This article models the dynamics of cilia-based devices (soft cantilever-type, vibrating devices that are excited by external vibrations) for mixing and manipulating liquids in microfluidic applications. The main contribution of this article is to develop a model, which shows that liquid sloshing and the added-mass effect play substantial roles in generating large-amplitude motion of the cilia. Additionally, experimental mixing results, with and without cilia, are comparatively evaluated to show more than one order-of-magnitude reduction in the mixing time with the use of cilia.

References

References
1.
Miller
,
C. E.
, 1968, “
The Kinematics and Dynamics of Ciliary Fluid Systems
,”
J. Exp. Biol.
,
49
, pp.
617
629
.
2.
Sleigh
,
M. A.
, 1974,
Cilia and Flagella
,
Academic
,
New York
.
3.
Brennen
,
C.
, 1974, “
An Oscillating-Boundary-Layer Theory for Ciliary Propulsion
,”
J. Fluid Mech.
,
65
(
4
), pp.
799
824
.
4.
Tuck
,
E. O.
, 1968, “
A Note on a Swimming Problem
,”
J. Fluid Mech.
,
31
, pp.
305
308
.
5.
Ramia
,
M.
,
Tullock
,
D. L.
, and
Phanthien
,
N.
, 1993, “
The Role of Hydrodynamic Interaction in the Locomotion of Microorganisms
,”
Biophys. J.
,
65
, pp.
755
778
.
6.
Gueron
,
S.
, and
Levit-Gurevich
,
K.
, 1998, “
Computation of the Internal Forces in Cilia: Application to Ciliary Motion, the Effects of Viscosity, and Cilia Interactions
,”
Biophys. J.
,
74
, pp.
1658
1676
.
7.
Bovender
,
C. R.
, 1977, “
Nasal Filter
,” U.S. Patent No. 4052983.
8.
Ataka
,
M.
,
Omodaka
,
A.
,
Takeshima
,
N.
, and
Fujita
,
H.
, 1993, “
Fabrication and Operation of Polyimide Bimorph Actuators for a Ciliary Motion Ssystem
,”
J. Microelectromech. Syst.
,
2
(
4
), pp.
146
150
.
9.
Chen
,
Z.
,
Shatara
,
S.
, and
Tan
,
X. B.
, 2010, “
Modeling of Biomimetic Robotic Fish Propelled by an Ionic PolymerMmetal Composite Caudal Fin
,”
IEEE/ASME Trans. Mechatron.
,
15
(
3
), pp.
448
459
.
10.
Behkam
,
B.
, and
Sitti
,
M.
, 2006, “
Design Methodology for Biomimetic Propulsion of Miniature Swimming Robots
,”
ASME J. Dyn. Syst. Meas. Control
,
128
(
1
), pp.
36
43
.
11.
Alvarado
,
P. V. Y.
, and
Youcef-Toumi
,
K.
, 2006, “
Design of Machines With Compliant Bodies for Biomimetic Locomotion in Liquid Environments
,”
ASME J. Dyn. Syst. Meas. Control
,
128
(
1
), pp.
3
13
.
12.
Saif
,
M. T. A.
,
Alaca
,
B. E,
and
Sehitoglu
,
H.
, 1999, “
Analytical Modeling of Electrostatic Membrane Actuator for Micro Pumps
,”
IEEE J. Microelectromech. Syst.
,
8
(
3
), pp.
335
345
.
13.
Oh
,
K.
,
Chung
,
J.-H.
,
Devasia
,
S.
, and
Riley
,
J. J.
, 2009, “
Bio-Mimetic Silicone Cilia for Microfluidic Manipulation
,”
Lab Chip
,
9
(
11
), pp.
1561
1566
.
14.
Khatavkar
,
V. V.
,
Anderson
,
P. D.
,
den Toonder
,
J. M. J.
, and
Meijer
,
H. E. H.
, 2007, “
Active Micromixer Based on Artificial Cilia
,”
Phys. Fluids
,
19
(
8
),
083605
.
