Parking 3-sphere swimmer II. The long arm asymptotic regime

TL;DR

This paper analyzes the behavior of a three-ball low-Reynolds-number swimmer with long arms, deriving its governing dynamics and exploring energy-efficient self-propulsion in the asymptotic regime.

Contribution

It provides the asymptotic governing equations for a three-ball swimmer with long arms and investigates its energy-efficient propulsion mechanisms.

Findings

Derived the Stokes flow governing dynamics for long-arm regime.

Identified energy-minimizing self-propulsion strategies.

Validated theoretical results through experiments.

Abstract

The paper carries on our previous investigations on the complementary version of Purcell's rotator: a low-Reynolds-number swimmer composed of three balls of equal radii. In the asymptotic regime of very long arms, the Stokes induced governing dynamics is derived and then experimented in the context of energy minimizing self-propulsion characterized in the first part of the paper.