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

Published online by Cambridge University Press:  31 January 2022

Lloyd Fung Open the ORCID record for Lloyd Fung [Opens in a new window] ,
Rachel N. Bearon  and
Yongyun Hwang Open the ORCID record for Yongyun Hwang [Opens in a new window]
Lloyd Fung*
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
Rachel N. Bearon
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
Yongyun Hwang
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: lloyd.fung12@imperial.ac.uk
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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.

JFM classification

Complex Fluids: Suspensions Mass Transport: Dispersion Biological Fluid Dynamics: Collective behaviour

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 935 , 25 March 2022 , A24
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© The Author(s), 2022. Published by Cambridge University Press

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References

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