Research Papers

Individually Controllable Magnetic Cilia: Mixing Application

[+] Author and Article Information
Nathan Banka, Yau Luen Ng

Ultra Precision Control Laboratory,
Department of Mechanical Engineering,
University of Washington,
Seattle, Washington 98195

Santosh Devasia

Fellow ASME
Ultra Precision Control Laboratory,
Department of Mechanical Engineering,
University of Washington,
Seattle, Washington 98195
e-mail: devasia@uw.edu

1Corresponding author.

Manuscript received February 29, 2016; final manuscript received January 20, 2017; published online June 27, 2017. Assoc. Editor: Rafael V. Davalos.

J. Med. Devices 11(3), 031003 (Jun 27, 2017) (10 pages) Paper No: MED-16-1053; doi: 10.1115/1.4035984 History: Received February 29, 2016; Revised January 20, 2017

This paper introduces a new design for individually controlled magnetic artificial cilia for use in fluid devices and specifically intended to improve the mixing in DNA microarray experiments. The design has been implemented using a low-cost prototype that can be fabricated using polydimethylsiloxane (PDMS) and off-the-shelf parts and achieves large cilium deflections (59% of the cilium length). The device's performance is measured via a series of mixing experiments using different actuation patterns inspired by the blinking vortex theory. The experimental results, quantified using the relative standard deviation of the color when mixing two colored inks, show that exploiting the individual control leads to faster mixing (38% reduction in mixing time) than when operating the device in a simultaneous-actuation mode with the same average cilium beat frequency. Furthermore, the experimental results show an optimal beating pattern that minimizes the mixing time. The existence and character of this optimum is predicted by simulations using a blinking-vortex approach for 2D ideal flow, suggesting that the blinking-vortex model can be used to predict the effect of parameter variation on the experimental system.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Suh, Y. K. , and Kang, S. , 2010, “ A Review on Mixing in Microfluidics,” Micromachines, 1(3), pp. 82–111. [CrossRef]
Stangegaard, M. , 2009, “ Gene Expression Analysis Using Agilent DNA Microarrays,” DNA Microarrays for Biomedical Research: Methods and Protocols, Humana Press, Totowa, NJ, pp. 133–145.
Dugas, V. , Broutin, J. , and Souteyrand, E. , 2010, “ Mixing and Dispensing Homogeneous Compounds of a Reactant on a Surface,” U.S. Patent No. 7772010. https://www.google.com/patents/US7772010
Wei, C.-W. , Cheng, J.-Y. , Huang, C.-T. , Yen, M.-H. , and Young, T.-H. , 2005, “ Using a Microfluidic Device for 1 μl DNA Microarray Hybridization in 500 s,” Nucleic Acids Res., 33(8), p. e78. [CrossRef] [PubMed]
Cola, B. A. , Schaffer, D. K. , Fisher, T. S. , and Stremler, M. A. , 2006, “ A Pulsed Source-Sink Fluid Mixing Device,” J. Microelectromech. Syst., 15(1), pp. 259–266. [CrossRef]
Sartor, M. , Schwanekamp, J. , Halbleib, D. , Mohamed, I. , Karyala, S. , Medvedovic, M. , and Tomlinson, C. R. , 2004, “ Microarray Results Improve Significantly as Hybridization Approaches Equilibrium,” Biotechniques, 36(5), pp. 790–796. http://www.biotechniques.com/BiotechniquesJournal/2004/May/Microarray-results-improve-significantly-as-hybridization-approaches-equilibrium/biotechniques-116761.html [PubMed]
