Abstract

Using intrinsic coordinates, the slip flow in a minute meandering channel is studied by perturbation about the small ratio of curvature to inverse half gap width. The exact solution for an annulus shows this ratio can be as large as 0.5 with less than 1% error. Velocity slip on the walls and the pressure drop depend on the slip factor. Formula for the pressure drop in a channel with a single bend is derived.

References

1.
Nguyen
,
N. T.
, and
Wereley
,
S. T.
,
2006
,
Fundamentals and Applications of Microfluidics
, 2nd ed.,
Artech House
,
Boston, MA
.
2.
White
,
F. M.
,
2006
,
Viscous Fluid Flow
, 3rd ed.,
McGraw-Hill
,
New York
.
3.
Wang
,
C. Y.
,
2003
, “
Flow Over a Surface With Parallel Grooves
,”
Phys. Fluids
,
15
(
5
), pp.
1114
1121
.10.1063/1.1560925
4.
Wang
,
C. Y.
,
2002
, “
Low Reynolds Number Slip Flow in a Curved Rectangular Duct
,”
ASME J. Appl. Mech.
,
69
(
2
), pp.
189
194
.10.1115/1.1445142
5.
Wang
,
C. Y.
,
2003
, “
Slip Flow in a Curved Tube
,”
ASME J. Fluids Eng.
,
125
(
3
), pp.
443
446
.10.1115/1.1567309
6.
Wang
,
C. Y.
,
2016
, “
Ritz Method for Slip Flow in Curved Microducts and Application to the Elliptic Duct
,”
Meccanica
,
51
(
5
), pp.
1069
1076
.10.1007/s11012-015-0288-8
7.
Wang
,
C. Y.
,
2011
, “
On Stokes Slip Flow Through a Transversely Wavy Channel
,”
Mech. Res. Commun.
,
38
(
3
), pp.
249
254
.10.1016/j.mechrescom.2011.02.006
8.
Kawaguti
,
M.
,
1969
, “
Numerical Study of the Flow of a Viscous Fluid on a Curved Channel
,”
Phys. Fluids
,
12
(
12
), pp.
11
101
.10.1063/1.1692420
9.
Zhang
,
L.
, and
Potherat
,
A.
,
2013
, “
Influence of the Geometry on the Two- and Three Dimensional Dynamics of the Flow in a 180 Deg Sharp Bend
,”
Phys. Fluids
,
25
(
5
), p.
053605
.10.1063/1.4807070
10.
Khuri
,
S. A.
, and
Wang
,
C. Y.
,
1997
, “
Stokes Flow Around a Bend
,”
Q. Appl. Math.
,
55
(
3
), pp.
573
600
.10.1090/qam/1466150
11.
Goldstein
,
S.
,
1965
,
Modern Developments in Fluid Dynamics
, Vol.
1
,
Dover
,
Mineola, NY
, Chap.
4
.
12.
Wang
,
C. Y.
,
1980
, “
Flow in Narrow Curved Channels
,”
ASME J. Appl. Mech.
,
47
(
1
), pp.
7
10
.10.1115/1.3153642
13.
Van Dyke
,
M.
,
1983
, “
Laminar Flow in a Meandering Channel
,”
SIAM J. Appl. Math.
,
43
(
4
), pp.
696
702
.10.1137/0143047
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