A viscous flow through a long two-dimensional channel, one wall of which is formed by a finite-length membrane, experiences flow limitation when the channel is highly collapsed over a narrow region under high external pressure. Simple approximate relations between flow rate and pressure drop are obtained for this configuration by the use of matched asymptotic expansions. Weak inertial effects are also considered.

1.
Jensen
O. E.
,
1997
, “
The thin liquid lining of a weakly curved cylindrical tube
,”
J. Fluid Mech.
, Vol.
331
, pp.
373
403
.
2.
Jones
A. F.
, and
Wilson
S. D. R.
,
1978
, “
The film drainage region in droplet coalescence
,”
J. Fluid Mech.
, Vol.
87
, pp.
263
288
.
3.
Kamm
R. D.
, and
Pedley
T. J.
,
1989
, “
Flow in collapsible tubes: a brief review
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
111
, pp.
177
179
.
4.
Lowe
T. W.
, and
Pedley
T. J.
,
1995
, “
Computation of Stokes flow in a channel with a collapsible segment
,”
J. Fluids Struct.
, Vol.
9
, pp.
885
905
.
5.
Luo
X.-Y.
, and
Pedley
T. J.
,
1995
, “
A numerical simulation of steady flow in a 2-D collapsible channel
,”
J. Fluids Struct.
, Vol.
9
, pp.
149
174
.
6.
Luo
X.-Y.
, and
Pedley
T. J.
,
1996
, “
A numerical simulation of unsteady flow in a two-dimensional collapsible channel
,”
J. Fluid Mech.
, Vol.
314
, pp.
191
225
.
7.
Pedley
T. J.
,
1992
, “
Longitudinal tension variation in collapsible channels: a new mechanism for the breakdown of steady flow
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
114
, pp.
60
67
.
8.
Rast
M. P.
,
1994
, “
Simultaneous solution of the Navier-Stokes and elastic membrane equations by a finite element method
,”
Int. J. Numer. Methods Fluids
, Vol.
19
, pp.
1115
1135
.
9.
Wilson, T. A., Rodarte, J. R., and Butler, J. P., 1986, “Wave-speed and viscous flow limitation,” Hdb. Physl. Respir., Pt. 1, Sec. 3, Vol. 3, pp. 55–61.
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