Three-sphere low-Reynolds-number swimmer with a passive elastic arm

  • Alessandro Montino
  • Antonio DeSimoneEmail author
Open Access
Regular Article


One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer’s geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers.

Graphical abstract


Living systems: Biomimetic Systems 


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.GSSI - Gran Sasso Science InstituteL’AquilaItaly
  2. 2.SISSA - International School for Advanced StudiesTriesteItaly

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