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Isotropically active colloids under uniform force fields: from forced to spontaneous motion

Published online by Cambridge University Press:  14 April 2021

Saikat Saha Open the ORCID record for Saikat Saha [Opens in a new window] ,
Ehud Yariv Open the ORCID record for Ehud Yariv [Opens in a new window]  and
Ory Schnitzer Open the ORCID record for Ory Schnitzer [Opens in a new window]
Saikat Saha
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa32000, Israel
Ehud Yariv*
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa32000, Israel
Ory Schnitzer
Affiliation:
Department of Mathematics, Imperial College London, LondonSW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

We consider the inertia-free motion of an isotropic chemically active particle which is exposed to a weak uniform force field. This problem is characterised by two velocity scales, a ‘chemical’ scale associated with diffusio-osmosis and a ‘mechanical’ scale associated with the external force. The motion animated by the force deforms the originally spherically symmetric solute cloud surrounding the particle, thus resulting in a concomitant diffusio-osmotic flow which, in turn, modifies the particle speed. A weak-force linearisation furnishes a closed-form expression for the particle velocity as a function of the intrinsic Péclet number $\alpha$ associated with the chemical velocity scale. We find that the predicted velocity may become singular at $\alpha =4$, and that this happens under the same conditions on the surface parameters for which the associated unforced problem is known to exhibit, for $\alpha >4$, a symmetry-breaking instability giving rise to steady spontaneous motion (Michelin, Lauga & Bartolo, Phys. Fluids, vol. 25, 2013, 061701). Here, a local analysis in a distinguished region near $\alpha =4$, wherein the velocity scaling is amplified, yields a closed-form description of the imperfect bifurcation which bridges between a perturbed stationary state and a perturbed spontaneous motion. Remarkably, while the direction of spontaneous motion in the absence of an external force is random, in the perturbed case that motion is rendered steady solely in the directions parallel or antiparallel to the external force.

JFM classification

Complex Fluids: Active matter Mass Transport: Coupled diffusion and flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A47
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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