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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: [email protected]
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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
Type
Papers
Information
Journal of Fluid Mechanics , Volume 824 , 10 August 2017 , pp. 931 - 961
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Copyright
© 2017 Cambridge University Press 

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References

Blake, J. R. 1971a Infinite model for ciliary propulsion. J. Fluid Mech. 49 (2), 209–222.Google Scholar
Blake, J. R. 1971b A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46 (1), 199–208.CrossRefGoogle Scholar
Blake, J. R. 1972 A model for the micro-structure in ciliated organisms. J. Fluid Mech. 55 (1), 1–23.Google Scholar
Blake, J. R. & Chwang, A. T. 1974 Fundamental singularities of viscous flow. Part II. J. Engng Maths 8 (1), 113–124.Google Scholar
Brennen, C. & Winet, H. 1977 Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9, 339–398.Google Scholar
Chanez, P. 2005 Severe asthma is an epithelial disease. Eur. Respir. J. 25 (6), 945–946.Google Scholar
Chatelin, R.2013 Méthodes numériques pour l’écoulement de Stokes 3D: fluides à viscosité variable en géométrie complexe mobile; application aux fluides biologiques. PhD thesis, Institut de Mathématiques de Toulouse.Google Scholar
Chatelin, R. & Poncet, P. 2016 A parametric study of mucociliary transport by numerical simulations of 3D non-homogeneous mucus. J. Biomech. 49 (9), 1772–1780.Google Scholar
Chen, C. Y., Chen, C. Y., Lin, C. Y. & Hu, Y. T. 2013 Magnetically actuated artificial cilia for optimum mixing performance in microfluidics. Lab on a Chip 13 (14), 2834–2839.CrossRefGoogle ScholarPubMed
Dauptain, A., Favier, J. & Bottaro, A. 2008 Hydrodynamics of ciliary propulsion. J. Fluids Struct. 24 (8), 1156–1165.Google 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.Google Scholar
Downton, M. T. & Stark, H. 2009 Beating kinematics of magnetically actuated cilia. Europhys. Lett. 85, 44002.Google Scholar
Elgeti, J. & Gompper, G. 2013 Emergence of metachronal waves in cilium arrays. Proc. Natl Acad. Sci. USA 110 (12), 4470–4475.Google Scholar
Eloy, C. & Lauga, E. 2012 Kinematics of the most efficient cilium. Phys. Rev. Lett. 109, 038101.Google Scholar
Fauci, L. J. & Dillon, R. 2006 Biofluidmechanics of reproduction. Annu. Rev. Fluid Mech. 38, 371–394.Google Scholar
Gardiner, M. B. 2005 The importance of being cilia. HHMI Bulletin 64, 32–36.Google Scholar
Gauger, E. M., Downton, M. T. & Stark, H. 2009 Fluid transport at low Reynolds number with magnetically actuated artificial cilia. Eur. Phys. J. E 28 (2), 231–242.Google ScholarPubMed
Gueron, S. & Levit-Gurevich, K. 1999 Energetic considerations of ciliary beating and the advantage of metachronal coordination. Proc. Natl Acad. Sci. USA 96 (22), 12240–12245.Google Scholar
Gueron, S., Levit-Gurevich, K., Liron, N. & Blum, J. J. 1997 Cilia internal mechanism and metachronal coordination as the result of hydrodynamical coupling. Proc. Natl Acad. Sci. USA 94 (12), 6001–6006.CrossRefGoogle ScholarPubMed
Guo, H., Nawroth, J., Ding, Y. & Kanso, E. 2014 Cilia beating patterns are not hydrodynamically optimal. Phys. Fluids 26, 091901.Google Scholar
Guo, Z. & Shu, C. 2013 Lattice Boltzmann Method and its Applications in Engineering. World Scientific.Google Scholar
Hussong, J., Breugem, W. P. & Westerweel, J. 2011 A continuum model for flow induced by metachronal coordination between beating cilia. J. Fluid Mech. 684, 137–162.Google Scholar
Keller, S. R. & Brennen, C. 1968 A traction-layer model for ciliary propulsion. In Proceedings of the Symposium on Swimming and Flying in Nature, California Institute of Technology, Pasadena, pp. 253–271. Plenum Press.Google Scholar
Kelley, D. H. & Ouellette, N. T. 2011 Separating stretching from folding in fluid mixing. Nat. Phys. 7, 477–480.Google Scholar
Khaderi, S. N., Baltussen, M. G. H. M., Anderson, P. D., den Toonder, J. M. J. & Onck, P. R. 2010 Breaking of symmetry in microfluidic propulsion driven by artificial cilia. Phys. Rev. E 82, 027302.Google 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.Google Scholar
Kim, Y. W. & Netz, R. R. 2006 Pumping fluids with periodically beating grafted elastic filaments. Phys. Rev. Lett. 96 (15), 158101.Google Scholar
Kirkham, S., Sheehan, J. K., Knight, D., Richardson, P. S. & Thornton, D. J. 2002 Heterogeneity of airways mucus: variations in the amounts and glycoforms of the major oligomeric mucins MUC5AC and MUC5B. Biochem. J. 361 (3), 537–546.Google Scholar
