Efficiency of surface-driven motion: nano-swimmers beat micro-swimmers

TL;DR

This paper compares the efficiency of nano- and micro-swimmers driven by surface interactions, deriving a scaling relation and showing nano-swimmers can outperform micro-swimmers in certain regimes.

Contribution

It introduces a general scaling relation for propulsion efficiency and demonstrates nano-swimmers can surpass micro-swimmers in efficiency based on size and interaction range.

Findings

Efficiency is significant only when swimmer size is comparable to or smaller than interaction range.

Upper bound for efficiency at maximum power is 50%.

Numerical results for diffusiophoresis align with analytical predictions.

Abstract

Surface interactions provide a class of mechanisms which can be employed for propulsion of micro- and nanometer sized particles. We investigate the related efficiency of externally and self-propelled swimmers. A general scaling relation is derived showing that only swimmers whose size is comparable to, or smaller than, the interaction range can have appreciable efficiency. An upper bound for efficiency at maximum power is 1/2. Numerical calculations for the case of diffusiophoresis are found to be in good agreement with analytical expressions for the efficiency.