The present study considers both the hydrodynamic and thermal characteristics of combined electroosmotic and pressure driven flow in a microannulus. Analytical solutions are presented using the Debye–Hückel linearization along with the uniform Joule heating and negligible viscous dissipation assumptions, whereas exact results are achieved numerically. Here, the range of validity for the Debye–Hückel linearization is found to be about two times of that for a parallel plate microchannel. Accordingly, this linearization may successfully be used to evaluate the potential and velocity distributions up to the zeta potentials of 100 mV, provided that the dimensionless Debye–Hückel parameter is above 10; nevertheless, the calculated wall shear stresses may be significantly different from the exact ones, even for lower zeta potentials. The viscous heating effects are found to be limited to low values of the dimensionless Debye–Hückel parameter. These effects are pronounced in the presence of a favorable pressure gradient, whereas the opposite is true for an opposed pressure gradient. Furthermore, the influence of increasing the annular geometry parameter, that is the inner to outer radii ratio, generally is to decrease both the inner and outer Nusselt numbers. It is also revealed that the pressure effects vanish at higher values of this parameter.

References

References
1.
Reuss
,
F. F.
, 1809, “
Charge-Induced Flow
,”
Proceedings of the Imperial Society of Naturalists of Moscow
, Vol.
3
, pp.
327
344
.
2.
Wang
,
X.
,
Wang
,
S.
,
Gendhar
,
B.
,
Cheng
,
C.
,
Byun
,
C. K.
,
Li
,
G.
,
Zhao
,
M.
, and
Liu
,
S.
, 2009, “
Electroosmotic Pumps for Microflow Analysis
,”
Trends Analyt. Chem.
,
28
, pp.
64
74
.
3.
Burgreen
,
D.
, and
Nakache
,
F. R.
, 1964, “
Electrokinetic Flow in Ultrafine Capillary
,”
J. Phys. Chem.
,
68
, pp.
1084
1091
.
4.
Rice
,
C. L.
, and
Whitehead
,
R.
, 1965, “
Electrokinetic Flow in a Narrow Cylindrical Capillary
,”
J. Phys. Chem.
,
69
, pp.
4017
4024
.
5.
Levine
,
S.
,
Marriott
,
J. R.
,
Neale
,
G.
, and
Epstein
,
N.
, 1975, “
Theory of Electrokinetic Flow in Fine Cylindrical Capillaries at High Zeta-Potentials
,”
J. Colloid Interface Sci.
,
52
, pp.
136
149
.
6.
Arulanandam
,
S.
, and
Li
,
D.
, 2000, “
Liquid Transport in Rectangular Microchannels by Electroosmotic Pumping
,”
Colloids Surf., A
,
161
, pp.
89
102
.
7.
Wang
,
C. Y.
,
Liu
,
Y. H.
, and
Chang
,
C. C.
, 2008, “
Analytical Solution of Electro-Osmotic Flow in a Semicircular Microchannel
,”
Phys. Fluids
,
20
, p.
063105
.
8.
Xuan
,
X.
, and
Li
,
D.
, 2005, “
Electroosmotic Flow in Microchannels With Arbitrary Geometry and Arbitrary Distribution of Wall Charge
,”
J. Colloid Interface Sci.
,
289
, pp.
291
303
.
9.
Talapatra
,
S.
, and
Chakraborty
,
S.
, 2008, “
Double Layer Overlap in AC Electroosmosis
,”
Eur. J. Mech. B/Fluids
,
27
, pp.
297
308
.
10.
Talapatra
,
S.
, and
Chakraborty
,
S.
, 2009, “
Squeeze-Flow Electroosmotic Pumping Between Charged Parallel Plates
,”
Int. J. Fluid Mech. Res.
,
36
, pp.
460
472
.
11.
Sharma
,
A.
, and
Chakraborty
,
S.
, 2008, “
Semi Analytical Solution of the Extended Graetz Problem for Combined Electroosmotically and Pressure Driven Microchannel Flows With Step Change in Wall Temperature
,”
Int. J. Heat Mass Transfer
,
51
, pp.
