Analytic results for the three-sphere swimmer at low Reynolds number

TL;DR

This paper provides analytical insights into the behavior of a three-sphere low Reynolds number swimmer, including velocity, power, and efficiency, considering both deterministic and noisy stroke cycles.

Contribution

It offers the first comprehensive analytical analysis of the three-sphere swimmer's dynamics, including effects of noise and coherence in stroke cycles.

Findings

Derived explicit formulas for swimming velocity and power consumption.

Analyzed the impact of noise and coherence on swimmer performance.

Identified optimal stroke patterns for efficiency.

Abstract

The simple model of a low Reynolds number swimmer made from three spheres that are connected by two arms is considered in its general form and analyzed. The swimming velocity, force--velocity response, power consumption, and efficiency of the swimmer are calculated both for general deformations and also for specific model prescriptions. The role of noise and coherence in the stroke cycle is also discussed.