Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-19T20:17:06.766Z Has data issue: false hasContentIssue false
  • English
  • Français

Microfluidic propulsion by the metachronal beating of magnetic artificial cilia: a numerical analysis

Published online by Cambridge University Press:  20 October 2011

S. N. Khaderi ,
J. M. J. den Toonder  and
P. R. Onck
S. N. Khaderi
Affiliation:
Zernike Institute for Advanced Materials, University of Groningen, NL-9747 AG Groningen, The Netherlands
J. M. J. den Toonder
Affiliation:
Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands
P. R. Onck*
Affiliation:
Zernike Institute for Advanced Materials, University of Groningen, NL-9747 AG Groningen, The Netherlands
*
†Email address for correspondence: p.r.onck@rug.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

In this work we study the effect of metachronal waves on the flow created by magnetically driven plate-like artificial cilia in microchannels using numerical simulations. The simulations are performed using a coupled magneto-mechanical solid–fluid computational model that captures the physical interactions between the fluid flow, ciliary deformation and applied magnetic field. When a rotating magnetic field is applied to super-paramagnetic artificial cilia, they mimic the asymmetric motion of natural cilia, consisting of an effective and recovery stroke. When a phase difference is prescribed between neighbouring cilia, metachronal waves develop. Due to the discrete nature of the cilia, the metachronal waves change direction when the phase difference becomes sufficiently large, resulting in antiplectic as well as symplectic metachrony. We show that the fluid flow created by the artificial cilia is significantly enhanced in the presence of metachronal waves and that the fluid flow becomes unidirectional. Antiplectic metachrony is observed to lead to a considerable enhancement in flow compared to symplectic metachrony, when the cilia spacing is small. Obstruction of flow in the direction of the effective stroke for the case of symplectic metachrony was found to be the key mechanism that governs this effect.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics Biological Fluid Dynamics: Propulsion
Type
Papers
Information
Journal of Fluid Mechanics , Volume 688 , 10 December 2011 , pp. 44 - 65
Copyright
Copyright © Cambridge University Press 2011

