Transport and dispersion of active particles in periodic porous media

Roberto Alonso-Matilla, Brato Chakrabarti, and David Saintillan
Phys. Rev. Fluids 4, 043101 – Published 1 April 2019
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Abstract

The transport of self-propelled particles such as bacteria and phoretic swimmers through crowded heterogeneous environments is relevant to many natural and engineering processes, from biofilm formation and contamination processes to transport in soils and biomedical devices. While there has been experimental progress, a theoretical understanding of mean transport properties in these systems has been lacking. In this work, we apply generalized Taylor dispersion theory to analyze the long-time statistics of an active self-propelled Brownian particle transported under an applied flow through the interstices of a periodic lattice that serves as an idealization of a porous medium. Our theoretical model, which we validate against Brownian dynamics simulations, is applied to unravel the roles of motility, fluid flow, and lattice geometry on asymptotic mean velocity and dispersivity. In weak flows, transport is dominated by active dispersion, which results from self-propulsion in the presence of noise and is hindered by the obstacles that act as entropic barriers. In strong flows, shear-induced Taylor dispersion becomes the dominant mechanism for spreading, with pillars now acting as regions of shear production that enhance dispersion. The interplay of these two effects leads to complex and unexpected trends, such as a nonmonotonic dependence of axial dispersivity on flow strength and a reduction in dispersion due to swimming activity in strong flows. Brownian dynamics are used to cast light on the preasymptotic regime, where tailed distributions are observed in agreement with recent experiments on motile microorganisms. Our results also highlight the subtle effects of pillar shape, which can be used to control the magnitude of dispersion and to drive a net particle migration in quiescent systems.

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  • Received 31 August 2018

DOI:https://doi.org/10.1103/PhysRevFluids.4.043101

©2019 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary PhysicsPhysics of Living SystemsFluid DynamicsStatistical Physics & ThermodynamicsPolymers & Soft Matter

Authors & Affiliations

Roberto Alonso-Matilla*, Brato Chakrabarti, and David Saintillan

  • Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA

  • *Present address: Department of Chemical Engineering, Columbia University, New York, New York 10027, USA.
  • dstn@ucsd.edu

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Issue

Vol. 4, Iss. 4 — April 2019

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