Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-17T14:35:20.097Z Has data issue: false hasContentIssue false
  • English
  • Français

The mechanics of cilium beating: quantifying the relationship between metachronal wavelength and fluid flow rate

Published online by Cambridge University Press:  23 March 2020

Jon Hall Open the ORCID record for Jon Hall [Opens in a new window]  and
Nigel Clarke
Jon Hall*
Affiliation:
Department of Physics and Astronomy, University of Sheffield, Western Bank, SheffieldS10 2TN, UK
Nigel Clarke
Affiliation:
Department of Physics and Astronomy, University of Sheffield, Western Bank, SheffieldS10 2TN, UK
*
†Email address for correspondence: jon.hall@sheffield.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the relationship between the metachronal wavelength of an array of beating cilia and the resulting fluid flow rate through numerical simulations. Our model is based on a hybrid immersed boundary lattice Boltzmann algorithm. Our results suggest that varying the metachronal wavelength of the cilium array affects the fluid flow rate by increasing or decreasing the spread of cilia during their active strokes. We quantify this behaviour by constructing an analytical model of the system and deriving an equation for free area within the cilium array that depends on the metachronal wavelength. We show that there is a strong correlation between free area and fluid flow rate that holds for different values of cilium spacing.

JFM classification

Biological Fluid Dynamics: Pulmonary fluid mechanics Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 891 , 25 May 2020 , A20
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barton, C. & Raynor, S. 1967 Analytical investigation of cilia induced fluid flow. Bull. Math. Biophys. 29 (3), 419–428.CrossRefGoogle Scholar
Chateau, S., Favier, J., D’Ortona, U. & Poncet, S. 2017 Transport efficiency of metachronal waves in 3D cilium arrays immersed in a two-phase flow. J. Fluid Mech. 824, 931–961.CrossRefGoogle Scholar
Ding, Y., Nawroth, J. C., McFall-Ngai, M. J. & Kanso, E. 2014 Mixing and transport by ciliary carpets: a numerical study. J. Fluid Mech. 743, 124–140.CrossRefGoogle Scholar
Feriani, L., Juenet, M., Fowler, C. J., Bruot, N., Chioccioli, M., Holland, S. M., Bryant, C. E. & Cicuta, P. 2017 Assessing the collective dynamics of motile cilia in cultures of human airway cells by multiscale DDM. Biophys. J. 113 (1), 109–119.CrossRefGoogle ScholarPubMed
Fulford, G. R. & Blake, J. R. 1986 Mucociliary transport in the lung. J. Theor. Biol. 121 (4), 381–402.CrossRefGoogle ScholarPubMed
Gheber, L. & Priel, Z. 1997 Extraction of cilium beat parameters by the combined application of photoelectric measurements and computer simulation. Biophys. J. 72 (1), 449–462.CrossRefGoogle ScholarPubMed
Kesimer, M., Ehre, C., Burns, K. A., Davis, C. W., Sheehan, J. K. & Pickles, R. J. 2013 Molecular organization of the mucins and glycocalyx underlying mucus transport over mucosal surfaces of the airways. Mucosal Immunol. 6 (2), 379–392.CrossRefGoogle ScholarPubMed
Khaderi, S. N., den Toonder, J. M. J. & Onck, P. R. 2011 Microfluidic propulsion by the metachronal beating of magnetic artificial cilia: a numerical analysis. J. Fluid Mech. 688, 44–65.CrossRefGoogle Scholar
Kruger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G. & Viggen, E. 2017 The Lattice Boltzmann Method Principles and Practice, Graduate Texts in Physics, vol. 1, pp. 653–687. Springer.CrossRefGoogle Scholar
Li, Z., Favier, J., D’Ortona, U. & Poncet, S. 2016 An immersed boundary-lattice Boltzmann method for single- and multi-component fluid flows. J. Comput. Phys. 304, 424–440.CrossRefGoogle Scholar
Pinelli, A., Naqavi, I. Z., Piomelli, U. & Favier, J. 2010 Immersed-boundary methods for general finite-difference and finite-volume Navier–Stokes solvers. J. Comput. Phys. 229 (24), 9073–9091.CrossRefGoogle Scholar