Steger, D. , Berry, D. , Haider, S. , Horn, M. , Wagner, M. , Stocker, R. , and Loy, A. , 2011, “ Systematic Spatial Bias in DNA Microarray Hybridization is Caused by Probe Spot Position-Dependent Variability in Lateral Diffusion,” PloS One, 6(8), p. e23727. [CrossRef] [PubMed]
den Toonder, J. , Bos, F. , Broer, D. , Filippini, L. , Gillies, M. , de Goede, J. , Mol, T. , Reijme, M. , Talen, W. , Wilderbeek, H. , Khatavkar, V. , and Anderson, P. , 2008, “ Artificial Cilia for Active Micro-Fluidic Mixing,” Lab Chip, 8(4), pp. 533–541. [CrossRef] [PubMed]
Oh, K. , Chung, J. , Devasia, S. , and Riley, J. , 2009, “ Bio-Mimetic Silicone Cilia for Microfluidic Manipulation,” Lab Chip, 9(11), pp. 1561–1566. [CrossRef] [PubMed]
Keißner, A. , and Brucker, C. , 2012, “ Directional Fluid Transport Along Artificial Ciliary Surfaces With Base-Layer Actuation of Counter-Rotating Orbital Beating Patterns,” Soft Matter, 8(19), pp. 5342–5349. [CrossRef]
Khaderi, S. , Craus, C. , Hussong, J. , Schorr, N. , Belardi, J. , Westerweel, J. , Prucker, O. , Rühe, J. , Den Toonder, J. , and Onck, P. , 2011, “ Magnetically-Actuated Artificial Cilia for Microfluidic Propulsion,” Lab Chip, 11(12), pp. 2002–2010. [CrossRef] [PubMed]
Vilfan, M. , Potočnik, A. , Kavčič, B. , Osterman, N. , Poberaj, I. , Vilfan, A. , and Babič, D. , 2010, “ Self-Assembled Artificial Cilia,” Proc. Natl. Acad. Sci., 107(5), p. 1844. [CrossRef]
Shields, A. , Fiser, B. , Evans, B. , Falvo, M. , Washburn, S. , and Superfine, R. , 2010, “ Biomimetic Cilia Arrays Generate Simultaneous Pumping and Mixing Regimes,” Proc. Natl. Acad. Sci., 107(36), pp. 15670–15675. [CrossRef]
Downton, M. , and Stark, H. , 2009, “ Beating Kinematics of Magnetically Actuated Cilia,” Europhys. Lett., 85(4), p. 44002. [CrossRef]
Khaderi, S. , Baltussen, M. , Anderson, P. , den Toonder, J. , and Onck, P. , 2010, “ Breaking of Symmetry in Microfluidic Propulsion Driven by Artificial Cilia,” Phys. Rev. E, 82(2), p. 027302. [CrossRef]
Khaderi, S. , den Toonder, J. , and Onck, P. , 2012, “ Fluid Flow Due to Collective Non-Reciprocal Motion of Symmetrically-Beating Artificial Cilia,” Biomicrofluidics, 6(1), p. 014106. [CrossRef]
Gauger, E. M. , Downton, M. T. , and Stark, H. , 2009, “ Fluid Transport at Low Reynolds Number With Magnetically Actuated Artificial Cilia,” Eur. Phys. J. E: Soft Matter Biol. Phys., 28(2), pp. 231–242. [CrossRef]
Brennen, C. , and Winet, H. , 1977, “ Fluid Mechanics of Propulsion by Cilia and Flagella,” Ann. Rev. Fluid Mech., 9(1), pp. 339–398. [CrossRef]
Khaderi, S. , Hussong, J. , Westerweel, J. , den Toonder, J. , and Onck, P. , 2013, “ Fluid Propulsion Using Magnetically-Actuated Artificial Cilia–Experiments and Simulations,” RSC Adv., 3(31), pp. 12735–12742. [CrossRef]
Rahbar, M. , Shannon, L. , and Gray, B. L. , 2014, “ Microfluidic Active Mixers Employing Ultra-High Aspect-Ratio Rare-Earth Magnetic Nano-Composite Polymer Artificial Cilia,” J. Micromech. Microeng., 24(2), p. 025003. [CrossRef]
Chen, C.-Y. , Chen, C.-Y. , Lin, C.-Y. , and Hu, Y.-T. , 2013, “ Magnetically Actuated Artificial Cilia for Optimum Mixing Performance in Microfluidics,” Lab Chip, 13(14), pp. 2834–2839. [CrossRef] [PubMed]
Coq, N. , Ngo, S. , Du Roure, O. , Fermigier, M. , and Bartolo, D. , 2010, “ Three-Dimensional Beating of Magnetic Microrods,” Phys. Rev. E, 82(4), p. 041503. [CrossRef]
