Optimal Ciliary Locomotion of Axisymmetric Microswimmers

TL;DR

This study optimizes the ciliary motion of axisymmetric microswimmers, revealing shape-dependent efficiency improvements and novel motion patterns, with potential implications for designing efficient microscale swimmers.

Contribution

It introduces a numerical optimization framework for ciliary motion in non-spherical microswimmers, highlighting shape effects on efficiency and motion strategies.

Findings

Prolate microswimmers achieve up to two-fold efficiency increase.

Concave microswimmers exhibit qualitatively different optimal ciliary motion.

Constraining ciliary length generally improves efficiency.

Abstract

Many biological microswimmers locomote by periodically beating the densely-packed cilia on their cell surface in a wave-like fashion. While the swimming mechanisms of ciliated microswimmers have been extensively studied both from the analytical and the numerical point of view, the optimization of the ciliary motion of microswimmers has received limited attention, especially for non-spherical shapes. In this paper, using an envelope model for the microswimmer, we numerically optimize the ciliary motion of a ciliate with an arbitrary axisymmetric shape. The forward solutions are found using a fast boundary integral method, and the efficiency sensitivities are derived using an adjoint-based method. Our results show that a prolate microswimmer with a 2:1 aspect ratio shares similar optimal ciliary motion as the spherical microswimmer, yet the swimming efficiency can increase two-fold. More interestingly, the optimal ciliary motion of a concave microswimmer can be qualitatively different from that of the spherical microswimmer, and adding a constraint to the ciliary length is found to improve, on average, the efficiency for such swimmers.