Base flow decomposition for complex moving objects in linear hydrodynamics: Application to helix-shaped flagellated microswimmers.

The motion of microswimmers in complex flows is ruled by the interplay between swimmer propulsion and the dynamics induced by the fluid velocity field. Here we study the motion of a chiral microswimmer whose propulsion is provided by the spinning of a helical tail with respect to its body in a simple shear flow. Thanks to an efficient computational strategy that allowed us to simulate thousands of different trajectories, we show that the tail shape dramatically affects the swimmer's motion. In the shear dominated regime, the swimmers carrying an elliptical helical tail show several different Jeffery-like (tumbling) trajectories depending on their initial configuration. As the propulsion torque increases, a progressive regularization of the motion is observed until, in the propulsion dominated regime, the swimmers converge to the same final trajectory independently on the initial configuration. Overall, our results show that elliptical helix swimmer presents a much richer variety of trajectories with respect to the usually studied circular helix tails.