Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T11:56:46.626Z Has data issue: false hasContentIssue false

Fluid–structure interaction of three-dimensional magnetic artificial cilia

Published online by Cambridge University Press:  08 August 2012

S. N. Khaderi
Affiliation:
Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen, The Netherlands
P. R. Onck*
Affiliation:
Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen, The Netherlands
*
Email address for correspondence: [email protected]

Abstract

A numerical model is developed to analyse the interaction of artificial cilia with the surrounding fluid in a three-dimensional setting in the limit of vanishing fluid inertia forces. The cilia are modelled using finite shell elements and the fluid is modelled using a boundary element approach. The coupling between both models is performed by imposing no-slip boundary conditions on the surface of the cilia. The performance of the model is verified using various reference problems available in the literature. The model is used to simulate the fluid flow due to magnetically actuated artificial cilia. The results show that narrow and closely spaced cilia create the largest flow, that metachronal waves along the width of the cilia create a significant flow in the direction of the cilia width and that the recovery stroke in the case of the out-of-plane actuation of the cilia strongly depends on the cilia width.

Type
Papers
Copyright
Copyright © Cambridge University Press 2012

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. Ainley, J., Durkin, S., Embid, R., Boindala, P. & Cortez, R. 2008 The method of images for regularized stokeslets. J. Comput. Phys. 227 (9), 46004616.CrossRefGoogle Scholar
2. Allman, D. J. 1984 A compatible triangular element including vertex rotations for plane elasticity analysis. Comput. Struct. 19 (1–2), 18 (special memorial issue).CrossRefGoogle Scholar
3. Bathe, K. J. & Ho, L. W. 1981 A simple and effective element for analysis of general shell structures. Comput. Struct. 13 (5–6), 673681.CrossRefGoogle Scholar
4. Batoz, J. L., Bathe, K. J. & Ho, L. W. 1980 A study of three-node triangular plate bending elements. Intl J. Numer. Meth. Engng 15, 17711812.CrossRefGoogle Scholar
5. Belardi, J., Schorr, N., Prucker, O. & Ruhe, J. 2011 Artificial cilia: generation of magnetic actuators in microfluidic systems. Adv. Funct. Mater. 21, 33143320.CrossRefGoogle Scholar
6. Blake, J. R. 1971 A note on the image system for a Stokeslet in a no-slip boundary. Math. Proc. Cambridge Phil. Soc. 70 (02), 303310.CrossRefGoogle Scholar
7. Blake, J. R. 1972 A model for the micro-structure in ciliated organisms. J. Fluid Mech. 55 (01), 123.CrossRefGoogle Scholar
8. Chen, Z. S., Hofstetter, G. & Mang, H. A. 1998 A Galerkin-type Be–Fe formulation for elasto-acoustic coupling. Comput. Meth. Appl. Mech. Engng 152 (1–2), 147155 (containing papers presented at the symposium on Advances in Computational Mechanics).CrossRefGoogle Scholar
9. Childress, S. 1981 Mechanics of Swimming and Flying. Cambridge University Press.CrossRefGoogle Scholar
10. Donea, J., Giuliani, S. & Halleux, J. P. 1982 An arbitrary Lagrangian–Eulerian finite element method for transient dynamic fluid–structure interactions. Comput. Meth. Appl. Mech. Engng 33 (1–3), 689723.CrossRefGoogle Scholar
11. Fahrni, F., Prins, M. W. J. & van IJzendoorn, L. J. 2009 Micro-fluidic actuation using magnetic artificial cilia. Lab on a Chip 9, 34133421.CrossRefGoogle ScholarPubMed
12. Fulford, G. R. & Blake, J. R 1986 Muco-ciliary transport in the lung. J. Theor. Biol. 121 (4), 381402.CrossRefGoogle ScholarPubMed
13. 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, 231242.CrossRefGoogle ScholarPubMed
14. Gerstenberger, A. & Wall, W. A. 2008 An extended finite element method/Lagrange multiplier based approach for fluid–structure interaction. Comput. Meth. Appl. Mech. Engng 197 (19–20), 16991714 (computational methods in fluid–structure interaction).CrossRefGoogle Scholar
15. Gerstenberger, A. & Wall, W. A 2010 An embedded Dirichlet formulation for 3d continua. Intl J. Numer. Meth. Engng 82 (5), 537563.CrossRefGoogle Scholar
16. Happel, J. & Brenner, H. 1986 Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media. Martinus Nijhoff.Google Scholar
17. Hughes, T. J. R. & Liu, W. K. 1981 Nonlinear finite element analysis of shells: Part I. Three-dimensional shells. Comput. Meth. Appl. Mech. Engng 26 (3), 331362.CrossRefGoogle Scholar
18. Hussong, J., Schorr, N., Belardi, J., Prucker, O., Ruhe, J. & Westerweel, J. 2011 Experimental investigation of the flow induced by artifiial cilia. Lab on a Chip 11, 20172022.CrossRefGoogle Scholar
19. Jog, C. S. & Kelkar, P. P. 2006 Non-linear analysis of structures using high performance hybrid elements. Intl J. Numer. Meth. Engng 68, 473501.CrossRefGoogle Scholar
20. 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
21. 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
22. Khaderi, S. N., Craus, C. B., Hussong, J., Schorr, N., Belardi, J., Westerweel, J., Prucker, O., Ruhe, J., den Toonder, J. M. J. & Onck, P. R. 2011a Magnetically-actuated artificial cilia for microfluidic propulsion. Lab on a Chip 11, 20022010.CrossRefGoogle ScholarPubMed
23. Khaderi, S. N., den Toonder, J. M. J. & Onck, P. R. 2011b Microfluidic propulsion by the metachronal beating of magnetic artificial cilia: a numerical analysis. J. Fluid Mech. 688, 4465.CrossRefGoogle Scholar
24. Laser, D. J & Santiago, J. G 2004 A review of micropumps. J. Micromech. Microengng 14 (6), R35R64.CrossRefGoogle Scholar
25. 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, 806823.CrossRefGoogle Scholar
26. Masud, A., Tham, C. L. & Liu, W. K. 2000 A stabilized 3-d co-rotational formulation for geometrically nonlinear analysis of multi-layered composite shells. Comput. Mech. 26, 112.CrossRefGoogle Scholar
27. van Oosten, C. L., Bastiaansen, C. W. M. & Broer, D. J. 2009 Printed artificial cilia from liquid-crystal network actuators modularly driven by light. Nat. Mater. 8, 677682.CrossRefGoogle ScholarPubMed
28. Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11 (-1), 479517.CrossRefGoogle Scholar
29. Pozrikidis, C. 2002 A Practical Guide to Boundary Element Methods. Chapman & Hall/CRC.Google Scholar
30. Salsac, A. V., Biesel, D. B. & Tallec, P. L. 2010 Coupling of finite element and boundary integral methods for a capsule in a Stokes flow. Intl J. Numer. Meth. Engng 829850.Google Scholar
31. Schneider, S. 2008 Fe/fmbe coupling to model fluidstructure interaction. Intl J. Numer. Meth. Engng 21372156.CrossRefGoogle Scholar
32. 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), 533541.CrossRefGoogle Scholar
33. Zienkiewicz, O. C. & Taylor, R. L. 2002 The Finite Element Method. Butterworth-Heinemann.Google Scholar