How efficient is towing a cargo by a micro-swimmer?

TL;DR

This paper derives a simple formula for the efficiency of micro-swimmers towing cargo in viscous fluids, showing efficiency bounds and the potential for hydrodynamic assistance, supported by numerical simulations.

Contribution

It provides a closed-form expression for towing efficiency and demonstrates that hydrodynamic coupling can enhance load dragging, challenging previous assumptions.

Findings

Efficiency is bounded from above despite potential for high efficiency.

Hydrodynamic coupling can assist in load towing, contrary to prior beliefs.

Numerical simulations confirm theoretical predictions for specific swimmer shapes.

Abstract

We study the properties of arbitrary micro-swimmers towing a passive load through a viscous liquid. The simple close-form expression for the dragging efficiency of a general micro-swimmer dragging a distant load is found, and the leading order approximation for finite mutual separation is derived. We show that, while swimmer can be arbitrarily efficient, dragging efficiency is always bounded from above. It is also demonstrated, that opposite to Purcell's assumption, the hydrodynamic coupling can ''help" the swimmer to drag the load. We support our conclusions by rigorous numerical calculations for the "necklace-shaped" swimmer, towing a spherical cargo positioned at a finite distance.