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, optimisation 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 optimise the ciliary motion of a ciliate with an arbitrary axisymmetric shape. 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 cilia length is found to improve, on average, the efficiency for such swimmers.
Highlights
Many swimming microorganisms propel themselves by periodically beating the active slender appendages on their cell surfaces
We extended the work of Michelin & Lauga (2010) and studied the optimal ciliary motion for a microswimmer with an arbitrary axisymmetric shape
We studied the constrained and unconstrained optimal ciliary motions of microswimmers with a variety of shapes, including spherical, prolate spheroidal and concave shapes which are narrow around the equator
Summary
Many swimming microorganisms propel themselves by periodically beating the active slender appendages on their cell surfaces These slender appendages are known as cilia or flagella depending on their lengths and distribution density. We study the (hydrodynamic) swimming efficiency of ciliated microswimmers of an arbitrary axisymmetric shape. In a seminal work, Michelin & Lauga (2010) studied the optimal beating stroke of a spherical swimmer using the envelope model. The flow field, power loss, swimming efficiency as well as their sensitivities, thereby, were computed explicitly using spherical harmonics Their optimisation showed that the envelope surface deforms in a wave-like fashion, which significantly breaks the time symmetry at the organism level similar to the metachronal waves observed in biological microswimmers.
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