A modified Ritz method for solving nonuniform slip flow in a duct is applied to the semicircular duct and the isosceles triangular duct. These ducts are important in microfluidics. Detailed flow fields and Poiseuille numbers show the large effects of nonuniform slip. A rare exact solution for the semicircular duct with nonzero slip is also found.

References

References
1.
Nguyen
,
N. T.
, and
Wereley
,
S. T.
,
2006
,
Fundamentals and Applications of Microfluidics
, 2nd ed.,
Artech House
,
Boston, MA
.
2.
Seo
,
C. T.
,
Bae
,
C. H.
,
Eun
,
D. S.
,
Shin
,
J. K.
, and
Lee
,
J. H.
,
2004
, “
Fabrication of Circular Type Microchannel Using Photoresist Reflow and Isotropic Etching for Microfluidic Devices
,”
Jap. J. Appl. Phys.
,
43
(
11A
), pp.
7773
7776
.
3.
Yu
,
H. B.
, and
Zhou
,
G. Y.
,
2013
, “
Deformable Mold Based on-Demand Microchannel Fabrication Technology
,”
Sens. Actuators B: Chem.
,
183
, pp.
40
45
.
4.
Pekas
,
N.
,
Zhang
,
Q.
,
Nannini
,
M.
, and
Juncker
,
D.
,
2010
, “
Wet Etching of Structures With Straight Facets and Adjustable Taper Into Glass Substrates
,”
Lab Chip
,
10
(
4
), pp.
494
498
.
5.
Sharipov
,
F.
, and
Seleznev
,
V.
,
1988
, “
Data on Internal Rarefied Gas Flows
,”
J. Phys. Chem. Ref. Data
,
27
(
3
), pp.
657
706
.
6.
Choi
,
C. H.
, and
Kim
,
C. J.
,
2006
, “
Large Slip of Aqueous Liquid Flow Over a Nanoengineered Superhydrophobic Surface
,”
Phys. Rev. Lett.
,
96
(
6
), p.
066001
.
7.
Varoutis
,
S.
,
Naris
,
S.
,
Hauer
,
V.
,
Day
,
C.
, and
Valougeorgis
,
D.
,
2009
, “
Experimental and Computational Investigation of Gas Flows Through Long Channels of Various Cross Sections in the Whole Range of the Knudsen Number
,”
J. Vac. Sci. Tech. A
,
27
(
1
), pp.
89
100
.
8.
Struchtrup
,
H.
, and
Taheri
,
P.
,
2011
, “
Macroscopic Transport Models for Rarefied Gas Flow- a Brief Review
,”
IMA J. Appl. Math.
,
76
(
5
), pp.
672
697
.
9.
Ng
,
C. O.
, and
Wang
,
C. Y.
,
2010
, “
Apparent Slip Arising From Stokes Shear Flow Over a Bidirectional Patterned Surface
,”
Microfluid. Nanofluid.
,
8
(
3
), pp.
361
371
.
10.
Duan
,
Z.
, and
Muzychka
,
Y. S.
,
2007
, “
Sip Flow in Non-Circular Microchannels
,”
Microfluid. Nanofluid.
,
3
(
4
), pp.
473
484
.
11.
Hooman
,
K.
,
2008
, “
A Superposition Approach to Study Slip Flow Forced Convection in Straight Microchannels of Uniform but Arbitrary Cross Section
,”
Int. J. Heat Mas Trans.
,
51
(
15–16
), pp.
3753
3762
.
12.
Bahrami
,
M.
,
Tamayol
,
A.
, and
Taheri
,
P.
,
2009
, “
Slip- Flow Pressure Drop in Microchannels of General Cross Section
,”
ASME J. Fluids Eng.
,
131
(
3
), p.
031201
.
13.
Wang
,
C. Y.
,
2012
, “
Brief Review of Exact Solutions in Ducts and Channels
,”
ASME J. Fluids Eng.
,
134
(
9
), p.
094501
.
14.
Jang
,
J.
, and
Kim
,
Y. H.
,
2010
, “
Gaseous Slip Flow of a Rectangular Microchannel With Nonuniform Slip Boundary Conditions
,”
Microfluid. Nanofluid.
,
9
(
2–3
), pp.
513
522
.
15.
Sparrow
,
E. M.
, and
Siegel
,
R.
,
1959
, “
A Variational Method for Fully Developed Laminar Heat Transfer in Ducts
,”
ASME J. Heat Transfer
,
81
, pp.
157
167
.
16.
Banerjee
,
S.
, and
Hadaller
,
G. I.
,
1973
, “
Longitudinal Laminar Flow Between Cylinders Arranged in a Rectangular Array by a Variational Technique
,”
ASME J. Appl. Mech.
,
40
(
4
), pp.
1136
1138
.
17.
Wang
,
C. Y.
,
2014
, “
Ritz Method for Slip Flow in Super-Elliptic Ducts
,”
Eur. J. Mech./B Fluids
,
43
, pp.
85
89
.
18.
Rektorys
,
K.
,
1972
,
Variational Methods in Mathematics, Science and Engineering
,
Academic Press
,
New York
.
19.
Lei
,
Q. M.
, and
Trupp
,
A. C.
,
1989
, “
Maximum Velocity Location and Pressure Drop of Fully Developed Laminar Flow in Circular Sector Ducts
,”
ASME J. Heat Transfer
,
111
(
4
), pp.
1085
1087
.
20.
Wang
,
C. Y.
,
2003
, “
Slip Flow in a Triangular Duct- an Exact Solution
,”
Z. Angew. Math. Mech.
,
83
(
9
), pp.
629
631
.
You do not currently have access to this content.