15.
Dreyfus
,
R.
,
Baudry
,
J.
,
Roper
,
M. L.
,
Fermigier
,
M.
,
Stone
,
H. A.
, and
Bibette
,
J.
, 2005, “
Microscopic Artificial Swimmers
,”
Nature (London)
,
437
(7060), pp.
862
865
.
16.
Hill
,
D. E.
, and
Baumgarten
,
J. R.
, 1992, “
Control of Spin-Stabilized Spacecraft With Sloshing Fluid Stores
,”
ASME J. Dyn. Syst., Meas., Control
,
114
(
4
), pp.
728
731
.
17.
Ibrahim
,
R. A.
, 2005,
Liquid Sloshing Dynamics: Theory and Applications
,
Cambridge University
,
New York
.
18.
Stokes
,
G. G.
, 1850, “
On the Effect of the Internal Friction of Fluids on the Motion of Pendulums
,”
Trans. Cambridge Philos. Soc.
,
9
(
2
), pp.
8
106
.
19.
Ferrers
,
N. M.
, ed., 1970, Green’s paper on “ Researches on the Vibration of Pendulums in Fluid Media,” from the Transactions of the Royal Society of Edinburgh, 1833, Mathematical Papers of George Green, Chelsea Publishing, New York.
20.
Lindholm
,
U. S.
,
Kana
,
D. D.
,
Chu
,
W.-H.
, and
Abramson
,
H. N.
, 1965, “
Elastic Vibration Characteristics of Cantilever Plates in Water
,”
J. Ship Res.
,
9
, pp.
11
22
.
21.
Landau
,
L. D.
, and
Lifshitz
,
E. M.
, 1987, “
Fluid Mechanics
,”
Course of Theoretical Physics
,
2nd ed.
,
Pergamon
,
New York
, Sec. 24, Vol.
6
.
22.
Stroock
,
A. D.
,
Dertinger
,
S. K. W.
,
Ajdari
,
A.
,
Mezic
,
I.
,
Stone
,
H. A.
, and
Whitesides
,
G. M.
, 2002, “
Chaotic Mixer for Microchannels
,”
Science
,
295
(5555), pp.
647
651
.
23.
Yaralioglu
,
G. G.
,
Wygant
,
I. O.
,
Marentis
,
T. C.
, and Khuri-
Yakub
,
B. T.
, 2004, “
Ultrasonic Mixing in Microfluidic Channels Using Integrated Transducers
,”
Anal. Chem.
,
76
,
3694
3698
.
24.
Hawkes
,
J. J.
,
Barber
,
R. W.
,
Emerson
,
D. R.
, and
Coakley
,
W. T.
, 2004, “
Continuous Cell Washing and Mixing Driven by an Ultrasound Standing Wave Within a Microfluidic Channel
,”
Lab Chip
,
4
(
5
), pp.
446
452
.
25.
Grumann
,
M.
,
Geipe
,
A.
,
Riegger
,
L.
,
Zengerle
,
R.
, and
Ducree
,
J.
, 2005, “
Batch-Mode Mixing on Centrifugal Microfluidic Platforms
,”
Lab Chip
,
5
(
5
), pp.
560
565
.
26.
Herrmann
,
M.
,
Veres
,
T.
, and
Tabrizian
,
M.
, 2006, “
Enzymatically-Generated Fluorescent Detection in Micro-Channels with Internal Magnetic Mixing for the Development of Parallel Microfluidic Elisa
,”
Lab Chip
,
6
(
4
), pp.
555
560
.
27.
Vilfan
,
M.
,
Potočnik
,
A.
,
Kavčič
,
B.
,
Osterman
,
N.
,
Poberaj
,
I.
,
Vilfan
,
A.
, and
Babič
,
D.
, 2010, “
Self-Assembled Artificial Cilia
,”
Proc. Natl. Acad. Sci. U.S.A.
,
107
(
5
), pp.
1844
1847
.
