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Artificial chemotaxis of phoretic swimmers: instantaneous and long-time behaviour

Published online by Cambridge University Press:  12 October 2018

Maria Tătulea-Codrean Open the ORCID record for Maria Tătulea-Codrean [Opens in a new window]  and
Eric Lauga
Maria Tătulea-Codrean
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Eric Lauga*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: e.lauga@damtp.cam.ac.uk
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Abstract

Phoretic swimmers are a class of artificial active particles that has received significant attention in recent years. By making use of self-generated gradients (e.g. in temperature, electric potential or some chemical product) phoretic swimmers are capable of self-propulsion without the complications of mobile body parts or a controlled external field. Focusing on diffusiophoresis, we quantify in this paper the mechanisms through which phoretic particles may achieve chemotaxis, both at the individual and the non-interacting population level. We first derive a fully analytical law for the instantaneous propulsion and orientation of a phoretic swimmer with general axisymmetric surface properties, in the limit of zero Péclet number and small Damköhler number. We then apply our results to the case of a Janus sphere, one of the most common designs of phoretic swimmers used in experimental studies. We next put forward a novel application of generalised Taylor dispersion theory in order to characterise the long-time behaviour of a population of non-interacting phoretic swimmers. We compare our theoretical results with numerical simulations for the mean drift and anisotropic diffusion of phoretic swimmers in chemical gradients. Our results will help inform the design of phoretic swimmers in future experimental applications.

JFM classification

Complex Fluids: Colloids Biological Fluid Dynamics: Propulsion

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JFM Papers
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Journal of Fluid Mechanics , Volume 856 , 10 December 2018 , pp. 921 - 957
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© 2018 Cambridge University Press 

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