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Isotropically active particle closely fitting in a cylindrical channel: spontaneous motion at small Péclet numbers

Published online by Cambridge University Press:  26 January 2024

Rodolfo Brandão Open the ORCID record for Rodolfo Brandão [Opens in a new window]
Rodolfo Brandão*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: r.brandao@princeton.edu
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Abstract

Spontaneous motion due to symmetry breaking has been predicted theoretically for both active droplets and isotropically active particles in an unbounded fluid domain, provided that their intrinsic Péclet number $Pe$ exceeds a critical value. However, due to their inherently small $Pe$, this phenomenon has yet to be observed experimentally for active particles. In this paper, we demonstrate theoretically that spontaneous motion for an active spherical particle closely fitting in a cylindrical channel is possible at arbitrarily small $Pe$. Scaling arguments in the limit where the dimensionless clearance is $\epsilon \ll 1$ reveal that when $Pe=O(\epsilon ^{1/2})$, the confined particle reaches speeds comparable to those achieved in an unbounded fluid at moderate (supercritical) $Pe$ values. We use matched asymptotic expansions in that distinguished limit, where the fluid domain decomposes into several asymptotic regions: a gap region, where the lubrication approximation applies; particle-scale regions, where the concentration is uniform; and far-field regions, where solute transport is one-dimensional. We derive an asymptotic formula for the particle speed, which is a monotonically decreasing function of $\overline {Pe}=Pe/\epsilon ^{1/2}$ and approaches a finite limit as $\overline {Pe}\searrow 0$. Our results could pave the way for experimental realisations of symmetry-breaking spontaneous motion in active particles.

JFM classification

Complex Fluids: Active matter Mass Transport: Coupled diffusion and flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 980 , 10 February 2024 , A2
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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