Mixing in a microfluidic device is a major challenge due to creeping flow, which is a significant roadblock for development of lab-on-a-chip device. In this study, an analytical model is presented to study the fluid flow behavior in a microfluidic mixer using time-periodic electro-osmotic flow. To facilitate mixing through microvortices, nonuniform surface charge condition is considered. A generalized analytical solution is obtained for the time-periodic electro-osmotic flow using a stream function technique. The electro-osmotic body force term is accounted as a slip boundary condition on the channel wall, which is a function of time and space. To demonstrate the applicability of the analytical model, two different surface conditions are considered: sinusoidal and step change in zeta potential along the channel surface. Depending on the zeta potential distribution, we obtained diverse flow patterns and vortices. The flow circulation and its structures depend on channel size, charge distribution, and the applied electric field frequency. Our results indicate that the sinusoidal zeta potential distribution provides elliptical shaped vortices, whereas the step change zeta potential provides rectangular shaped vortices. This analytical model is expected to aid in the effective micromixer design.
Issue Section:
Fundamental Issues and Canonical Flows
References
1.
Choi
, J. W.
, Oh
, K. W.
, Thomas
, J. H.
, Heineman
, W. R.
, Halsall
, H. B.
, Nevin
, J. H.
, Helmicki
, A. J.
, Henderson
, H. T.
, and Ahn
, C. H.
, 2002
, “An Integrated Microfluidic Biochemical Detection System for Protein Analysis With Magnetic Bead-Based Sampling Capabilities
,” Lab Chip
, 2
(1
), pp. 27
–30
.2.
Wei
, C. W.
, Young
, T. H.
, and Cheng
, J. Y.
, 2005
, “Electroosmotic Mixing Induced by Non-Uniform Zeta Potential and Application for DNA Microarray in Microfluidic Channel
,” Biomed. Eng.: Appl., Basis Commun.
, 17
(6
), pp. 281
–283
.3.
Dittrich
, P. S.
, and Manz
, A.
, 2006
, “Lab-on-a-Chip: Microfluidics in Drug Discovery
,” Nat. Rev. Drug Discovery
, 5
(3
), pp. 210
–218
.4.
Nandigana
, V. V. R.
, and Aluru
, N. R.
, 2013
, “Nonlinear Electrokinetic Transport Under Combined AC and DC Fields in Micro/Nanofluidic Interface Devices
,” ASME J. Fluids Eng.
, 135
(2
), p. 021201.5.
Huh
, D.
, Gu
, W.
, Kamotani
, Y.
, Grotberg
, J. B.
, and Takayama
, S.
, 2005
, “Microfluidics for Flow Cytometric Analysis of Cells and Particles
,” Physiol. Meas.
, 26
(3
), pp. R73
–R98
.6.
Bhatt
, K. H.
, Grego
, S.
, and Velev
, O. D.
, 2005
, “An AC Electrokinetic Technique for Collection and Concentration of Particles and Cells on Patterned Electrodes
,” Langmuir
, 21
(14
), pp. 6603
–6612
.7.
Perozziello
, G.
, 2017
, “Nanoplasmonic and Microfluidic Devices for Biological Sensing
,” Nano-Optics: Principles Enabling Basic Research and Applications. NATO Science for Peace and Security Series B: Physics and Biophysics
, B.
Di Bartolo
, J
Collins
, and L.
Silvestri
, eds., Springer
, Dordrecht
, The Netherlands, pp. 247
–274
.8.
Sajeesh
, P.
, and Sen
, A. K.
, 2014
, “Particle Separation and Sorting in Microfluidic Devices: A Review
,” Microfluid. Nanofluid.
, 17
(1
), pp. 1
–52
.9.
Hossan
, M. R.
, Dutta
, D.
, Islam
, N.
, and Dutta
, P.
, 2018
, “Review: Electric Field Driven Pumping in Microfluidic Device
,” Electrophoresis
, 39
(5–6
), pp. 702
–731
.10.
Capretto
, L.
, Cheng
, W.
, Hill
, M.
, and Zhang
, X.
, 2011
, “Micromixing Within Microfluidic Devices
,” Microfluidics. Topics in Current Chemistry
, Vol. 304
, B.
Lin
, ed., Springer
, Berlin
, pp. 27
–68
.11.
Chen
, C. H.
, and Santiago
, J. G.
, 2002
, “A Planar Electroosmotic Micropump
,” J. Microelectromech. Syst.