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

1. Annabattula, R. K., Huck, W. T. S. & Onck, P. R. 2010 Micron-scale channel formation by the release and bond-back of pre-stressed thin films: a finite element analysis. J. Mech. Phys. Solids 58, 447–465.CrossRefGoogle Scholar
2. Baaijens, F. P. T. 2001 A fictitious domain/mortar element method for fluid–structure interaction. Intl J. Numer. Meth. Fluids 35 (7), 743–761.3.0.CO;2-A>CrossRefGoogle Scholar
3. Belardi, J., Schorr, N., Prucker, O., Wells, S., Patel, V. & Ruhe, J. 2010 Fabrication of artificial rubber cilia by photolithography. In Second European Conference on Microfluidics, paper no. 112.Google Scholar
4. Blake, J. R. 1971a Infinite models for ciliary propulsion. J. Fluid Mech. 49 (2), 209–222.CrossRefGoogle Scholar
5. Blake, J. R. 1971b A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46 (1), 199–208.CrossRefGoogle Scholar
6. Blake, J. R. 1972 A model for the micro-structure in ciliated organisms. J. Fluid Mech. 55 (1), 1–23.CrossRefGoogle Scholar
7. Blake, J. R. & Sleigh, M. A. 1974 Mechanics of ciliary locomotion. Biol. Rev. 49, 85–125.CrossRefGoogle ScholarPubMed
8. Brennen, C. & Winet, H. 1977 Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9, 339–398.CrossRefGoogle Scholar
9. Chen, L., Ma, J., Tan, F. & Guan, Y. 2003 Generating high-pressure sub-microliter flow rate in packed microchannel by electroosmotic force: potential application in microfluidic systems. Sensors Actuators B: Chemical 88, 260–265.CrossRefGoogle Scholar
10. Cook, R. D., Malkus, D. S., Plesha, M. E., Malkus, D. S. & Plesha, M. E. 2001 Concepts and Applications of Finite Element Analysis. Wiley.Google Scholar
11. Dauptain, A., Favier, J. & Bottaro, A. 2008 Hydrodynamics of ciliary propulsion. J. Fluids Struct. 24 (8), 1156–1165.CrossRefGoogle Scholar
12. Evans, B. A., Shields, A. R., Carroll, R. L, Washburn, S., Falvo, M. R. & Superfine, R. 2007 Magnetically actuated nanorod arrays as biomimetic cilia. Nano Lett. 7 (5), 1428–1434.CrossRefGoogle ScholarPubMed
13. Fahrni, F., Prins, M. W. J. & van IJzendoorn, L. J. 2009 Micro-fluidic actuation using magnetic artificial cilia. Lab on a Chip 9, 3413–3421.CrossRefGoogle ScholarPubMed
14. 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, 231–242.CrossRefGoogle ScholarPubMed
15. 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.CrossRefGoogle ScholarPubMed
16. 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
17. Jeon, N. L., Dertinger, S. K. W., Chiu, D. T., Choi, I. S., Stroock, A. D. & Whitesides, G. M. 2000 Generation of solution and surface gradients using microfluidic systems. Langmuir 16 (22), 8311–8316.CrossRefGoogle Scholar
18. Khaderi, S. N., Baltussen, M. G. H. M., Anderson, P. D., Ioan, D., den Toonder, J. M. J. & Onck, P. R. 2009 Nature-inspired microfluidic propulsion using magnetic actuation. Phys. Rev. E 79 (4), 046304.CrossRefGoogle ScholarPubMed
19. Khaderi, S. N., Baltussen, M. G. H. M., Anderson, P. D., den Toonder, J. M. J. & Onck, P. R. 2010 The breaking of symmetry in microfluidic propulsion driven by artificial cilia. Phys. Rev. E 82, 027302.CrossRefGoogle ScholarPubMed
20. Kim, Y. W. & Netz, R. R. 2006 Pumping fluids with periodically beating grafted elastic filaments. Phys. Rev. Lett. 96 (15), 158101.CrossRefGoogle ScholarPubMed
21. Kinosita, H. & Murakami, A. 1967 Control of ciliary motion. Physiol. Rev. 47, 53–82.CrossRefGoogle ScholarPubMed
22. Laser, D. J & Santiago, J. G 2004 A review of micropumps. J. Micromech. Microengng 14 (6), R35–R64.CrossRefGoogle Scholar
23. Liron, N. 1978 Fluid transport by cilia between parallel plates. J. Fluid Mech. 86 (4), 705–726.CrossRefGoogle Scholar
24. van Loon, R., Anderson, P. D. & van de Vosse, F. N. 2006 A fluid–structure interaction method with solid–rigid contact for heart valve dynamics. J. Comput. Phys. 217, 806–823.CrossRefGoogle Scholar
25. Malvern, L. E. 1977 Introduction to the Mechanics of a Continuous Medium. Prentice-Hall.Google Scholar
26. Mitran, S. M. 2007 Metachronal wave formation in a model of pulmonary cilia. Computers and Structures 85, 763774.CrossRefGoogle Scholar
27. Niedermayer, T., Eckhardt, B. & Lenz, P. 2008 Synchronization, phase locking, and metachronal wave formation in ciliary chains. Chaos: An Interdisciplinary Journal of Nonlinear Science 18 (3), 037128.CrossRefGoogle ScholarPubMed
