The twirling tax and the role of geometry in the modeling and optimization of arbitrary-shape chiral squirmers

While axisymmetric squirmers in free space move in a straight line, a non-axisymmetric swimmer shape or slip velocity can lead to helical motion. Given a prolate spheroid, we define an arbitrary slip velocity profile in terms of tangential basis functions and derive analytical expressions for the resulting translational and rotational velocities, allowing us to explore the effect of aspect ratio on these rigid body velocities. Then, for a given arbitrary swimmer shape of spherical topology, we investigate which slip profile minimizes power loss. A partial minimization is performed in which the direction of net motion of the swimmer is prescribed, followed by a global optimization procedure in which the best net motion direction is determined. The optimization results suggest that the competition between linear and rotational optimal motion is linked to symmetries in the swimmer shape.