Efficacy of self-phoretic colloids and microswimmers

TL;DR

This paper introduces a unified mathematical framework for self-phoretic colloids and microswimmers, defining a new efficacy measure to compare their performance across various geometries and surface activity patterns.

Contribution

It provides a simple integral kernel for particle velocity from surface flux, defines efficacy as a new performance metric, and maps efficacy across different geometries and surface bipartitions.

Findings

Efficacy varies with particle shape and surface activity pattern.

Intermediate aspect ratios optimize efficacy.

Comparison with experimental data validates the model.

Abstract

Within a unified formulation, encompassing self-electrophoresis, self-diffusiophoresis, and self-thermophoresis, we provide a simple integral kernel transforming the relevant surface flux to particle velocity for any spheroid with axisymmetric surface activity and uniform phoretic mobility. We define efficacy, a dimensionless efficiency-like quantity expressing the speed resulting from unit absolute flux density on the surface, which allows a meaningful comparison of the performance of different motor designs. For bipartite designs with piecewise uniform flux over complementary surface regions, the efficacy is mapped out over the entire range of geometry (discotic through sphere to rod-like) and of bipartitioning, and intermediate aspect ratios that maximize efficacy are identified. Comparison is made to experimental data from the literature.