The friction numbers for laminar flows of water in microtubes, determined from the temperature rise due to the viscous dissipation heating assuming a velocity slip, show a strong dependence on the diameter and aspect ratio. The calculated values compare well with those determined from experimental data for water flows in glass and diffused silica microtubes (16101μm in diameter D and aspect ratios LD=4991479). With a slip, the friction number almost exponentially decreases as D decreases and, to a lesser extent, as LD increases. For D>400μm, the friction number approaches the theoretical Hagen–Poiseuille for macrotubes (64) when LD>1500, but higher values at smaller LD. The developed semiempirical analytical expression for calculating the friction number is in good agreement with the numerical and experimental results. The results suggest the presence of a velocity slip in the experiments and the plausible presence of a thin nanolayer at the walls of the microtubes. For D>200μm, this layer, if exists, is estimated to be 18.9nm, but increases to 21.5nm for D<200μm, when R¯e=800 and LD=1479.

1.
Celata
,
G. P.
, 2006, personal communications,
ENEA Institute of Thermal Fluid Dynamics
, Rome, Italy, Oct.
2.
Celata
,
G. P.
,
Cumo
,
M.
,
McPhail
,
S.
, and
Zummo
,
G.
, 2006, “
Characterization of Fluid Dynamic Behavior and Channel Wall Effects in Microtubes
,”
Int. J. Heat Fluid Flow
0142-727X,
27
, pp.
135
143
.
3.
Rands
,
C.
,
Webb
,
B. W.
, and
Maynes
,
D.
, 2006, “
Characterization of Transition to Turbulence in Microchannels
,”
Int. J. Heat Mass Transfer
0017-9310,
49
, pp.
2924
2930
.
4.
Shah
,
R. K.
, and
London
,
A. L.
, 1978,
Laminar Flow Forced Convection in Ducts: A Source Book for Compact Heat Exchanger Analytical Data
,
Academic
,
New York
.
5.
Xu
,
B.
,
Ooi
,
K. T.
,
Wong
,
N. T.
, and
Choi
,
W. K.
, 2000, “
Experimental Investigation of Flow Friction for Liquid Flow in Microchannels
,”
Int. Commun. Heat Mass Transfer
0735-1933,
27
(
8
), pp.
1165
1176
.
6.
Kandilkar
,
S. G.
,
Joshi
,
S.
, and
Tian
,
S.
, 2003, “
Effect of Surface Roughness on Heat Transfer and Fluid Fllow Characteristics at Low Reynolds Numbers in Small Diameter Tubes
,”
Heat Transfer Eng.
0145-7632,
24
, pp.
4
16
.
7.
Lelea
,
D.
,
Nishio
,
S.
, and
Takano
,
K.
, 2004, “
The Experimental Research on Microtube Heat Transfer and Fluid Flow of Distilled Water
,”
Int. J. Heat Mass Transfer
0017-9310,
47
,
2817
2830
.
8.
Qu
,
W.
,
Mala
,
Gh. M.
, and
Dongqing
,
L.
, 2000, “
Pressure-Driven Water Flows in Trapezoidal Silicon Microchannels
,”
Int. J. Heat Mass Transfer
0017-9310,
43
, pp.
353
364
.
9.
Churchill
,
S. W.
, 1977, “
Friction-Factor Equation Spans All Fluid-Flow Regimes
,”
Chem. Eng. J.
0300-9467,
84
, pp.
91
92
.
10.
Judy
,
J.
,
Maynes
,
D.
, and
Webb
,
B. W.
, 2002, “
Characterization of Frictional Pressure Drop for Liquid Flows Through Microchannels
,”
Int. J. Heat Mass Transfer
0017-9310,
45
, pp.
3477
3489
.
11.
Baudry
,
J.
,
Charlaix
,
E.
,
Tonck
,
A.
, and
Mazuyer
,
D.
, 2001, “
Experimental Evidence for a Large Slip Effect at a Nonwetting Fluid-Solid Interface
,”
Langmuir
0743-7463,
17
, pp.
5232
5236
.
12.
Andrienko
,
D.
,
Dunweg
,
B.
, and
Vinogradova
,
O. I.
, 2003, “
Boundary Slip as a Result of a Prewetting Transition
,”
J. Chem. Phys.
0021-9606,
119
, pp.
13106
13113
.
13.
Bonaccurso
,
E.
,
Butt
,
H.-J.
, and
Craig
,
V. S. J.
, 2003, “
Surface Roughness and Hydrodynamic Boundary Slip of a Newtonian Fluid in a Completely Wetting System
,”
Phys. Rev. Lett.
0031-9007,
90
(
14
), pp.
144501
.
14.
Neto
,
C.
,
Evans
,
D. R.
,
Bonaccurso
,
E.
,
Butt
,
H.-J.
, and
Craig
,
V. S. J.
, 2005, “
Boundary Slip in Newtonian Liquids: A Review of Experimental Studies
,”
Rep. Prog. Phys.
0034-4885,
68
, pp.
2859
2897
.
15.
Tretheway
,
D. C.
, and
Meinhart
,
C. D.
, 2004, “
A Generating Mechanism for Apparent Fluid Slip in Hydrophobic Microchannels
,”
Phys. Fluids
1070-6631,
16
(
5
), pp.
1509
1515
.
16.
Gad-el-Hak
,
M.