, 11
(6
), pp. 672
–683
.12.
Lemoff
, A. V.
, and Lee
, A. P.
, 2000
, “An AC Magnetohydrodynamic Micropump
,” Sens. Actuators B
, 63
(3
), pp. 178
–185
.13.
Wang
, P.
, Chen
, Z. L.
, and Chang
, H. C.
, 2006
, “A New Electro-Osmotic Pump Based on Silica Monoliths
,” Sens. Actuators B
, 113
(1
), pp. 500
–509
.14.
Vanlintel
, H. T. G.
, Vandepol
, F. C. M.
, and Bouwstra
, S.
, 1988
, “A Piezoelectric Micropump Based on Micromachining of Silicon
,” Sens. Actuators
, 15
(2
), pp. 153
–167
.15.
Gobby
, D.
, Angeli
, P.
, and Gavriilidis
, A.
, 2001
, “Mixing Characteristics of T-Type Microfluidic Mixers
,” J. Micromech. Microeng.
, 11
(2
), pp. 126
–132
.16.
Lin
, C. H.
, Fu
, L. M.
, and Chien
, Y. S.
, 2004
, “Microfluidic T-Form Mixer Utilizing Switching Electroosmotic Flow
,” Anal. Chem.
, 76
(18
), pp. 5265
–5272
.17.
Wu
, Z. M.
, and Li
, D. Q.
, 2008
, “Micromixing Using Induced-Charge Electrokinetic Flow
,” Electrochim. Acta
, 53
(19
), pp. 5827
–5835
.18.
Sudarsan
, A. P.
, and Ugaz
, V. M.
, 2006
, “Multivortex Micromixing
,” Proc. Natl. Acad. Sci. U. S. A.
, 103
(19
), pp. 7228
–7233
.19.
Mengeaud
, V.
, Josserand
, J.
, and Girault
, H. H.
, 2002
, “Mixing Processes in a Zigzag Microchannel: Finite Element Simulations and Optical Study
,” Anal. Chem.
, 74
(16
), pp. 4279
–4286
.20.
Liu
, R. H.
, Yang
, J. N.
, Pindera
, M. Z.
, Athavale
, M.
, and Grodzinski
, P.
, 2002
, “Bubble-Induced Acoustic Micromixing
,” Lab Chip
, 2
(3
), pp. 151
–157
.21.
Lu
, L. H.
, Ryu
, K. S.
, and Liu
, C.
, 2002
, “A Magnetic Microstirrer and Array for Microfluidic Mixing
,” J. Microelectromech. Syst.
, 11
(5
), pp. 462
–469
.22.
Chang
, C. C.
, and Yang
, R. J.
, 2007
, “Electrokinetic Mixing in Microfluidic Systems
,” Microfluid. Nanofluid.
, 3
(5
), pp. 501
–525
.23.
Wang
, Y.
, Zhe
, J.
, Dutta
, P.
, and Chung
, B. T.
, 2007
, “A Microfluidic Mixer Utilizing Electrokinetic Relay Switching and Asymmetric Flow Geometries
,” ASME J. Fluids Eng.
, 129
(4
), pp. 395
–403
.24.
Green
, N. G.
, Ramos
, A.
, Gonzalez
, A.
, Morgan
, H.
, and Castellanos
, A.
, 2000
, “Fluid Flow Induced by Nonuniform AC Electric Fields in Electrolytes on Microelectrodes—I: Experimental Measurements
,” Phys. Rev. E
, 61
(4
), pp. 4011
–4018
.25.
Song
, H. J.
, Cai
, Z. L.
, Noh
, H.
, and Bennett
, D. J.
, 2010
, “Chaotic Mixing in Microchannels Via Low Frequency Switching Transverse Electroosmotic Flow Generated on Integrated Microelectrodes
,” Lab Chip
, 10
(6
), pp. 734
–740
.26.
Oddy
, M. H.
, Santiago
, J. G.
, and Mikkelsen
, J. C.
, 2001
, “Electrokinetic Instability Micromixing
,” Anal. Chem.
, 73
(24
), pp. 5822
–5832
.27.
Biddiss
, E.
, Erickson
, D.
, and Li
, D. Q.
, 2004
, “Heterogeneous Surface Charge Enhanced Micromixing for Electrokinetic Flows
,” Anal. Chem.
, 76
(11
), pp. 3208
–3213
.28.
Dutta
, P.
, and Beskok
, A.
