A device constructed from a flexible magnetic filament connected to a human red blood cell will swim when subject to an oscillating magnetic field (Dreyfus et al., Nature, 437, 862 (2005)). The magnetic filament tail is composed of paramagnetic beads linked to each other by flexible DNA molecules. Such a device offers a physical model with which to study the kinematics of low Reynolds number swimming and the behavior of microorganisms. We have been conducting particle based simulations of the artificial swimmer where the filament tail is treated as a series of rigid paramagnetic spheres joined by short flexible rods. A large non-magnetic sphere is tethered to one end of the filament and represents the red blood cell in the experiments.
Dreyfus et al. induced swimming by using the magnetic torques produced by a planar oscillating field to generate bending waves in the filament tail. With our simulation techniques, we demonstrated that using a rotating field, the device will swim by deforming into a corkscrew shape and spiraling its way through the fluid.
The time composite motion of the swimmer driven by the magnetic field B = (-B0, -B0cosω t, -B0sinω t) for increasing frequencies. At low frequencies (left), the swimmer rotates as a rigid body aligned with the field. The viscous stresses will deform the filament tail at modest frequencies while at high frequencies (right), they reduce the amplitude of the deformation.
From these results, we parameterized the motion as a function of pitch, phase shift and distance from the axis of rotation and used a resistive force/continuous elastica model to relate the swimming speed to the swimmer geometry and the driving forces in the low frequency limit.
Following this study, we investigated the interactions between co-moving artificial swimmers driven by both planar and rotating applied fields in stacked and consecutive configurations.
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The left figure shows the resulting repulsion and precession velocities for spiral swimmers in the stacked configuration. The dashed and dotted lines are predictions based on low order force multipole expansions and decay as h-2 where h is the swimmer separation. The swimming speeds for two planar swimmers in the consecutive configuration are shown on the right. The dashed line indicates the average speed.
The swimming speed shared by both swimmers in the stacked configuration was less than that of a single swimmer. The swimmers also moved apart and, in the case of spiral actuation, tended to precess around each other. This behavior is tied to the hydrodynamic interactions and at large separations coincides with predictions based on a low order force multipole expansion of the force distribution associated with the swimmers. Consecutive swimmers move with different speeds with the rear swimmer moving faster than the front swimmer. At most separations, the average value is equal to the swimming speed of an isolated swimmer.