Propulsion in Viscous Fluids: Purcell's Three-Link Swimmer

  Professor Annette Hosoi, Brian Chan
Massachusetts Institute of Technology

E.M. Purcell Introduced the concept of a three-link swimmer as the simplest organism that could move in the low Reynolds number limit. At this limit, the fluid can be seen as quasi-static and the position of an organism only depends on the its configuration, not it's instantaneous velocity. Therefore an organism needs to produce a motion that is time-irreversible. A two-link swimmer would not be able to swim in any direction; it would only oscillate in place. The three link swimmer however, should be able to propel itself.

A two-link swimmer like a scallop cannot swim in the low-Reynolds number limit. The forward stroke would push it a certain distance, but the back stroke would return the scallop to the exact place it was before.

Construction

We built a swimmer 5 cm from tip to tip to test which direction it would travel. The links are all approximately the same size. The two fins are actuated by a central cam, driven by a coiled leaf spring. The third video shows the rotation of the cam. The swimmer is mainly built from polycarbonate to withstand the impact of being dropped by careless graduate students.

Videos of the three-link swimmer in silicone oil

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The last movie shows the swimmer in silicone oil with suspended lines of colored oil for flow visualization. The lines are always connected at the same locations on the swimmer at all times, but are stretched out as the swimmer moves forward. There is a backward facing bulge in the line because the swimmer displaces fluid backwards as it swims forward.

References