The Efficiency of Self-Phoretic Propulsion Mechanisms with Surface Reaction Heterogeneity

TL;DR

This paper analyzes how surface reaction heterogeneity affects the efficiency of self-phoretic colloidal swimmers, revealing that localized reactivity at poles maximizes efficiency and informing design strategies.

Contribution

It introduces a swimmer efficiency functional and analytically proves that localized surface reactivity maximizes propulsion efficiency.

Findings

Maximum efficiency occurs with reactivity localized at poles

Propulsion speed is highly sensitive to surface reactivity details

Insights can guide the design of more efficient self-phoretic swimmers

Abstract

We consider the efficiency of self-phoretic colloidal particles (swimmers) as a function of the heterogeneity in the surface reaction rate. The set of fluid, species, and electrostatic continuity equations is solved analytically using a linearization and numerically using a finite-element method. To compare spherical swimmers of different size and with heterogeneous catalytic conversion rates, a 'swimmer efficiency' functional $\eta$ is introduced. It is proven, that in order to obtain maximum swimmer efficiency the reactivity has to be localized at the pole(s). Our results also shed light on the sensitivity of the propulsion speed to details of the surface reactivity, a property that is notoriously hard to measure. This insight can be utilized in the design of new self-phoretic swimmers.