Passive pumping using gravity-driven flow is a fascinating approach for microfluidic systems. When designing a passive pumping system, generated flow rates should be known precisely. While reported models used to estimate the flow rates do not usually consider capillary forces, this paper shows that their exclusion is unrealistic in typical gravity-driven systems. Therefore, we propose a new analytical model to estimate the generated flow rates. An extensive set of measurements is used to verify that the proposed model provides a remarkably more precise approximation of the real flow rates compared to the previous models. It is suggested that the developed model should be used when designing a gravity-driven pumping system.
Issue Section:
Flows in Complex Systems
References
1.
Young
, E. W. K.
, and Beebe
, D. J.
, 2010
, “Fundamentals of Microfluidic Cell Culture in Controlled Microenvironments
,” Chem. Soc. Rev.
, 39
(3
), pp. 1036
–1048
.10.1039/b909900j2.
Berthier
, E.
, and Beebe
, D. J.
, 2007
, “Flow Rate Analysis of a Surface Tension Driven Passive Micropump
,” Lab Chip
, 7
(11
), pp. 1475
–1478
.10.1039/b707637a3.
Resto
, P. J.
, Mogen
, B. J.
, Berthier
, E.
, and Williams
, J. C.
, 2010
, “An Automated Microdroplet Passive Pumping Platform for High-Speed and Packeted Microfluidic Flow Applications
,” Lab Chip
, 10
(1
), pp. 23
–26
.10.1039/b917147a4.
Dimov
, I. K.
, Kijanka
, G.
, Park
, Y.
, Ducrée
, J.
, Kang
, T.
, and Lee
, L. P.
, 2011
, “Integrated Microfluidic Array Plate (iMAP) for Cellular and Molecular Analysis
,” Lab Chip
, 11
(16
), pp. 2701
–2710
.10.1039/c1lc20105k5.
Kim
, T.
, and Cho
, Y.-H.
, 2011
, “A Pumpless Cell Culture Chip With the Constant Medium Perfusion-Rate Maintained by Balanced Droplet Dispensing
,” Lab Chip
, 11
(10
), pp. 1825
–1830
.10.1039/c1lc20234k6.
Kim
, T.
, Doh
, I.
, and Cho
, Y.-H.
, 2012
, “On-Chip Three-Dimensional Tumor Spheroid Formation and Pump-Less Perfusion Culture Using Gravity-Driven Cell Aggregation and Balanced Droplet Dispensing
,” Biomicrofluidics
, 6
(3
), p. 034107
.10.1063/1.47394607.
Sung
, J. H.
, Kam
, C.
, and Shuler
, M. L.
, 2010
, “A Microfluidic Device for a Pharmacokinetic–Pharmacodynamic (PK–PD) Model on a Chip
,” Lab Chip
, 10
(4
), pp. 446
–455
.10.1039/b917763a8.
Zhu
, X.
, Chu
, L. Y.
, Chueh
, B.-H.
, Shen
, M.
, Hazarika
, B.
, Phadke
, N.
, and Takayama
, S.
, 2004
, “Arrays of Horizontally Oriented Mini-Reservoirs Generate Steady Microfluidic Flows for Continuous Perfusion Cell Culture and Gradient Generation
,” Analyst
, 129
(11
), pp. 1026
–1031
.10.1039/b407623k9.
Gao
, Y.
, Sun
, J.
, Lin
, W.-H.
, Webb
, D. J.
, and Li
, D.
, 2012
, “A Compact Microfluidic Gradient Generator Using Passive Pumping
,” Microfluid. Nanofluid.
, 12
(6
), pp. 887
–895
.10.1007/s10404-011-0908-010.
Chen
, S.-Y. C.
, Hung
, P. J.
, and Lee
, P. J.
, 2011
, “Microfluidic Array for Three-Dimensional Perfusion Culture of Human Mammary Epithelial Cells
,” Biomed. Microdevices
, 13
(4
), pp. 753
–758
.10.1007/s10544-011-9545-311.
Sun
, K.
, Wang
, Z.
, and Jiang
, X.
, 2008
, “Modular Microfluidics for Gradient Generation
,” Lab Chip
, 8
(9
), pp. 1536
–1543
.10.1039/b806140h12.
Lam
, E. W.
, Cooksey
, G. A.
, Finlayson
, B. A.
, and Folch
, A.
, 2006
, “Microfluidic Circuits With Tunable Flow Resistances
,” Appl. Phys. Lett.
