The development of microfluidics platforms in recent years has led to an increase in the number of applications involving the flow of multiple immiscible layers of viscous electrolyte fluids. In this study, numerical results as well as analytic equations for velocity and shear stress profiles were derived for N layers with known viscosities, assuming steady laminar flow in a microchannel driven by pressure and/or electro-static (Coulomb) forces. Numerical simulation results, using a commercial software package, match analytical results for fully-developed flow. Entrance flow effects with centered fluid-layer shrinking were studied as well. Specifically, cases with larger viscosities in the inner layers show a very good agreement with experimental correlations for the dimensionless entrance length as a function of inlet Reynolds number. However, significant deviations may occur for multilayer flows with smaller viscosities in the inner layers. A correlation was deduced for the two-layer electroosmotic flow and the pressure driven flow, both being more complex when compared with single-layer flows. The impact of using power-law fluids on resulting velocity profiles has also been explored and compared to Newtonian fluid flows. The present model readily allows for an exploration of the impact of design choices on velocity profiles, shear stress, and channel distribution in multilayer microchannel flows as a function of layered viscosity distribution and type of driving force.

References

1.
Ganan-Calvo
,
A. M.
,
Gonzalez-Prieto
,
R.
,
Riesco-Chueca
,
P.
,
Herrada
,
M. A.
, and
Flores-Mosquera
,
M.
, 2007, “
Focusing Capillary Jets Close to the Continuum Limit
,”
Nat. Phys.
,
3
(
10
), pp.
737
742
.
2.
Okushima
,
S.
,
Nisisako
,
T.
,
Torri
,
T.
, and
Higuchi
,
T.
, 2004, “
Controlled Production of Monodisperse Double Emulsions by Two-Step Droplet Breakup in Microfluidic Devices
,”
Langmuir
,
20
(
23
), pp.
9905
9908
.
3.
Ward
,
T.
,
Faivre
,
M.
,
Abkarian
,
M.
, and
Stone
,
H. A.
, 2005, “
Microfluidic Flow Focusing: Drop Size and Scaling in Pressure Versus Flow-Rate-Driven Pumping
,”
Electrophoresis
,
26
(
19
), pp.
3716
3724
.
4.
Zheng
,
B.
,
Tice
,
J. D.
,
Roach
,
L. S.
, and
Ismagilov
,
R. F.
, 2004, “
A Droplet-Based, Composite PDMS/Glass Capillary Microfluidic System for Evaluating Protein Crystallization Conditions by Microbatch and Vapor-Diffusion Methods with On-Chip X-ray Diffraction
,”
Angew. Chem., Int. Ed.
,
43
(
19
), pp.
2508
2511
.
5.
Garstecki
,
P.
,
Gitlin
,
I.
,
Diluzio
,
W.
,
Whitesides
,
G. M.
,
Kumacheva
,
E.
, and
Stone
,
H. A.
,.2004, “
Formation of Monodisperse Bubbles in a Microfluidic Flow-Focusing Device
,”
Appl. Phys. Lett.
,
85
(
13
), pp.
2649
2651
.
6.
Hettiarachchi
,
K.
,
Lee
,
A. P.
,
Zhang
,
S.
,
Feingold
,
S.
, and
Dayton
,
P.A.
, 2009, “
Controllable Microfluidic Synthesis of Multiphase Drug-Carrying Lipospheres for Site-Targeted Therapy
,”
Biotechnol. Prog.
,
25
(
4
), pp.
938
945
.
7.
Chen
,
C. H.
,
Shah
,
R. K.
,
Abate
,
A. R.
, and
Weitz
,
D. A.
, 2009, “
Janus Particles Template from Double Emulsion Droplets Generated Using Microfluidics
,”
Langmuir
,
25
(
8
), pp.
4320
4323
.
8.
Guillot
,
P.
,
Moulin
,
T.
,
Kotitz
,
R.
,
Guirardel
,
M.
,
Dodge
,
A.
,
Joanicot
,
M.
,
Colin
,
A.
,
Bruneau
,
C. H.
, and
Colin
,
T.
, 2008, “
Towards a Continuous Microfluidic Rheometer
,”
Microfluid. Nanofluid.
,
5
(
5
), pp.
619
630
.
9.
Gunther
,
A.
, and
Jensen
,
K. F.
, 2006, “
Multiphase Microfluidic: From Flow Characteristics to Chemical and Materials Synthesis
,”
Lab Chip
,
6
(
12
), pp.
1487
1503
.
10.
Kobayashi
,
J.
,
Mori
,
Y.
,
Okamoto
,
K.
,
Akiyama
,
R.
,
Ueno
,
M.
,
Kitamori
,
T.
, and
Kobayashi
,
S.
, 2004, “
A Microfluidic Device for Conducting Gas-Liquid-Solid Hydrogenation Reactions
,”
Science
,
304
(
5675
), pp.
1305
1308
.
11.
Maruyama
,
T.
,
Matsushita
,
H.
,
Uchida
,
J.
,
Kubota
,
F.
,
Kamiya
,
N.
, and
Goto
,
M.
, 2004, “
Liquid Membrane Operations in a Microfluidic Device for Selective Separation of Metal Ions
,”
Anal. Chem.
,
76
(
15
), pp.
4495
4500
.
12.
Maruyama
,
T.
,
Uchida
,
J.
,
Ohkawa
,
T.
,
Futami
,
T.
,
Katayama
,
K.
