A local approximation model for macroscale transport of biased active Brownian particles in a flowing suspension

TL;DR

This paper develops a local approximation model for the transport of biased active Brownian particles in flowing suspensions, capturing complex drift and dispersion phenomena with improved applicability to various flow fields.

Contribution

It introduces a novel local transport equation that approximates drifts and dispersions based on the flow field, extending applicability beyond previous dispersion-based methods.

Findings

Model accurately predicts particle transport in gyrotactic suspensions.

Performance is best when particle taxis is weak.

Uncovers new drift and dispersion effects from particle orientation dynamics.

Abstract

A dilute suspension of motile microorganisms subjected to a strong ambient flow, such as algae in the ocean, can be modelled as a population of non-interacting, orientable active Brownian particles (ABPs). Using the Smoluchowski equation (i.e. Fokker-Planck equation in space and orientation), one can describe the non-trivial transport phenomena of ABPs such as taxis and shear-induced migration. This work transforms the Smoluchowski equation into a transport equation, in which the drifts and dispersions can be further approximated as a function of the local flow field. The new model can be applied to any global flow field due to its local nature, unlike previous methods such as those utilising the generalised Taylor dispersion theory. The transformation shows that the overall drift includes both the biased motility of individual particles in the presence of taxis and the shear-induced migration in the absence of taxis. In addition, it uncovers other new drifts and dispersions caused by the interactions between the orientational dynamics and the passive advection-diffusion of ABPs. Finally, the performance of this model is assessed using examples of gyrotactic suspensions, where the proposed model is demonstrated to be most accurate when the biased motility of particles (i.e. taxis) is weak.