Efficient shapes for microswimming: from three-body swimmers to helical flagella

TL;DR

This paper presents a numerical framework combining swimmer equations and a bead-shell model to optimize and analyze microswimmer shapes, revealing key factors influencing efficiency and identifying optimal geometries including biologically inspired designs.

Contribution

It introduces a generalized approach for optimizing microswimmer shapes based on hydrodynamic interactions, applicable to arbitrary geometries, and explores optimal configurations for three-body and helical flagella swimmers.

Findings

Efficiency depends on the single body friction coefficient in long-arm regimes.

Minimal approachable distance influences efficiency in short-arm regimes.

Two distinct optimal shapes for helical flagella, one differing from natural forms.

Abstract

We combine a general formulation of microswimmmer equations of motion with a numerical bead-shell model to calculate the hydrodynamic interactions with the fluid, from which the swimming speed, power and efficiency are extracted. From this framework, a generalized Scallop Theorem emerges. The applicability to arbitrary shapes allows for the optimization of the efficiency with respect to the swimmer geometry. We apply this scheme to `three-body swimmers' of various shapes and find that the efficiency is characterized by the single body friction coefficient in the long-arm regime, while in the short-arm regime the minimal approachable distance becomes the determining factor. Next, we apply this scheme to a biologically inspired swimmer that propels itself using a rotating helical flagellum. Interestingly, we find two distinct optimal shapes, one of which is fundamentally different from the shapes observed in nature (e.g. bacteria).