,
Nishizawa
,
K.
,
Sotowa
,
K.
,
Kubota
,
F.
,
Kamiyaa
,
N.
, and
Goto
,
M.
, 2003, “
Enzymatic Degradation of p-Chlorophenol in a Two-Phase Flow Microchannel System
,”
Lab Chip
,
3
(
4
), pp.
308
312
.
13.
Surmerian
,
M.
,
Slyadnev
,
M. N.
,
Hisamoto
,
H.
,
Hibara
,
A.
,
Uchiyama
,
K.
, and
Kitamori
,
T.
, 2002, “
Three-Layer Flow Membrane System on a Microchip for Investigation of Molecular Transport
,”
Anal. Chem.
,
74
(
9
), pp.
2014
2020
.
14.
Zhao
,
B.
,
Viernes
,
N. O. L.
,
Moore
,
J. S.
, and
Beebe
,
D. J.
2002, “
Control and Applications of Immiscible Liquids in Microchannels
,”
J. Am. Chem. Soc.
,
124
(
19
), pp.
5284
5285
.
15.
Soohoo
,
J. R.
, and
Walker
,
G. M.
, 2009, “
Microfluidic Aqueous Two Phase System for Leukocyte Concentration from Whole Blood
,”
Biomedical Microdevices
,
11
(
2
), pp.
323
329
.
16.
Wang
,
F.
,
Wang
,
H.
,
Wang
,
J.
,
Wang
,
H. Y.
,
Rummel
,
P. L.
,
Garimella
,
S. V.
, and
Lu
,
C.
, 2008, “
Microfluidic Delivery to Small Molecules into Mammalian Cells Based on Hydrodynamic Focusing
,”
Biotechnol. Bioeng.
,
100
(
1
), pp.
150
158
.
17.
Takayama
,
S.
,
Ostuni
,
E.
,
LeDuc
,
P.
,
Naruse
,
K.
,
Ingber
,
D. E.
, and
Whitesides
,
G. M.
, 2003, “
Selective Chemical Treatment of Cellular Microdomains Using Multiple Laminar Streams
,”
Chem. Biol.
,
10
(
2
), pp.
123
130
.
18.
Kleinstreuer
,
C.
, 2010,
Modern Fluid Dynamics: Basic Theory and Selected Applications in Macro- and Micro-Devices
(
Springer, Dordrecht
,
The Netherlands
).
19.
Dutta
,
P.
, and
Beskok
,
A.
, 2001, “
Analytical Solution of Combined Electroosmotic/Pressure Driven Flows in Two-Dimensional Straight Channels: Finite Debye Layer Effects
,”
Anal. Chem.
,
73
(
9
), pp.
1979
1986
.
20.
Gao
,
Y.
,
Wang
,
C.
,
Wong
,
T. N.
,
Nguyen
,
N. T.
, and
Ooi
,
K.T.
, 2007, “
Electro-Osmotic Control of the Interface Position of Two-Liquid Flow Through a Microchannel
,”
Journal of Micromechanics and Microengineering
,
17
, pp.
358
366
.
21.
Gao
,
Y.
,
Wong
,
T. N.
,
Yang
,
C.
, and
Ooi
,
K.T.
, 2005, “
Two-Fluid Electroosmotic Flow in Microchannels
,”
J. Colloid. Int. Sci.
,
284
, pp.
306
314
.
22.
Li
,
H.
,
Wong
,
T. N.
, and
Nguyen
,
N -T.
, 2010, “
Time –dependent Model of Mixed Electroosmotic/Pressure-Driven Three Immiscible Fluids in a Rectangular Microchannel
,”
Int. J. Heat Mass Trans.
,
53
, pp.
772
785
.
23.
Nguyen
,
N -T.
, and
Wereley
,
S. T.
, 2006,
Fundamentals and Applications of Microfluidics
(
Artech House
,
Boston, London
).
24.
Kirby
,
B. J.
, 2010,
Micro and Nanoscale Fluid Mechanics-Transport in Microfluidic Devices and Nanoscale Fluid Mechanics-Transport in Microfluidic Devices
(
Cambridge University
,
Cambridge
).
25.
Arkinson
,
B.
,
Brocklebank
,
M. P.
,
Card
,
C. C.
, and
Smith
,
J. M.
, 1969, “
Low Reynolds Number Developing Flows
,”
AIChE J.
,
15
(
4
), pp.
548
553
.
26.
Chen
,
R.-Y.
, 1973, “
Flow in the Entrance Region at Low Reynolds Numbers
,”
ASME J. Fluids Eng.
,
95
, pp.
153
158
.
27.
Gu
,
Y.
, and
Li
,
D.
, 1997, “
An Electrical Suspension Method for Measuring the Electric Charge on Small Silicon Oil Droplets Dispersed in Aqueous Solutions
,”
J. Colloid Int. Sci.
,
195
, pp.
343
352
.
28.
Gu
,
Y.
, and
Li
,
D.
, 1998, “
The ξ-Potential of Silicone Oil Droplets Dispersed in Aqueous Solutions
,”
J. Colloid Interface Sci.
,
206
, pp.
346
349
.
29.
Li
,
H.
,
Wong
,
T. N.
, and
Nguyen
,
N -T.
, 2009, “
Electroosmotic Control of Width and Position of Liquid Streams in Hydrodynamic Focusing
,”
Microfluid. Nanofluid.
,
7
, pp.
489
497
.
You do not currently have access to this content.