28.
Sader
,
J. E.
,
Chon
,
J. W. M.
, and
Mulvaney
,
P
, 2000,“
Experimental Validation of Theoretical Models for the Frequency Response of Atomic Force Microscope Cantilever Beams Immersed in Fluids
,”
J. Appl. Phys.
,
87
(
8
), pp.
3978
3988
.
29.
Zhang
,
W.
, and
Turner
,
K.
, 2007, “
Frequency Dependant Fluid Damping of Micro/Nano Flexural Resonators: Experiment, Model and Analysis
,”
Sens. Actuators, A
,
137
, pp.
594
599
.
30.
Wang
,
K.-L.
, and
Jones
T.B.
, 2005, “
Electrowetting Dynamics of Microfluidic Actuation
,”
Langmuir
,
21
(
9
), pp.
4211
4217
.
31.
Hosseini
,
M. K. A.
,
Omidi
,
O.
,
Meghdari
,
A.
, and
Vossoughi
,
G.
, 2006, “
A Composite Rigid Body Algorithm for Modeling and Simulation of an Underwater Vehicle Equipped with Manipulator Arms
,”
J. Offshore Mech. Arct. Eng.
,
128
, pp.
119
132
.
32.
Kongthon
,
J.
,
Mckay
,
B.
,
Iamratanakul
,
D.
,
Oh
,
K.
,
Chung
,
J.-H.
,
Riley
,
J. J.
, and
Devasia
,
S.
2010, “
Added-Mass Effect in Modeling of Cilia-Based Devices for Microfluidic Systems
,”
J. Vib. Acoust.
,
132
,
024501
.
33.
Inman
D. J.
, 2001,
Engineering Vibration
,
2nd ed.
,
Prentice-Hall
,
New Jersey
.
34.
Yum
,
K.
,
Wang
,
Z.
,
Suryavanshi
,
A. P.
, and
Yu
,
M. F.
, 2004, “
Experimental Measurement and Model Analysis of Damping Effect in Nanoscale Mechanical Beam Resonators in Air
,”
J. Appl. Phys.
,
96
(
7
), pp.
3933
3938
.
35.
Zhang
,
C.
,
Xu
G.
, and
Jiang
,
Q.
, 2003, “
Analysis of the Air-Damping Effect on a Micromachined Beam Resonator
,”
Math. Mech. Solids
,
8
, pp.
315
325
.
36.
Blevins
R. D.
, 1977,
Flow-Induced Vibration
,
Van Nostrand Reinhold Company
,
New York
.
37.
Sumer
,
B. M.
, and
Fredsoe
,
J.
, 2006,“
Hydrodynamics Around Cylindrical Structures
,”
Advanced Series on Ocean Engineering
,
World Scientific
,
New Jersey
, Vol.
26
,
revised ed.
38.
Mitra
,
S.
, and
Sinhamahapatra
,
K. P.
, 2007, “
Slosh Dynamics of Liquid-Filled Containers With Submerged Components Using Pressure-Based Finite Element Method
,”
J. Sound Vib.
,
304
(
1-2
), pp.
361
381
.
39.
Nise
,
N. S,
2004,
Control Systems Engineering
,
4th ed.
,
Wiley
,
Hoboken, NJ
.
40.
Oh
,
K.
,
Smith
,
B.
,
Devasia
,
S.
,
Riley
,
J. J.
, and Chung, J.-H., 2010, “
Characterization of Mixing Performance for Bio-Mimetic Silicone Cilia
,”
Microfluid. Nanofluid.
,
9
, pp.
645
655
.
41.
Jeon
,
N. L.
,
Dertinger
,
S. K. W.
,
Chiu
,
D. T.
,
Choi
,
I. S.
,
Stroock
,
A. D.
, and
Whitesides
,
G. M.
, 2000, “
Generation of Solution and Surface Gradients Using Microfluidic Systems
,”
Langmuir
,
16
, pp.
8311
8316
.
You do not currently have access to this content.