Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions

Interest in the design of bioinspired robotic microswimmers is growing rapidly, motivated by the spectacular capabilities of their unicellular biological templates. Predicting the swimming speed and efficiency of such devices in a reliable way is essential for their rational design, and to optimize their performance. The hydrodynamic simulations needed for this purpose are demanding and simplified models that neglect nonlocal hydrodynamic interactions (e.g., resistive force theory for slender, filament-like objects that are the typical propulsive apparatus for unicellular swimmers) are commonly used. We show through a detailed case study of a model robotic system consisting of a spherical head powered by a rotating helical flagellum that (a) the errors one makes in the prediction of swimming speed and efficiency by neglecting hydrodynamic interactions are never quite acceptable and (b) there are simple ways to correct the predictions of the simplified theories to make them more accurate. We also formulate optimal design problems for the length of the helical flagellum giving maximal energetic efficiency, maximal distance traveled per motor turn, or maximal distance traveled per unit of work expended, and exhibit optimal solutions.