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Shape matters: a Brownian microswimmer in a channel

Published online by Cambridge University Press:  06 April 2021

Hongfei Chen Open the ORCID record for Hongfei Chen [Opens in a new window]  and
Jean-Luc Thiffeault Open the ORCID record for Jean-Luc Thiffeault [Opens in a new window]
Hongfei Chen*
Affiliation:
Department of Mathematics, University of Wisconsin – Madison, 480 Lincoln Dr., Madison, WI53706, USA
Jean-Luc Thiffeault*
Affiliation:
Department of Mathematics, University of Wisconsin – Madison, 480 Lincoln Dr., Madison, WI53706, USA
*
†Email addresses for correspondence: hchen475@wisc.edu, jeanluc@math.wisc.edu
†Email addresses for correspondence: hchen475@wisc.edu, jeanluc@math.wisc.edu
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Abstract

We consider the active Brownian particle model for a two-dimensional microswimmer with fixed speed, whose direction of swimming changes according to a Brownian process. The probability density for the swimmer obeys a Fokker–Planck equation defined on the configuration space, whose structure depends on the swimmer's shape, centre of rotation and domain of swimming. We enforce zero probability flux at the boundaries of configuration space. At first neglecting hydrodynamic interactions, we derive a reduced equation for a swimmer in an infinite channel, in the limit of small rotational diffusivity, and find that the invariant density depends strongly on the swimmer's precise shape and centre of rotation. We also give a formula for the mean reversal time: the expected time taken for a swimmer to completely reverse direction in the channel. Using homogenization theory, we find an expression for the effective longitudinal diffusivity of a swimmer in the channel, and show that it is bounded by the mean reversal time. Finally, we include hydrodynamic interactions with walls, and examine the role of shape.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A15
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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