Knight-Jones, E. W. 1954 Relations between metachronism and the direction of ciliary beat in Metazoa. J. Cell Sci. s3‐95, 503–521.Google Scholar
Lafforgue, O., Poncet, S., Seyssiecq-Guarente, I. & Favier, J. 2016 Rheological characterization of macromolecular colloidal gels as simulant of bronchial mucus. In 32nd International Conference of the Polymer Processing Society (PPS-32), Lyon, France. The Polymer Processing Society.Google Scholar
Lai, S. K., Wang, Y. Y., Wirtz, D. & Hanes, J. 2009 Micro- and macrorheology of mucus. Adv. Drug Deliv. Rev. 61 (2), 86–100.CrossRefGoogle ScholarPubMed
Lauga, E. & Eloy, C. 2013 Shape of optimal active flagella. J. Fluid Mech. 730, R1.CrossRefGoogle Scholar
Li, H., Tan, J. & Zhang, M. 2009 Dynamics modeling and analysis of a swimming microrobot for controlled drug delivery. IEEE T-ASE 6 (2), 220–227.Google Scholar
Li, Z., Favier, J., D’Ortona, U. & Poncet, S. 2016 An improved explicit immersed boundary method to couple with lattice Boltzmann model for single- and multi-component fluid flows. J. Comput. Phys. 304, 424–440.Google Scholar
Lighthill, J. 1976 Flagellar hydrodynamics. SIAM Rev. 18, 161–230.CrossRefGoogle Scholar
Lukens, S., Yang, X. & Fauci, L. 2010 Using Lagrangian coherent structures to analyze fluid mixing by cilia. Chaos 20 (1), 017511.Google Scholar
Matsui, H., Randell, S. H., Peretti, S. W., Davis, W. C. & Boucher, R. C. 1998 Coordinated clearance of periciliary liquid and mucus from airway surfaces. J. Clin. Invest. 102 (6), 1125–1131.CrossRefGoogle ScholarPubMed
Mitran, S. M. 2007 Metachronal wave formation in a model of pulmonary cilia. Comput. Struct. 85 (11–14), 763–774.Google Scholar
Niedermayer, T., Eckhardt, B. & Lenz, P. 2008 Synchronization, phase locking, and metachronal wave formation in ciliary chains. Chaos 18 (3), 037128.Google Scholar
Norton, M. M., Robinson, R. J. & Weinstein, S. J. 2011 Model of ciliary clearance and the role of mucus rheology. Phys. Rev. E 83, 011921.Google Scholar
Osterman, N. & Vilfan, A. 2011 Finding the ciliary beating pattern with optimal efficiency. Proc. Natl. Acad. Sci. USA 108 (38), 15727–15732.CrossRefGoogle ScholarPubMed
Phan-Thien, N., Tran-Cong, T. & Ramia, M. 1987 A boundary-element analysis of flagellar propulsion. J. Fluid Mech. 184, 533–549.Google Scholar
Porter, M. L., Coon, E. T., Kang, Q., Moulton, J. D. & Carey, J. W. 2012 Multicomponent interparticle-potential lattice Boltzmann model for fluids with large viscosity ratios. Phys. Rev. E 86, 036701.Google Scholar
Reynolds, A. J. 1965 The swimming of minute organisms. J. Fluid Mech. 23 (2), 241–260.Google Scholar
Sanderson, M. J. & Sleigh, M. A. 1981 Ciliary activity of cultured rabbit tracheal epithelium: beat pattern and metachrony. J. Cell Sci. 47, 331–341.Google Scholar
Satir, P. & Christensen, S. 2007 Overview of structure and function of mammalian cilia. Annu. Rev. Physiol. 69, 377–400.Google Scholar
Sedaghat, M. H., Shahmardan, M. M., Norouzi, M., Jayathilake, P. G. & Nazari, M. 2016 Numerical simulation of muco-ciliary clearance: immersed boundary lattice Boltzmann method. Comput. Fluids 131, 91–101.Google Scholar
Shan, X. & Chen, H. 1993 Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47 (3), 1815–1819.Google ScholarPubMed
Shan, X. & Chen, H. 1994 Simulation of nonideal gases and liquid–gas phase transitions by the lattice Boltzmann equation. Phys. Rev. E 49 (4), 2941–2948.Google ScholarPubMed
Sleigh, M. A. 1962 The Biology of Cilia and Flagella. Pergamon Press.Google Scholar
Sleigh, M. A., Blake, J. R. & Liron, N. 1988 The propulsion of mucus by cilia. Am. Rev. Respir. Dis. 137 (3), 726–741.Google Scholar
Smith, D. J., Gaffney, E. A. & Blake, J. R. 2007 Discrete cilia modelling with singularity distributions: application to the embryonic node and the airway surface liquid. Bull. Math. Biol. 69 (5), 1477–1510.Google Scholar
Taylor, G. 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209 (1099), 447–461.Google Scholar
Tuck, E. O. 1968 A note on a swimming problem. J. Fluid Mech. 31 (2), 305–308.CrossRefGoogle Scholar
Widdicombe, J. H. & Widdicombe, J. G. 1995 Regulation of human airway surface liquid. Resp. Physiol. 99 (1), 3–12.Google Scholar
Winters, S. L. & Yeates, D. B. 1997 Roles of hydration, sodium, and chloride in regulation of canine mucociliary transport system. J. Appl. Phys. 83 (4), 1360–1369.Google Scholar
Zou, Q., Hou, S., Chen, S. & Doolen, G. D. 1995 A improved incompressible lattice Boltzmann model for time-independent flows. J. Stat. Phys. 81 (1), 35–48.Google Scholar

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