Self-diffusiophoretic propulsion in wedge confinement: The role of phoretic interactions

TL;DR

This study models the self-diffusiophoretic motion of active particles in wedge-shaped confinements, revealing how geometry influences particle velocity through concentration interactions, with potential applications in microfluidic control.

Contribution

It introduces a systematic analytical framework for calculating phoretic velocities in wedge geometries, focusing on concentration interactions without hydrodynamics.

Findings

Wedge geometry significantly alters particle velocity magnitude and direction.

Derived leading-order expressions for self-induced phoretic velocity in far-field limit.

Concentration disturbances near corners critically influence particle motion.

Abstract

We investigate the self-diffusiophoretic motion of a catalytically active spherical particle confined within a wedge-shaped domain. Using the Fourier-Kontorovich-Lebedev transform, we solve the Laplace equation for the concentration field in the diffusion-dominated regime. The method of images is employed to obtain the first and second reflections of the concentration field, accounting for both monopole and dipole contributions of the particle's surface activity. Based on these results, we derive leading-order expressions for the self-induced phoretic velocity in the far-field limit and examine how it varies with the wedge opening angle and the particle's position within the domain. We focus on the contributions to the phoretic velocities arising from phoretic interactions, without accounting for hydrodynamic effects. Our findings reveal that the wedge geometry significantly affects both the magnitude and direction of particle motion. Our study provides a systematic framework for calculating the contributions to the phoretic velocity arising from concentration disturbances near corners, with implications for microfluidic design and control of autophoretic particles in confined geometries.