Near-field hydrodynamic interactions determine travelling wave directions of collectively beating cilia

Author:

Cheng Ziqi12,Vilfan Andrej34ORCID,Wang Yanting125,Golestanian Ramin36ORCID,Meng Fanlong125ORCID

Affiliation:

1. CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences , Beijing 100190, People’s Republic of China

2. School of Physical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road , Beijing 100049, People’s Republic of China

3. Max Planck Institute for Dynamics and Self-Organization (MPIDS) , 37077 Göttingen, Germany

4. Jožef Stefan Institute , 1000 Ljubljana, Slovenia

5. Wenzhou Institute, University of Chinese Academy of Sciences , Wenzhou, Zhejiang 325000, People’s Republic of China

6. Rudolf Peierls Centre for Theoretical Physics, University of Oxford , Oxford OX1 3PU, UK

Abstract

Cilia can beat collectively in the form of a metachronal wave, and we investigate how near-field hydrodynamic interactions between cilia can influence the collective response of the beating cilia. Based on the theoretical framework developed in the work of Meng et al . (Meng et al . 2021 Proc. Natl Acad. Sci. USA 118 , e2102828118), we find that the first harmonic mode in the driving force acting on each individual cilium can determine the direction of the metachronal wave after considering the finite size of the beating trajectories, which is confirmed by our agent-based numerical simulations. The stable wave patterns, e.g. the travelling direction, can be controlled by the driving forces acting on the cilia, based on which one can change the flow field generated by the cilia. This work can not only help to understand the role of the hydrodynamic interactions in the collective behaviours of cilia, but can also guide future designs of artificial cilia beating in the desired dynamic mode.

Funder

National Natural Science Foundation of China

Wenzhou Institute

Beijing National Laboratory for Condensed Matter

Alexander von Humboldt Foundation

Max Planck Society

Publisher

The Royal Society

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