Simulations of Magnetic Micro-swimmers

Simulations of Magnetic Micro-swimmers

The reversibility of low Reynolds number flow sets a constraint on the swimming strategies an object can employ to produce a net translation. E. Coli bacteria swim by rotating a helical flagellar bundle while spermatazoa propel themselves by generating a travelling wave which propagates down the length of their flagellum tail. In a recent study, Dreyfus et al. (Nature, 437, 862-865, 2005) produced an artificial micro-swimmer whose mechanism of propulsion is the magnetically driven undulation of a flagellum-like tail composed of chemically linked paramagnetic beads.

To examine the behavior of this swimmer, we developed a model of the filament tail as a series of spheres connected by inextensible, but flexible, links. This model accounts for the discrete nature of the magnetic tail and allows for the inclusion of higher order hydrodynamic interactions into the description.

With this model, we have explored the use of alternative applied fields to compare different swimming strategies. For example, using rotating fields, we produced a rotary propulsion scheme similar to that of E. Coli.

In addition, we studied the interactions of two swimmers in various configurations. We would like to understand how the swimming speed changes due to the presence of other swimmers.

In this movie, one hundred swimmers, oriented in the same direction, are actuated using the method described by Dreyfus et al. with sperm number Sp=3 and magnetoelastic number Mn=3. The volume fraction is ~3%. The beating of the swimmers' tails are synchonized with the oscillation of the applied field. Zippering of the magnetic tails is also evident in the simulation. (Eric Keaveny)