, 1999, “
The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture
,”
ASME J. Fluids Eng.
0098-2202,
121
, pp.
5
33
.
17.
Cieplak
,
M.
,
Koplik
,
J.
, and
Banavar
,
J. R.
, 2001, “
Boundary Conditions at a Fluid-Solid Interface
,”
Phys. Rev. Lett.
0031-9007,
86
(
5
), pp.
803
806
.
18.
Craig
,
V. S. J.
,
Neto
,
C.
, and
Williams
,
D. R. M.
, 2001, “
Shear-Dependent Boundary Slip in an Aqueous Newtonian Liquid
,”
Phys. Rev. Lett.
0031-9007,
87
(
5
),
054504
.
19.
Nagayama
,
G.
, and
Cheng
,
P.
, 2004, “
Effects of Interface Wettability on Microscale Flow by Molecular Dynamics Simulation
,”
Int. J. Heat Mass Transfer
0017-9310,
47
, pp.
501
513
.
20.
Zhu
,
Y.
, and
Granick
,
S.
, 2001, “
Rate-Dependent Slip of Newtonian Liquid at Smooth Surfaces
,”
Phys. Rev. Lett.
0031-9007,
87
(
9
),
096105
.
21.
Zhu
,
Y. X.
, and
Granick
,
S.
, 2002, “
Limits of the Hydrodynamic No-Slip Boundary Condition
,”
Phys. Rev. Lett.
0031-9007,
88
(
10
),
106102
.
22.
Maxwell
,
J. C.
, 1879, “
On Stresses in Rarefied Gases Arising From Inequalities of Temperature
,”
Philos. Trans. R. Soc. London
0370-2316,
170
,
231
256
.
23.
Watanabe
,
K.
,
Udagawa
,
Y.
, and
Udagawa
,
H.
, 1999, “
Drag Reduction of Newtonian Fluid in a Circular Pipe With a Highly Water-Repellent Wall
,”
J. Fluid Mech.
0022-1120,
381
, pp.
225
238
.
24.
Morini
,
G. L.
, 2005, “
Viscous Heating in Liquid Flows in Micro-Channels
,”
Int. J. Heat Mass Transfer
0017-9310,
48
, pp.
3637
3647
.
25.
Jiang
,
X. N.
,
Zhou
,
Z. Y.
,
Huang
,
X. Y.
, and
Liu
,
C. Y.
, 1997, “
Laminar Flow Through Microchannels Used for Microscale Cooling Systems
,”
Proceedings IEEE/CPMT Electronic Packaging Technology Conference
, pp.
119
122
.
26.
Sharp
,
K. V.
, and
Adrian
,
R. J.
, 2004, “
Transition From Laminar to Turbulent Flow in Liquid Filled Microtubes
,”
Exp. Fluids
0723-4864,
36
, pp.
741
747
.
27.
Wu
,
H. Y.
, and
Cheng
,
P.
, 2003, “
Friction Factors in Smooth Trapezoidal Silicon Microchannels With Different Aspect Ratios
,”
Int. J. Heat Mass Transfer
0017-9310,
46
, pp.
2519
2525
.
28.
Weilin
,
Q.
,
Mala
,
G. M.
, and
Dongqing
,
L.
, 2000, “
Pressure-Driven Water Flows in Trapezoidal Silicon Microchannels
,”
Int. J. Heat Mass Transfer
0017-9310,
43
, pp.
353
364
.
29.
Pfund
,
D.
,
Rector
,
D.
,
Shekarriz
,
A.
,
Popescu
,
A.
, and
Welty
,
J.
, 2000, “
Pressure Drop Measurements in a Microchannel
,”
AIChE J.
0001-1541,
46
(
8
), pp.
1496
1507
.
30.
Park
,
H.
,
Pak
,
J. J.
,
Son
,
S. Y.
,
Lim
,
G.
, and
Song
,
I.
, 2003, “
Fabrication of a Microchannel Integrated With Inner Sensors and the Analysis of Its Laminar Flow Characteristics
,”
Sens. Actuators, A
0924-4247,
103
, pp.
317
329
.
31.
Hsieh
,
S.-S.
,
Lin
,
C.-Y.
,
Huang
,
C.-F.
, and
Tsai
,
H.-H.
, 2004, “
Liquid Flow in a Micro-Channel
,”
J. Micromech. Microeng.
0960-1317,
14
, pp.
436
445
.
32.
Hao
,
P.-F.
,
He
,
F.
, and
Zhu
,
K.-Q.
, 2005, “
Flow Characteristics in a Trapezoidal Silicon Microchannel
,”
J. Micromech. Microeng.
0960-1317,
15
, pp.
1362
1368
.
33.
Hetsroni
,
G.
,
Mosyak
,
A.
,
Pogrebnyak
,
E.
, and
Yarin
,
L. P.
, 2005, “
Fluid Flow in Micro-Channels
,”
Int. J. Heat Mass Transfer
0017-9310,
48
, pp.
1982
1998
.
34.
Li
,
Z.-X.
,
Du
,
D.-X.
, and
Guo
,
Z.-Y.
, 2003, “
Experimental Study on Flow Characteristics of Liquid in Circular Microtubes
,”
Microscale Thermophys. Eng.
1089-3954,
7
, pp.
253
265
.
You do not currently have access to this content.