Load response of shape-changing microswimmers scales with their energy efficiency

TL;DR

This paper demonstrates that the load response of shape-changing microswimmers is proportional to their energy efficiency, revealing a fundamental link between propulsion efficiency and response to external forces.

Contribution

It establishes a universal relation between load response and Lighthill efficiency for microswimmers, supported by analysis of a three-sphere swimmer model.

Findings

Cycle frequency change proportional to efficiency

Force-velocity relation modifies superposition principle

Load response scales with energy efficiency

Abstract

External forces acting on a microswimmer can feed back on its self-propulsion mechanism. We discuss this load response for a generic microswimmer that swims by cyclic shape changes. We show that the change in cycle frequency is proportional to the Lighthill efficiency of self-propulsion. As a specific example, we consider Najafi's three-sphere swimmer. The force-velocity relation of a microswimmer implies a correction for a formal superposition principle for active and passive motion.