, 2001
, “Analytical Solution of Time Periodic Electroosmotic Flows: Analogies to Stokes' Second Problem
,” Anal. Chem.
, 73
(21
), pp. 5097
–5102
.29.
Erickson
, D.
, and Li
, D. Q.
, 2003
, “Analysis of Alternating Current Electroosmotic Flows in a Rectangular Microchannel
,” Langmuir
, 19
(13
), pp. 5421
–5430
.30.
Moghadam
, A. J.
, 2013
, “Exact Solution of AC Electro-Osmotic Flow in a Microannulus
,” ASME J. Fluids Eng.
, 135
(9
), p. 091201.31.
Anderson
, J. L.
, and Keith Idol
, W.
, 1985
, “Electroosmosis Through Pores With Nonuniformly Charged Walls
,” Chem. Eng. Commun.
, 38
(3–6
), pp. 93
–106
.32.
Horiuchi
, K.
, Dutta
, P.
, and Ivory
, C. F.
, 2007
, “Electroosmosis With Step Changes in Zeta Potential in Microchannels
,” AIChE J.
, 53
(10
), pp. 2521
–2533
.33.
Ng
, C. O.
, and Chen
, B.
, 2013
, “Dispersion in Electro-Osmotic Flow Through a Slit Channel With Axial Step Changes of Zeta Potential
,” ASME J. Fluids Eng.
, 135
(10
), p. 101203.34.
Chu
, H. C. W.
, and Ng
, C. O.
, 2012
, “Electroosmotic Flow Through a Circular Tube With Slip-Stick Striped Wall
,” ASME J. Fluids Eng.
, 134
(11
), p. 111201.35.
Potoček
, B.
, Gaš
, B.
, Kenndler
, E.
, and Štědrý
, M.
, 1995
, “Electroosmosis in Capillary Zone Electrophoresis With Non-Uniform Zeta Potential
,” J. Chromatogr. A
, 709
(1
), pp. 51
–62
.36.
Lee
, J. S. H.
, Ren
, C. L.
, and Li
, D. Q.
, 2005
, “Effects of Surface Heterogeneity on Flow Circulation in Electroosmotic Flow in Microchannels
,” Anal. Chim. Acta
, 530
(2
), pp. 273
–282
.37.
Chang
, C. C.
, and Yang
, R. J.
, 2006
, “A Particle Tracking Method for Analyzing Chaotic Electroosmotic Flow Mixing in 3D Microchannels With Patterned Charged Surfaces
,” J. Micromech. Microeng.
, 16
(8
), pp. 1453
–1462
.38.
Tomotika
, S.
, 1935, “On the Instability of a Cylindrical Thread of a Viscous Liquid Surrounded by Another Viscous Fluid
,” Proc. R. Soc. Lond. A
, 150
(870), pp. 322
–337
.39.
Datta
, S.
, and Choudhary
, J. N.
, 2013
, “Effect of Hydrodynamic Slippage on Electro-Osmotic Flow in Zeta Potential Patterned Nanochannels
,” Fluid Dyn. Res.
, 45
(5
), p. 055502.40.
Schonecker
, C.
, Baier
, T.
, and Hardt
, S.
, 2014
, “Influence of the Enclosed Fluid on the Flow Over a Microstructured Surface in the Cassie State
,” J. Fluid Mech.
, 740
, pp. 168
–195
.41.
Chen
, J. K.
, Weng
, C. N.
, and Yang
, R. J.
, 2009
, “Assessment of Three AC Electroosmotic Flow Protocols for Mixing in Microfluidic Channel
,” Lab Chip
, 9
(9
), pp. 1267
–1273
.42.
Herr
, A. E.
, Molho
, J. I.
, Santiago
, J. G.
, Mungal
, M. G.
, Kenny
, T. W.
, and Garguilo
, M. G.
, 2000
, “Electroosmotic Capillary Flow With Nonuniform Zeta Potential
,” Anal. Chem.
, 72
(5
), pp. 1053
–1057
.43.
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
.44.
Panton
, R. L.
, 2006
, Incompressible Flow
, 3rd ed., Wiley
, New York
, Chap. 11.45.
Moghadam
, A. J.
, 2012
, “An Exact Solution of AC Electro-Kinetic-Driven Flow in a Circular Micro-Channel
,” Eur. J. Mech. B Fluids
, 34
, pp. 91
–96
.Copyright © 2019 by ASME
You do not currently have access to this content.