28. van Oosten, C. L., Bastiaansen, C. W. M. & Broer, D. J. 2009 Printed artificial cilia from liquid-crystal network actuators modularly driven by light. Nature Mater. 8, 677–682.CrossRefGoogle ScholarPubMed
29. Qian, B., Jiang, H., Gagnon, D. A., Breuer, K. S. & Powers, T. R. 2009 Minimal model for synchronization induced by hydrodynamic interactions. Phys. Rev. E 80 (6), 061919.CrossRefGoogle ScholarPubMed
30. van Rijsewijk, L. 2006Electrostatic and magnetic microactuation of polymer structures for fluid transport. Master’s thesis, Eindhoven University of Technology.Google Scholar
31. Roper, M., Dreyfus, R., Baudry, J., Fermigier, M., Bibette, J. & Stone, H. A. 2006 On the dynamics of magnetically driven elastic filaments. J. Fluid Mech. 554 (1), 167–190.CrossRefGoogle Scholar
32. Satir, P. & Sleigh, M. A 1990 The physiology of cilia and mucociliary interactions. Annu. Rev. Physiol. 52 (1), 137–155.CrossRefGoogle ScholarPubMed
33. Schilling, E. A., Kamholz, A. E. & Yager, P. 2002 Cell lysis and protein extraction in a microfluidic device with detection by a fluorogenic enzyme assay. Analyt. Chem. 74 (8), 1798–1804.CrossRefGoogle Scholar
34. Schorr, N., Belardi, J., Prucker, O., Wells, S., Patel, V. & Ruhe, J. 2010Magnetically actuated polymer flap arrays mimicking artificial cilia. In Second European Conference on Microfluidics, paper no. 105.Google Scholar
35. Shields, A. R., Fiser, B. L., Evans, B. A., Falvo, M. R., Washburn, S. & Superfine, R. 2010 Biomimetic cilia arrays generate simultaneous pumping and mixing regimes. Proc. Natl Acad. Sci 107 (36), 15670–15675.CrossRefGoogle ScholarPubMed
36. Sing, C. E., Schmid, L., Schneider, M. F., Franke, T. & Alexander-Katz, A. 2010 Controlled surface-induced flows from the motion of self-assembled colloidal walkers. Proc. Natl Acad. Sci. 107 (2), 535–540.CrossRefGoogle ScholarPubMed
37. Smith, D. J., Gaffney, E. A. & Blake, J. R. 2008 Modelling mucociliary clearance. Res. Physiol. Neurobiol. 163, 178188.Google ScholarPubMed
38. 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, 1477–1510.CrossRefGoogle Scholar
39. Tecplot, 2008 Tec360 user manual.Google Scholar
40. den Toonder, J., Bos, F., Broer, D., Filippini, L., Gillies, M., de Goede, J., Mol, T., Reijme, M., Talen, W., Wilderbeek, H., Khatavkar, V. & Anderson, P. 2008 Artificial cilia for active micro-fluidic mixing. Lab on a Chip 8 (4), 533–541.CrossRefGoogle Scholar
41. Vilfan, A. & Jülicher, F. 2006 Hydrodynamic flow patterns and synchronization of beating cilia. Phys. Rev. Lett. 96 (5), 058102.CrossRefGoogle ScholarPubMed
42. Vilfan, M., Potocnik, A., Kavcic, B., Osterman, N., Poberaj, I., Vilfan, A. & Babic, D. 2010 Self-assembled artificial cilia. Proc. Natl Acad. Sci. 107, 1844–1847.CrossRefGoogle ScholarPubMed
43. West, J., Karamata, B., Lillis, B., Gleeson, J. P., Alderman, J., Collins, J. K., Lane, W., Mathewson, A. & Berney, H. 2002 Application of magnetohydrodynamic actuation to continuous flow chemistry. Lab on a Chip 2, 224–230.CrossRefGoogle ScholarPubMed
44. Zeng, S., Chen, C. H., Santiago, J. G., Chen, J. R., Zare, R. N., Tripp, J. A., F., Svec & Fréchet, J. M. J. 2002 Electroosmotic flow pumps with polymer frits. Sensors Actuators B: Chemical 82 (2/3), 209–212.CrossRefGoogle Scholar

Khaderi et al. supplementary movies

Motion of fluid particles for anti-phase motion of cilia

Download Khaderi et al. supplementary movies(Video)
Video 6.9 MB

Khaderi et al. supplementary movies

Motion of fluid particles for anti-phase motion of cilia

Download Khaderi et al. supplementary movies(Video)
Video 6 MB

Khaderi et al. supplementary movies

Motion of fluid particles for symplectic metachronal motion of cilia

Download Khaderi et al. supplementary movies(Video)
Video 9.2 MB

Khaderi et al. supplementary movies

Motion of fluid particles for symplectic metachronal motion of cilia

Download Khaderi et al. supplementary movies(Video)
Video 4.1 MB

Khaderi et al. supplementary movies

Motion of fluid particles for antiplectic metachronal motion of cilia

Download Khaderi et al. supplementary movies(Video)
Video 7.6 MB

Khaderi et al. supplementary movies

Motion of fluid particles for antiplectic metachronal motion of cilia

Download Khaderi et al. supplementary movies(Video)
Video 6.6 MB