4875
4885
.
12.
Maynes
,
D.
, and
Webb
,
B. W.
, 2003, “
Fully Developed Electroosmotic Heat Transfer in Microchannels
,”
Int. J. Heat Mass Transfer
,
46
, pp.
1359
1369
.
13.
Maynes
,
D.
, and
Webb
,
B. W.
, 2004, “
The Effect of Viscous Dissipation in Thermally Fully Developed Electroosmotic Heat Transfer in Microchannels
,”
Int. J. Heat Mass Transfer
,
47
, pp.
987
999
.
14.
Liechty
,
B. C.
,
Webb
,
B. W.
, and
Maynes
,
R. D.
, 2005, “
Convective Heat Transfer Characteristics of Electro-Osmotically Generated Flow in Microtubes at High Wall Potential
,”
Int. J. Heat Mass Transfer
,
48
, pp.
2360
2371
.
15.
Iverson
,
B. D.
,
Maynes
,
D.
, and
Webb
,
B. W.
, 2004, “
Thermally Developing Electroosmotic Convection in Rectangular Microchannels With Vanishing Debye-Layer Thickness
,”
J. Thermophys. Heat Transfer
,
18
, pp.
486
493
.
16.
Broderick
,
S. L.
,
Webb
,
B. W.
, and
Maynes
,
D.
, 2005, “
Thermally Developing Electro-Osmotic Convection in Microchannels With Finite Debye-Layer Thickness
,”
Numer. Heat Transfer, Part A
,
48
, pp.
941
964
.
17.
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
, pp.
1979
1986
.
18.
Monazami
,
R.
, and
Manzari
,
M. T.
, 2007, “
Analysis of Combined Pressure-Driven Electroosmotic Flow Through Square Microchannels
,”
Microfluid. Nanofluid.
,
3
, pp.
123
126
.
19.
Horiuchi
,
K.
,
Dutta
,
P.
, and
Richards
,
C. D.
, 2007, “
Experiment and Simulation of Mixed Flows in a Trapezoidal Microchannel
,”
Microfluid. Nanofluid.
,
3
, pp.
347
358
.
20.
Waghmare
,
P. R.
, and
Mitra
,
S. K.
, 2008, “
Investigation of Combined Electro-Osmotic and Pressure-Driven Flow in Rough Microchannels
,”
J. Fluids Eng.
,
130
, p.
061204
.
21.
Chakraborty
,
S.
, 2006, “
Analytical Solutions of Nusselt Number for Thermally Fully Developed Flow in Microtubes Under a Combined Action of Electroosmotic Forces and Imposed Pressure Gradients
,”
Int. J. Heat Mass Transfer
,
49
, pp.
810
813
.
22.
Maynes
,
D.
, and
Webb
,
B. W.
, 2003, “
Fully-Developed Thermal Transport in Combined Pressure and Electro-Osmotically Driven Flow in Microchannels
,”
Trans. ASME J. Heat Transfer
,
125
, pp.
889
895
.
23.
Chen
,
C. H.
, 2009, “
Thermal Transport Characteristics of Mixed Pressure and Electro-Osmotically Driven Flow in Micro- and Nanochannels With Joule Heating
,”
Trans. ASME J. Heat Transfer
,
131
, p.
022401
.
24.
Garai
,
A.
, and
Chakraborty
,
S.
, 2009, “
Micro-Scale Thermo-Fluidic Transport in Two Immiscible Liquid Layers Subject to Combined Electroosmotic and Pressure-Driven Transport
,”
Int. J. Heat Mass Transfer
,
52
, pp.
2660
2666
.
25.
Liao
,
Q.
,
Zhu
,
X.
, and
Wen
,
T. Y.
, 2009, “
Thermal Effects on Mixed Electro-Osmotic and Pressure-Driven Flows in Triangle Microchannels
,”
Appl. Therm. Eng.