Zhou, Y. , Amirouche, F. , and Chen, L. , 2009, “ Design and Characterization of a Magnetically Driven Valveless Micropump for Drug Delivery,” ASME J. Med. Devices, 3(2), p. 027553. [CrossRef]
Haik, Y. , and Kanuri, S. , 2008, “ Mixing Efficiency of Red Blood Cells With Magnetic Microspheres for a Hybrid Separation System,” ASME J. Med. Devices, 2(3), p. 031006. [CrossRef]
Maréchal, L. , Foong, S. , Ding, S. , Wood, K. L. , Patil, V. , and Gupta, R. , 2016, “ Design Optimization of a Magnetic Field-Based Localization Device for Enhanced Ventriculostomy,” ASME J. Med. Devices, 10(1), p. 011006. [CrossRef]
Pamme, N. , 2006, “ Magnetism and Microfluidics,” Lab Chip, 6(1), pp. 24–38. [CrossRef] [PubMed]
Wiggins, S. , and Ottino, J. M. , 2004, “ Foundations of Chaotic Mixing,” Philos. Trans. R. Soc., A, 362(1818), pp. 937–970. [CrossRef]
Go, K. , Kim, Y. , Lee, A. H. , Staricha, K. , Messersmith, P. , and Glucksberg, M. , 2015, “ Design of Novel Mixer and Applicator for Two-Component Surgical Adhesives,” ASME J. Med. Devices, 9(4), p. 045001. [CrossRef]
Aref, H. , 1984, “ Stirring by Chaotic Advection,” J. Fluid Mech., 143(1), pp. 1–21. [CrossRef]
Purcell, E. M. , 1977, “ Life at Low Reynolds Number,” Am. J. Phys, 45(1), pp. 3–11. [CrossRef]
Kim, Y. W. , and Netz, R. R. , 2006, “ Pumping Fluids With Periodically Beating Grafted Elastic Filaments,” Phys. Rev. Lett., 96(15), p. 158101. [CrossRef] [PubMed]
Gorissen, B. , de Volder, M. , and Reynaerts, D. , 2015, “ Pneumatically-Actuated Artificial Cilia Array for Biomimetic Fluid Propulsion,” Lab Chip, 15(22), pp. 4348–4355. [CrossRef] [PubMed]
2006, “ Microarrays: Table of Suppliers,” Nature, 442(7106), pp. 1071–1072. [CrossRef]
Thomas, C. , and Geer, D. , 2011, “ Effects of Shear on Proteins in Solution,” Biotechnol. Lett., 33(3), pp. 443–456. [CrossRef] [PubMed]
International Commission on Illumination, 1978, Recommendations on Uniform Color Spaces, Color-Difference Equations, Psychometric Color Terms, CIE Publication, Vienna, Austria.
Paul, E. L. , Atiemo-Obeng, V. A. , and Kresta, S. M. , 2004, Handbook of Industrial Mixing: Science and Practice, Wiley, Hoboken, NJ.
McQuain, M. K. , Seale, K. , Peek, J. , Fisher, T. S. , Levy, S. , Stremler, M. A. , and Haselton, F. R. , 2004, “ Chaotic Mixer Improves Microarray Hybridization,” Anal. Biochem., 325(2), pp. 215–226. [CrossRef] [PubMed]
Olver, F. W. J. , Olde Daalhuis, A. B. , Lozier, D. W. , Schneider, B. I. , Boisvert, R. F. , Clark, C. W. , Miller, B. R. , and Saunders, B. V. , eds., 2016, “ NIST Digital Library of Mathematical Functions,” Ver. 1.0.13, DLMF, Gaithersburg, MD, accessed Sept. 16, 2016, http://dlmf.nist.gov/
Akhiezer, N. I. , 1990, Elements of the Theory of Elliptic Functions, Vol. 79, American Mathematical Society, Providence, RI.
Lee, S. , Lee, H. , Lee, I. , and Tseng, C. , 2004, “ Ink Diffusion in Water,” Eur. J. Phys., 25(2), p. 331. [CrossRef]
Cartwright, J. H. , Piro, O. , and Tuval, I. , 2004, “ Fluid-Dynamical Basis of the Embryonic Development of Left-Right Asymmetry in Vertebrates,” Proc. Natl. Acad. Sci. U. S. A., 101(19), pp. 7234–7239. [CrossRef] [PubMed]
Khatavkar, V. V. , Anderson, P. D. , den Toonder, J. M. , and Meijer, H. E. , 2007, “ Active Micromixer Based on Artificial Cilia,” Phys. Fluids, 19(8), p. 083605. [CrossRef]
Banka, N. , and Devasia, S. , 2013, “ Nonlinear Models for Optimal Placement of Magnetically-Actuated Cilium,” ASME Paper No. DSCC2013-3808.


