### Abstract

In this paper we study the self-propulsion of a dumbbell micro-robot submerged in a viscous fluid. The micro-robot consists of two rigid spherical beads connected by a rod or a spring; the rod/spring length changes periodically. The constant density of each sphere differs from the density of the fluid, while the whole micro-robot has neutral buoyancy. An effective oscillating gravity field is created via rigid-body oscillations of the fluid. Our calculations show that the micro-robot undertakes both translational and rotational motion. Using an asymptotic procedure containing a two-time method and a distinguished limit, we obtain analytic expressions for the averaged self-propulsion velocity and averaged angular velocity. The important special case of zero angular velocity represents rectilinear self-propulsion with constant velocity. In particular, we have shown that: (a) no unidirectional oscillations of a fluid result in self-propulsion; and (b) for the oscillations of a fluid in two directions rectilinear motion of a micro-robot can be achieved.

Original language | English |
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Pages (from-to) | R81-R811 |

Journal | Journal of Fluid Mechanics |

Volume | 717 |

DOIs | |

Publication status | Published - Feb 1 2013 |

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### Keywords

- micro-/nano-fluid dynamics
- propulsion
- stokesian dynamics

### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering