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Transport efficiency of metachronal waves in 3D cilium arrays immersed in a two-phase flow

Published online by Cambridge University Press:  14 July 2017

S. Chateau Open the ORCID record for S. Chateau [Opens in a new window] ,
J. Favier ,
U. D’Ortona  and
S. Poncet Open the ORCID record for S. Poncet [Opens in a new window]
S. Chateau*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France Faculté de Génie, Université de Sherbrooke, Sherbrooke, Québec, Canada
J. Favier
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France
U. D’Ortona
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France
S. Poncet
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France Faculté de Génie, Université de Sherbrooke, Sherbrooke, Québec, Canada
*
†Email address for correspondence: sylvain.chateau@usherbrooke.ca
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Abstract

This work reports the formation and characterization of antipleptic and symplectic metachronal waves in 3D cilium arrays immersed in a two-fluid environment, with a viscosity ratio of 20. A coupled lattice Boltzmann–immersed-boundary solver is used. The periciliary layer is confined between the epithelial surface and the mucus. Its thickness is chosen such that the tips of the cilia can penetrate the mucus. A purely hydrodynamical feedback of the fluid is taken into account and a coupling parameter $\unicode[STIX]{x1D6FC}$ is introduced, which allows tuning of both the direction of the wave propagation and the strength of the fluid feedback. A comparative study of both antipleptic and symplectic waves, mapping a cilium interspacing ranging from 1.67 up to 5 cilium lengths, is performed by imposing metachrony. Antipleptic waves are found to systematically outperform symplectic waves. They are shown to be more efficient for transporting and mixing the fluids, while spending less energy than symplectic, random or synchronized motions.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Multiphase and Particle-laden Flows: Multiphase flow Biological Fluid Dynamics: Pulmonary fluid mechanics

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Papers
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Journal of Fluid Mechanics , Volume 824 , 10 August 2017 , pp. 931 - 961
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© 2017 Cambridge University Press 

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Chateau et al. supplementary movie 1

Symplectic MCW obtained for α=3 and a cilia spacing a/L=0.47. 64 cilia are arranged in a row on a computational domain of size (Nx=449, Ny=101, Nz=50). The length of the cilia is L=22 lu and the PCL is set such as h/L=0.9. The ratio of viscosity is =15. Top view: The glyph represent the mean fluid velocity. In red is represented the mucus phase, while in blue is represented the PCL. Bottom view: The plan is colored with the dimensionless vorticity magnitude.

Download Chateau et al. supplementary movie 1(Video)
Video 10 MB

Chateau et al. supplementary movie 2

Antiplectic MCW obtained for α=-2.5 and a cilia spacing a/L=0.33. 36 cilia are arranged 18 × 2 array on a computational domain of size (Nx=91, Ny=11, Nz=50). The length of the cilia is L=15 lu and the PCL is set such as h/L=0.9. The ratio of viscosity is =15. The glyph represents the mean fluid velocity. In red is represented the mucus phase, while in blue is represented the PCL.

Download Chateau et al. supplementary movie 2(Video)
Video 2.7 MB