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.

References

1.
Suh
,
Y. K.
, and
Kang
,
S.
,
2010
, “
A Review on Mixing in Microfluidics
,”
Micromachines
,
1
(
3
), pp.
82
111
.
2.
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
.
3.
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
4.
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
.
5.
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
.
6.
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
7.
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
.
8.
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
.
9.
Oh
,
K.
,
Chung
,
J.
,
Devasia
,
S.
, and
Riley
,
J.
,
2009
, “
Bio-Mimetic Silicone Cilia for Microfluidic Manipulation
,”
Lab Chip
,
9
(
11
), pp.
1561
1566
.
10.
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
.
11.
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
.
12.
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
.
13.
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
.
14.
Downton
,
M.
, and
Stark
,
H.
,
2009
, “
Beating Kinematics of Magnetically Actuated Cilia
,”
Europhys. Lett.
,
85
(
4
), p.
44002
.
15.
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
.
16.
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
.
17.
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
.
18.
Brennen
,
C.
, and
Winet
,
H.
,
1977
, “
Fluid Mechanics of Propulsion by Cilia and Flagella
,”
Ann. Rev. Fluid Mech.
,
9
(
1
), pp.
339
398
.
19.
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
.
20.
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
.
21.
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
.
22.
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
.
23.
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
.
24.
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
.
25.
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
.
26.
Pamme
,
N.
,
2006
, “
Magnetism and Microfluidics
,”
Lab Chip
,
6
(
1
), pp.
24
38
.
27.
Wiggins
,
S.
, and
Ottino
,
J. M.
,
2004
, “
Foundations of Chaotic Mixing
,”
Philos. Trans. R. Soc., A
,
362
(
1818
), pp.
937
970
.
28.
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
.
29.
Aref
,
H.
,
1984
, “
Stirring by Chaotic Advection
,”
J. Fluid Mech.
,
143
(
1
), pp.
1
21
.
30.
Purcell
,
E. M.
,
1977
, “
Life at Low Reynolds Number
,”
Am. J. Phys
,
45
(
1
), pp.
3
11
.
31.
Kim
,
Y. W.
, and
Netz
,
R. R.
,
2006
, “
Pumping Fluids With Periodically Beating Grafted Elastic Filaments
,”
Phys. Rev. Lett.
,
96
(
15
), p.
158101
.
32.
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
.
33.
2006
, “
Microarrays: Table of Suppliers
,”
Nature
,
442
(
7106
), pp.
1071
1072
.
34.
Thomas
,
C.
, and
Geer
,
D.
,
2011
, “
Effects of Shear on Proteins in Solution
,”
Biotechnol. Lett.
,
33
(
3
), pp.
443
456
.
35.
International Commission on Illumination
,
1978
,
Recommendations on Uniform Color Spaces, Color-Difference Equations, Psychometric Color Terms
,
CIE Publication
, Vienna, Austria.
36.
Paul
,
E. L.
,
Atiemo-Obeng
,
V. A.
, and
Kresta
,
S. M.
,
2004
,
Handbook of Industrial Mixing: Science and Practice
,
Wiley
, Hoboken, NJ.
37.
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
.
38.
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/
39.
Akhiezer
,
N. I.
,
1990
,
Elements of the Theory of Elliptic Functions
, Vol.
79
,
American Mathematical Society
, Providence, RI.
40.
Lee
,
S.
,
Lee
,
H.
,
Lee
,
I.
, and
Tseng
,
C.
,
2004
, “
Ink Diffusion in Water
,”
Eur. J. Phys.
,
25
(
2
), p.
331
.
41.
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
.
42.
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
.
43.
Banka
,
N.
, and
Devasia
,
S.
,
2013
, “
Nonlinear Models for Optimal Placement of Magnetically-Actuated Cilium
,”
ASME
Paper No. DSCC2013-3808.
You do not currently have access to this content.