Can phoretic particles swim in two dimensions?

TL;DR

This paper investigates the swimming behavior of artificial phoretic particles in two dimensions, revealing that their velocity decays logarithmically over time unless advection effects are considered, which can stabilize their motion.

Contribution

It extends the classical steady-state diffusiophoresis model to two dimensions, addressing the lack of steady solutions and demonstrating how advection can regularize particle motion.

Findings

Swimming velocity decays logarithmically in time for fixed fluxes

Advection can prevent velocity decay by moving particles to reactant-rich regions

Finite Peclet numbers stabilize the particle motion in two dimensions

Abstract

Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution of the diffusion equation, from which chemical gradients, phoretic flows and ultimately the swimming velocity, may be derived. Motivated by disk-shaped particles in thin films and under confinement, we examine the extension to two dimensions. Because the two-dimensional diffusion equation lacks a steady state with the correct boundary conditions, Laplace transforms must be used to study the long-time behavior of the problem and determine the swimming velocity. For fixed chemical fluxes on the particle surface, we find that the swimming velocity ultimately always decays logarithmically in time. In the case of finite Peclet numbers, we solve the full advection-diffusion equation numerically and show that this decay can be avoided by the particle moving to regions of unconsumed reactant. Finite advection thus regularizes the two-dimensional phoretic problem.