Energetic cost of microswimmer navigation: the role of body shape

TL;DR

This paper investigates how the shape of microswimmers affects their energy efficiency and navigation, revealing a trade-off between optimal trajectories and dissipation, and identifying an optimal aspect ratio for minimal energy use.

Contribution

It introduces a model linking microswimmer shape to energetic costs and navigation efficiency, deriving optimal control policies for energy minimization.

Findings

Non-steering microswimmers follow time-optimal trajectories as shape varies from prolate to oblate.

Larger dissipation is required for swimming as the body becomes more oblate.

An optimal aspect ratio balances propulsion efficiency and navigation performance.

Abstract

We study the energetic efficiency of navigating microswimmers by explicitly taking into account the geometry of their body. We show that, as their shape transitions from prolate to oblate, non-steering microswimmers rotated by flow gradients naturally follow increasingly time-optimal trajectories. At the same time, they also require larger dissipation to swim. 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 problems.