Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer

TL;DR

This paper develops a linear response theory for self-propelled diffusiophoretic swimmers, analyzing their dynamics, energetics, and efficiency, including effects of solute convection and reaction-induced concentration distortions.

Contribution

It extends analytical models to small swimmers, incorporates solute convection, and introduces a new efficiency measure for randomly moving swimmers.

Findings

Reaction-induced concentration distortion affects swimmer speed.

Solute convection is crucial for accurate energy balance.

Efficiency scales inversely with transport distance.

Abstract

Active diffusiophoresis - swimming through interaction with a self-generated, neutral, solute gradient - is a paradigm for autonomous motion at the micrometer scale. We study this propulsion mechanism within a linear response theory. Firstly, we consider several aspects relating to the dynamics of the swimming particle. We extend established analytical formulae to describe small swimmers, which interact with their environment on a finite lengthscale. Solute convection is also taken into account. Modeling of the chemical reaction reveals a coupling between the angular distribution of reactivity on the swimmer and the concentration field. This effect, which we term "reaction induced concentration distortion", strongly influences the particle speed. Building on these insights, we employ irreversible, linear thermodynamics to formulate an energy balance. This approach highlights the importance of solute convection for a consistent treatment of the energetics. The efficiency of swimming is calculated numerically and approximated analytically. Finally, we define an efficiency of transport for swimmers which are moving in random directions. It is shown that this efficiency scales as the inverse of the macroscopic distance over which transport is to occur.