Grahic Jump Location
Fig. 5

Several locations were considered for the magnet (specifically, the position of the magnet when it is closest to the glass slide). A first set of trials is depicted by squares. The placements farthest from the cilium (7–9) were ineffective, so a second set of trials was performed (shown as circles). Finally, a placement was chosen between locations 11 and 12 as discussed in Sec. 2.4.

Grahic Jump Location
Fig. 6

Comparison of the beating patterns tested in the experiments of this paper. The top pattern represents the simultaneous case. The dots above and below the line each represent one beat of the left and right cilia, respectively.

Grahic Jump Location
Fig. 7

Comparison of the red–green a* channel (middle) and yellow–blue b* channel (bottom) for assessing the color variation in the image. The a* channel distinguishes between areas with and without ink but draws little distinction between the red and blue areas. The b* channel distinguishes between the red ink, blue ink, and no-ink areas.

Grahic Jump Location
Fig. 4

Schematic of the cilia fabrication process. (a) The Fe-PDMS mixture is poured onto a glass plate and bubbles removed in vacuum. (b) Narrow-gauge wire is used to create a constant-width spacer. A second glass plate is placed on top of the Fe-PDMS. (c) A weight is used to compress the Fe-PDMS sheet to ensure uniform thickness, and the assembly is placed in an oven to cure. (d) The top glass is pried away after curing. (e) The cured Fe-PDMS sheet is sliced to make cilia. (f) A rectangular PDMS chamber is cut where each cilium is to be mounted. (g) A drop of uncured PDMS is used on each side of the gap to glue the cilium in place. (h) Excess Fe-PDMS is used as support material (removed after curing) to create a gap between the cilium and the slide and ensure the cilium will be parallel to the slide. (i) A final curing step completes the fabrication of the cilia system.

Grahic Jump Location
Fig. 3

Photos showing the support structure of the cilia–mimetic mixer prototype. Left: the device with the mixing chamber removed to show the magnet wheels. Right: the apparatus with the cilia, chamber, and supporting slide mounted in a slide holder.

Grahic Jump Location
Fig. 2

Schematic of the proposed actuation approach for each cilium, showing the magnet wheel used as field source. As the magnet wheel rotates, the magnets move closer and farther from the cilium, causing a time-varying force to be applied. As shown in the side view on the right, the magnet wheel is offset from the cilium axis by a distance δ, resulting in transverse deflection of the cilium.

Grahic Jump Location
Fig. 1

A conceptual schematic of the proposed design for a cilia-based magnetic device capable of individual actuation. When a magnet is close to the slide on the left side, the left cilium deflects due to a distributed magnetic force f. Since the other cilium is far from the magnet, it is not affected.

Grahic Jump Location
Fig. 9

Photos showing diffusion in the cilia device. The full experiment is shown in Movie 1, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection: (a) initial ink distribution and (b) after 4 min, no mixing has occurred; cv(b*) = 0.33.