,
29
, pp.
807
814
.
26.
Sadeghi
,
A.
, and
Saidi
,
M. H.
, 2010, “
Viscous Dissipation Effects on Thermal Transport Characteristics of Combined Pressure and Electroosmotically Driven Flow in Microchannels
,”
Int. J. Heat Mass Transfer
,
53
, pp.
3782
3791
.
27.
Dey
,
R.
,
Chakraborty
,
D.
, and
Chakraborty
,
S.
, 2011, “
Analytical Solution for Thermally Fully Developed Combined Electroosmotic and Pressure-Driven Flows in Narrow Confinements With Thick Electrical Double Layers
,”
Trans. ASME J. Heat Transfer
,
133
, p.
024503
.
28.
Sadeghi
,
A.
,
Yavari
,
H.
,
Saidi
,
M. H.
, and
Chakraborty
,
S.
, 2011, “
Mixed Electroosmotically and Pressure Driven Flow With Temperature Dependent Properties
,”
J. Thermophys. Heat Transfer
,
25
, p.
432
442
.
29.
Jiang
,
L.
,
Mikkelsen
,
J.
,
Koo
,
J.
,
Huber
,
D.
,
Yao
,
S.
,
Zhang
,
L.
,
Zhou
,
P.
,
Maveety
,
J. G.
,
Prasher
,
R.
,
Santiago
,
J. G.
,
Kenny
,
T. W.
, and
Goodson
,
K. E.
, 2002, “
Closed-Loop Electroosmotic Microchannel Cooling System for VLSI Circuits
,”
IEEE Trans. Compon., Packag. Technol.
,
25
, pp.
347
355
.
30.
Eng
,
P. F.
,
Nithiarasu
,
P.
, and
Guy
,
O. J.
, 2010, “
An Experimental Study on an Electro-Osmotic Flow-Based Silicon Heat Spreader
,”
Microfluid. Nanofluid.
,
9
, pp.
787
795
.
31.
Al-Rjoub
,
M. F.
,
Roy
,
A. K.
,
Ganguli
,
S.
, and
Banerjee
,
R. K.
, 2011, “
Assessment of an Active-Cooling Micro-Channel Heat Sink Device, Using Electro-Osmotic Flow
,”
Int. J. Heat Mass Transfer
,
54
, pp.
4560
4569
.
32.
Jian
,
Y.
,
Yang
,
L.
, and
Liu
,
Q.
, 2010, “
Time Periodic Electro-Osmotic Flow Through a Microannulus
,”
Phys. Fluids
,
22
, p.
042001
.
33.
Tsao
,
H. K.
, 2000, “
Electroosmotic Flow Through an Annulus
,”
J. Colloid Interface Sci.
,
225
, pp.
247
250
.
34.
Kang
,
Y.
,
Yang
,
C.
, and
Huang
,
X.
, 2002, “
Electroosmotic Flow in a Capillary Annulus With High Zeta Potentials
,”
J. Colloid Interface Sci.
,
253
, pp.
285
294
.
35.
Park
,
H. M.
,
Lee
,
J. S.
, and
Kim
,
T. W.
, 2007, “
Comparison of the Nernst–Planck Model and the Poisson–Boltzmann Model for Electroosmotic Flows in Microchannels
,”
J. Colloid Interface Sci.
,
315
, pp.
731
739
.
36.
Probstein
,
R. F.
, 1994,
Physicochemical Hydrodynamics
, 2nd ed.,
Wiley
,
New York
.
37.
Yang
,
C.
,
Li
,
D.
, and
Masliyah
,
J. H.
, 1998, “
Modeling Forced Liquid Convection in Rectangular Microchannels With Electrokinetic Effects
,”
Int. J. Heat Mass Transfer
,
41
, pp.
4229
4249
.
38.
Karniadakis
,
G.
,
Beskok
,
A.
, and
Aluru
,
N.
, 2005,
Microflows and Nanoflows, Fundamentals and Simulation
,
Springer
,
New York
.
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