Autophoretic motion in three dimensions

TL;DR

This paper presents a theoretical framework for controlling three-dimensional autophoretic motion of Janus particles, enabling arbitrary trajectories including helical paths by tuning surface properties.

Contribution

It introduces a method to induce and control complex 3D motion in Janus particles through surface coverage design, extending beyond typical straight-line movement.

Findings

Trajectories can be helical with controllable pitch and radius.

Surface coverage determines the balance of translational and rotational motion.

A simple patch model guides the design of arbitrary phoretic spheres.

Abstract

Janus particles with the ability to move phoretically in self-generated chemical concentration gradients are model systems for active matter. Their motion typically consists of straight paths with rotational diffusion being the dominant reorientation mechanism. In this paper, we show theoretically that by a suitable surface coverage of both activity and mobility, translational and rotational motion can be induced arbitrarily in three dimensions. The resulting trajectories are in general helical, and their pitch and radius can be controlled by adjusting the angle between the translational and angular velocity. Building on the classical mathematical framework for axisymmetric self-phoretic motion under fixed-flux chemical boundary condition, we first show how to calculate the most general three-dimensional motion for an arbitrary surface coverage of a spherical particle. After illustrating our results on surface distributions, we next introduce a simple intuitive patch model to serve as a guide for designing arbitrary phoretic spheres.