Grahic Jump Location
Fig. 11

Experimental video images with the simultaneous beat pattern (see Fig. 6). Timestamps (mm:ss) are shown in the top corner of each image. The full experiment is shown in Movie 2, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection. (a)–(d) Initial distribution of ink and result after each of the first three cycles ((t/T)=0,2,4,6). A boundary is formed between the right and left sides due to symmetry (c); however, unsteady processes sometimes break symmetry and promote mixing (d). (e) As the experiment continues, the boundary remains and mixing largely occurs when ink moves from one side to the other along the bottom boundary. (f) Image with cv(b*) = 0.05.

Grahic Jump Location
Fig. 10

Degree of mixing, as quantified using the relative standard deviation cv(b*), plotted against time for representative experimental runs for each beat pattern; the data shown are those with mixing times close to the average for each actuation pattern given in Table 2. Lower values of cv(b*) indicate better-mixed fluid in the chamber. The dashed line indicates the threshold for the relative standard deviation, cv(b*), of 0.05, below which the chamber is considered mixed.

Grahic Jump Location
Fig. 8

Sequence of images showing one beat of the left cilium to illustrate the flow generation mechanism. This sequence shows the third beat of an L10-R10 actuation pattern, and the time between images is two frames (0.07 s). (a)–(d) As the cilium deflects, fluid is drawn into the expanding area to its left. (e)–(h) In these four images, the cilium touches the glass slide due to magnetic forces normal to the slide. The resulting friction forces cause the cilium to bend. (i)–(j) When the magnet moves too far from the cilium to overcome elastic forces, the cilium straightens and snaps back to its undeflected configuration. The snapback takes about 2 frames, or 0.07 s. (k)–(t) In these images, clockwise rotation of the flow to the right of the cilium can be observed. (u) Here, the cilium has begun to deflect once more.

Grahic Jump Location
Fig. 12

Experimental video images with the L10-R10 beat pattern (see Fig. 6). Timestamps (mm:ss) are shown in the top corner of each image. The full experiment is shown in Movie 3, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection. (a) Initial distribution of ink. (b) After half a cycle ((t/T)=10), a uniform blue region is found in the region of influence of the left cilium. (c) After a full cycle ((t/T)=20), the action of the right cilium has made the right half uniform, drawing in some of the blue ink. (d) and (e) After two further cycles ((t/T)=40,60) it is observed that the boundary between colors is consistent after each full cycle. However, the color of the two uniform regions converges to a uniform value after each cycle. (f) After sufficient cycles, the color reaches the threshold, cv(b*) = 0.05.

Grahic Jump Location
Fig. 13

Experimental video images with the L2-R2 beat pattern (see Fig. 6). Timestamps (mm:ss) are shown in the top corner of each image. The full experiment is shown in Movie 4, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection. (a)–(d) Images showing the initial development of the flow after each of the first three cycles ((t/T)=0,4,8,12). (e) Image showing the progression of the mixing flow. (f) Image with cv(b*) = 0.05.

Grahic Jump Location
Fig. 14

Comparison of the simulations (◻) with experimental results (○). The solid line is a smoothed and interpolated fit to the simulated data; the dashed lines indicate the result of perturbing the vortex circulation Γ by ±15%. Error bars for the experimental results indicate one standard deviation.

Grahic Jump Location
Fig. 15

Selected images from the simulations described in Sec. 4. Timestamps (mm:ss) show elapsed time. (a) Initial placement of tracer particles. (b) Results after 10 s of the simultaneous pattern. In this case, symmetry prevents mixing. (c) Results after 10 s (two cycles) of the L2-R2 pattern, showing tracer particles moving between the two sides. (d) Results after 50 s (10 cycles) of the L2-R2 pattern, showing that the chamber is mixed.

Grahic Jump Location
Fig. 16

Simulated mixing trials showing the effect of perturbing the vortex position x1 = Re(z1) by ±10%. The markers indicate simulated trials, and the solid lines represent smoothed and interpolated fits. For low beat number (n < 1), mixing time goes to infinity as the conditions approach the simultaneous-activation case, making computational costs prohibitive. As in the original blinking vortex theory, the vortex spacing is a key parameter for the overall mixing performance.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In