Self-propulsion velocity of N-sphere micro-robot

TL;DR

This paper derives an analytical formula for the self-propulsion velocity of a linear N-sphere micro-robot, revealing that interactions among triplets of spheres determine its main propulsion characteristics.

Contribution

It introduces a novel asymptotic method to analytically compute the velocity of N-sphere micro-robots with periodically changing link lengths.

Findings

Velocity depends on triplet interactions among spheres

Derived explicit formula for self-propulsion velocity

Applicable to micro-robots with arbitrary number of spheres

Abstract

The aim of this paper is to derive an analytical expression for the self-propulsion velocity of a micro-swimmer that consists of N spheres moving along a fixed line. The spheres are linked to each other by the rods of the prescribed lengths changing periodically. For the derivation we use the asymptotic procedure containing the two-timing method and a distinguished limit. Our final formula shows that in the main approximation the self-propulsion velocity is determined by the interactions between all possible triplets of spheres.