Transient dispersion process of active particles

TL;DR

This paper develops an analytical framework to study the transient dispersion of active particles in confined flows, revealing how swimming, shape, and flow conditions influence dispersion dynamics before reaching steady state.

Contribution

It introduces a biorthogonal expansion method for analyzing transient active particle dispersion, extending previous long-time studies to include temporal evolution and boundary effects.

Findings

Swimming accelerates local distribution equilibrium.

Wall accumulation affects distribution and drift but not the time to reach Taylor regime.

Particle shape influences dispersivity through shear-induced alignment.

Abstract

Active particles often swim in confined environments. The transport mechanisms, especially the global one as reflected by the Taylor dispersion model, are of great practical interest to various applications. For active dispersion process in confined flows, previous analytical studies focused on the long-time asymptotic values of dispersion characteristics. Only several numerical studies preliminarily investigated the temporal evolution. Extending recent studies of Jiang & Chen (J. Fluid Mech., vol. 877, 2019, pp. 1--34; J. Fluid Mech., vol. 899, 2020, A18), this work makes the first analytical attempt to investigate the transient process. The temporal evolution of the local distribution in the confined-section--orientation space, drift, dispersivity and skewness, is explored based on moments of distributions. We introduce the biorthogonal expansion method for solutions because the classic integral transform method for passive transport problems is not applicable due to the self-propulsion effect. Two types of boundary condition, the reflective condition and the Robin condition for wall accumulation, are imposed respectively. A detailed study on spherical and ellipsoidal swimmers dispersing in a plane Poiseuille flow demonstrates the influences of the swimming, shear flow, wall accumulation and particle shape on the transient dispersion process after a point-source release. The swimming-induced diffusion makes the local distribution reach its equilibrium state faster than that of passive particles. Though the wall accumulation significantly affects the evolution of the local distribution and the drift, the time scale to reach the Taylor regime is not obviously changed. The shear-induced alignment of ellipsoidal particles can enlarge the dispersivity but has less influence on the drift and the skewness.