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

TL;DR

This paper develops analytical models for the instantaneous and long-term chemotactic behavior of artificial phoretic swimmers, specifically Janus particles, using theory and simulations to inform future experimental design.

Contribution

It derives a comprehensive analytical law for individual swimmer propulsion and orientation, and applies generalized Taylor dispersion theory to describe population-level long-time behavior.

Findings

Analytical law for instantaneous propulsion and orientation of phoretic swimmers.

Application of Taylor dispersion theory to long-time population dynamics.

Validation of theoretical results with numerical simulations.

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 P\'{e}clet number and small Damk\"{o}hler 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.