Shapes enhancing the propulsion of multiflagellated helical microswimmers

TL;DR

This study uses shape optimization and Bayesian algorithms to enhance the propulsion efficiency of multi-flagellated helical microswimmers, revealing optimal tail and head configurations for different flagella arrangements.

Contribution

It introduces a shape optimization framework using Bayesian methods for designing efficient microswimmers with multiple flagella, highlighting the impact of shape and flagella placement on propulsion.

Findings

Optimal tail shapes are helices with large wavelengths.

Elongated heads improve speed with one or two flagella.

Round heads are optimal with more flagella.

Abstract

In this paper we are interested in optimizing the shape of multi-flagellated helical microswimmers. Mimicking the propagation of helical waves along the flagella, they self-propel by rotating their tails. The swimmer's dynamics is computed using the Boundary Element Method, implemented in the open source Matlab library $Gypsilab$. We exploit a Bayesian optimization algorithm to maximize the swimmer's speeds through their shape optimization. Our results show that the optimal tail shapes are helices with large wavelength, such that the shape periodicity is disregarded. Moreover, the best propulsion speed is achieved for elongated heads when the swimmer has one or two flagella. Surprisingly, a round head is obtained when more flagella are considered. Our results indicate that the position and number of flagella modify the propulsion pattern and play a significant role in the optimal design of the head. It appears that Bayesian optimization is a promising method for performance improvement in microswimming.