers respond more effectively to unsteady shear, altering their drift and dispersivity.

Abstract

Mass dispersion in oscillatory flows is intimately linked to various environmental and biological processes, offering a distinct contrast to dispersion in steady flows due to the periodic expansion and contraction of particle patches. In this study, we investigate the Taylor$\unicode{x2013}$Aris dispersion of active particles in laminar oscillatory flows between parallel plates. Two complementary approaches are employed: a two-time-variable expansion of the Smoluchowski equation is used to facilitate Aris' method of moments for the preasymptotic dispersion, while the generalised Taylor dispersion theory is extended to capture phase-dependent periodic drift and dispersivity in the long-time asymptotic limit. Applying both frameworks, we find that spherical non-gyrotactic swimmers can exhibit greater or lesser diffusivity than passive solutes in purely oscillatory flows, depending on the oscillation frequency. This behaviour arise primarily from the disruption of cross-streamline migration governed by Jeffery orbits. When a steady component is superimposed, oscillation induces a non-monotonic dual effect on diffusivity. We further examine two well-studied shear-related accumulation mechanisms, arising from gyrotaxis and elongation. Although these accumulation effects are less pronounced than in steady flows due to flow unsteadiness, gyrotactic swimmers respond more effectively to the unsteady shear profile, significantly altering their drift and dispersivity. This work offers new insights into the dispersion of active particles in oscillatory flows and also provides a foundation for studying periodic active dispersion beyond the oscillatory flow, such as periodic variations in shape and swimming speed.