Elastic three-sphere microswimmer in a viscous fluid

TL;DR

This paper analyzes the motion of an elastic three-sphere microswimmer in a viscous fluid, revealing how its swimming velocity varies with frequency due to elastic relaxation effects, extending previous models.

Contribution

It introduces a generalized elastic three-sphere microswimmer model and derives analytical expressions for its average velocity across different frequency regimes.

Findings

Velocity increases with frequency at low frequencies

Velocity decreases with frequency at high frequencies

Elastic relaxation dynamics influence swimming behavior

Abstract

We discuss the dynamics of a generalized three-sphere microswimmer in which the spheres are connected by two elastic springs. The natural length of each spring is assumed to undergo a prescribed cyclic change. We analytically obtain the average swimming velocity as a function of the frequency of the cyclic change in the natural length. In the low-frequency region, the swimming velocity increases with the frequency and its expression reduces to that of the original three-sphere model by Najafi and Golestanian. In the high-frequency region, conversely, the average velocity decreases with increasing the frequency. Such a behavior originates from the intrinsic spring relaxation dynamics of an elastic swimmer moving in a viscous fluid.