Energetic cost of microswimmer navigation: The role of body shape

We study the energetic efficiency of navigating microswimmers by explicitly taking into account the geometry of their body. We show that, whereas arguments based solely on propulsion efficiency lead one to conclude that needle-like swimmers are most energetically efficient, disk-like swimmers rotated by flow gradients naturally follow time-optimal trajectories. The coupling between body geometry and hydrodynamics thus leads to a generic trade-off between the energetic costs associated with propulsion and navigation, which is accompanied by the selection of a finite optimal aspect ratio. We derive from optimal control theory the steering policy ensuring overall minimum energy dissipation, and characterize how navigation performances vary with the swimmer shape. Our results highlight the important role of the swimmer geometry in realistic navigation scenarios.