, 89
(16
), p. 164105
.10.1063/1.236393113.
Song
, H.
, Wang
, Y.
, and Pant
, K.
, 2011
, “System-Level Simulation of Liquid Filling in Microfluidic Chips
,” Biomicrofluidics
, 5
(2
), p. 024107
.10.1063/1.358984314.
Oh
, K. W.
, Lee
, K.
, Ahn
, B.
, and Furlani
, E. P.
, 2012
, “Design of Pressure-Driven Microfluidic Networks Using Electric Circuit Analogy
,” Lab Chip
, 12
(3
), pp. 515
–545
.10.1039/c2lc20799k15.
Berthier
, J.
, and Silberzan
, P.
, 2010
, Microfluidics for Biotechnology
, Artech House
, Norwood, MA
.16.
Solovitz
, S. A.
, and Mainka
, J.
, 2011
, “Manifold Design for Micro-Channel Cooling With Uniform Flow Distribution
,” ASME J. Fluids Eng.
, 133
(5
), p. 051103
.10.1115/1.400408917.
Galvis
, E.
, Yarusevych
, S.
, and Culham
, J. R.
, 2012
, “Incompressible Laminar Developing Flow in Microchannels
,” ASME J. Fluids Eng.
, 134
(1
), p. 014503
.10.1115/1.400573618.
Bruus
, H.
, 2008
, Theoretical Microfluidics
, Oxford University Press Inc.
, New York
.19.
Fuerstman
, M. J.
, Lai
, A.
, Thurlow
, M. E.
, Shevkoplyas
, S. S.
, Stone
, H. A.
, and Whitesides
, G. M.
, 2007
, “The Pressure Drop Along Rectangular Microchannels Containing Bubbles
,” Lab Chip
, 7
(11
), pp. 1479
–1489
.10.1039/b706549c20.
Kang
, S.-W.
, and Banerjee
, D.
, 2011
, “Modeling and Simulation of Capillary Microfluidic Networks Based on Electrical Analogies
,” ASME J. Fluids Eng.
, 133
(5
), p. 054502
.10.1115/1.400409221.
Duffy
, D. C.
, McDonald
, J. C.
, Schueller
, O. J. A.
, and Whitesides
, G. M.
, 1998
, “Rapid Prototyping of Microfluidic Systems in Poly(Dimethylsiloxane)
,” Anal. Chem.
, 70
(23
), pp. 4974
–4984
.10.1021/ac980656z22.
Xiong
, R
., 2011
, “Fluid Flow in Trapezoidal Silicon Microchannels With 3D Random Rough Bottoms
,” ASME J. Fluids Eng.
, 133
(3
), p. 031102
.10.1115/1.400342323.
Akbari
, M.
, Sinton
, D.
, and Bahrami
, M.
, 2009
, “Pressure Drop in Rectangular Microchannels as Compared With Theory Based on Arbitrary Cross Section
,” ASME J. Fluids Eng.
, 131
(4
), p. 041202
.10.1115/1.307714324.
Lynn
, N. S.
, and Dandy
, D. S.
, 2009
, “Passive Microfluidic Pumping Using Coupled Capillary/Evaporation Effects
,” Lab Chip
, 9
(23
), pp. 3422
–3429
.10.1039/b912213c25.
Waghmare
, P. R.
, and Mitra
, S. K.
, 2010
, “Finite Reservoir Effect on Capillary Flow of Microbead Suspension in Rectangular Microchannels
,” J. Colloid Interface Sci.
, 351
(2
), pp. 561
–569
.10.1016/j.jcis.2010.08.03926.
Waghmare
, P. R.
, and Mitra
, S. K.
, 2012
, “A Comprehensive Theoretical Model of Capillary Transport in Rectangular Microchannels
,” Microfluid. Nanofluid.
, 12
(1–4
), pp. 53
–63
.10.1007/s10404-011-0848-827.
Chen
, C.-C.
, 2010
, “Modeling and Analysis of Bump Effect on Capillary Flow Through Microchannels
,” Int. Commun. Heat Mass Transfer
, 37
(9
), pp. 1321
–1325
.10.1016/j.icheatmasstransfer.2010.07.00228.
Gervais
, L.
, Hitzbleck
, M.
, and Delamarche
, E.
, 2011
, “Capillary-Driven Multiparametric Microfluidic Chips for One-Step Immunoassays
,” Biosens. Bioelectron.
, 27
(1
), pp. 64
–70
.10.1016/j.bios.2011.06.016Copyright © 2015 by ASME
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