The electrostatic double layer (EDL) effect on the linear hydrodynamic stability of microchannel flows is investigated. It is shown that the EDL destabilizes the Poiseuille flow considerably. The critical Reynolds number decreases by a factor five when the non-dimensional Debye-Huckel parameter κ is around ten. Thus, the transition may be quite rapid for microchannels of a couple of microns heights in particular when the liquid contains a very small number of ions. The EDL effect disappears quickly for κ150 corresponding typically to channels of heights 400 μm or larger. These results may explain why significantly low critical Reynolds numbers have been encountered in some experiments dealing with microchannel flows.

1.
Gad-el-Hak
,
M.
,
1999
, “
The Fluid Mechanics of Microdevices
,”
J. Fluids Eng.
,
121
, pp.
5
33
.
2.
Tardu, S., 2003, “Transferts thermiques dans les microcanaux,” Traite´ EGEM, Tome 6 Ch. 6, Microfluidique, 36p., Herme`s.
3.
Peng
,
X. F.
,
Peterson
,
G. P.
, and
Wang
,
B. X.
,
1994
, “
Heat Transfer Characteristics of Water Flowing through Microchannels
,”
Exp. Heat Transfer
,
7
,
265
283
.
4.
Wang
,
B. X.
, and
Peng
,
X. F.
,
1994
, “
Experimental Investigation on Liquid Forced Convection Heat Transfer through Microchannels
,”
Int. J. Heat Mass Transfer
,
37
,
73
82
.
5.
Ren
,
L.
,
Qu
,
W.
, and
Li
,
D.
,
2001
, “
Interfacial Electrokinetic Effects on Liquid Flow in Microchannels
,”
Int. J. Heat Mass Transfer
,
44
,
3125
3134
.
6.
Mala
,
G. M.
,
Li
,
D.
, and
Dale
,
J. D.
,
1997
, “
Heat Transfer and Fluid Flow in Microchannels
,”
Int. J. Heat Mass Transfer
,
40
(
13
),
3079
3088
.
7.
Von Kerczek
,
C. H.
,
1982
, “
The Instability of Oscillatory Poiseuille Flow
,”
J. Fluid Mech.
,
116
,
91
114
.
8.
Orszag
,
S. A.
,
1971
, “
Accurate Solution of Orr-Somerfeld Stability Equation
,”
J. Fluid Mech.
,
50
,
689
703
.
9.
Grosch
,
C. E.
, and
Salwen
,
H.
,
1968
, “
The Stability of Steady and Time-dependent Plane Poiseuille Flow
,”
J. Fluid Mech.
,
34
, pp.
177
205
.
10.
Drazin, P. G., and Reid, W. H., 1981, Hydrodynamic Stability, Cambridge University Press, Cambridge, UK, pp. 370–464.
11.
Orszag
,
S. A.
, and
Patera
,
A. T.
,
1983
, “
Secondary Instability of Wall-Bounded Shear Flows
,”
J. Fluid Mech.
,
128
, pp.
347
385
.
12.
Henningson
,
D. S.
, and
Kim
,
J.
,
1991
, “
On Turbulent Spots in Plane Poiseuille Flow
,”
J. Fluid Mech.
,
228
, pp.
183
205
.
13.
Itoh
,
N.
,
1974
, “
Spatial Growth of Finite Wave Disturbances in Parallel and Nearly Parallel Flows. Part 1: The Theoretical Analysis and the Numerical Results for Plane Poiseuille Flow
,”
Transactions of the Japan Society of Aeronautics and Space Sciences
,
17
,
160
174
.
14.
Stuart
,
J. T.
,
1960
, “
On the Nonlinear Mechanics of Wave Disturbances in Stable and Unstable Parallel Flows. Part 1: The Basic Behavior in Plane Poiseuille Flow
,”
J. Fluid Mech.
,
9
,
353
370
.
15.
Mala
,
G. M.
, and
Li
,
D.
,
1999
, “
Flow Characteristics of Water in Microtubes
,”
Int. J. Heat Fluid Flow
,
20
,
142
148
.
16.
Yang
,
C.
, and
Li
,
D.
,
1997
, “
Electrokinetic Effects on Pressure-driven Liquid Flows in Rectangular Microchannels
,”
J. Colloid Interface Sci.
,
194
,
95
107
.
17.
Yang
,
C.
, and
Li
,
D.
,
1998
, “
Analysis of Electrokinetic Effects on the Liquid Flow in Rectangular Microchannels
,”
Colloids Surf.
,
143
,
339
353
.
18.
Gao
,
P.
,
Le Person
,
S.
, and
Favre Marinet
,
M.
,
2002
, “
Scale effects on Hydrodynamics and Heat Transfer in Two-Dimensional Mini and Microchannels
,”
Int. J. Therm. Sci.
,
41
, p.
10
10
.
19.
Qu
,
W.
,
Mala
,
G. M.
,
Li
,
D.
,
2000
, “
Pressure-driven Water Flows in Trapezoidal Silicon Microchannels
,”
Int. J. Heat Mass Transfer
,
43
,
353
364
.
You do not currently have access to this content.