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Navigation control of flagellated magnetic microswimmer by parametric excitation

The paper presents a novel mechanism for controlling swimming behavior of a flagellated microswimmer by parametric excitation. The microswimmer design consists of a spherical rigid magnetic head attached to a slender rigid link (tail) via torsional spring joint. The swimmer is actuated by an oscillating magnetic field that produces undulatory coplanar motion. The parametric excitation consists of harmonic modulation of elastic stiffness of the spring joint. The equation of motion is described by the balance of forces and torques at low Reynolds number. The analytical solutions were obtained by harmonic balance method under small amplitude approximation. It is found that the parametric excitation modifies the symmetry and amplitude of beating patterns of the tail. The influence of these on microswimmer performance (time-averaged displacement and propulsion velocity along longitudinal and transverse directions) is analyzed. A comparison with the performance of a microswimmer without parametric excitation shows that the propulsion velocity can be enhanced or suppressed by tuning the phase difference between parametric excitation and magnetic actuation. Also, not only the longitudinal propulsion but a simultaneous transverse propulsion is generated by the parametric excitation. This facilitates the navigational control of the microswimmer by parametric modulation.