We analyze the liquid-liquid displacement in capillary tubes. The goal is to determine the amount of displaced liquid that remains attached to the tube wall and the configuration of the liquid-liquid interface at different operating parameters. The study encompasses both numerical and experimental approaches. The finite element method is used to solve the governing equations and, in order to validate the predictions, visualization experiments are performed to capture images of the interface. The numerical results were obtained for the assumption of negligible inertia, and the effects of viscosity ratio and capillary number are investigated. The predictions and experimental observations are in good agreement.

1.
Tsai
,
T. M.
, and
Miksis
,
M. J.
,
1994
, “
Dynamics of a Drop in a Constricted Capillary Tube
,”
J. Fluid Mech.
,
292
, pp.
197
217
.
2.
Olbricht
,
W. L.
, and
Kung
,
D. M.
,
1992
, “
The Deformation and Breakup of Liquid Drops in Low Reynolds Number Flow Through a Capillary
,”
Phys. Fluids A
,
4
(
7
), pp.
1347
1354
.
3.
Martinez
,
M. J.
, and
Udell
,
K. S.
,
1990
, “
Axisymmetric Creeping Motion of Drops Through Circular Tubes
,”
J. Fluid Mech.
,
210
, pp.
565
591
.
4.
Westborg
,
H.
, and
Hassager
,
O.
,
1989
, “
Creeping Motion of Long Bubbles and Drops in Capillary Tubes
,”
J. Colloid Interface Sci.
,
133
(
1
), pp.
135
147
.
5.
Olbricht
,
W. L.
,
1996
, “
Pore-Scale Prototypes of Multiphase Flow in Porous Media
,”
Annu. Rev. Fluid Mech.
,
28
, pp.
187
213
.
6.
Stark
,
J.
, and
Manga
,
M.
,
2000
, “
The Motion of Long Bubbles in a Network of Tubes
,”
Transp. Porous Media
,
40
, pp.
201
218
.
7.
Fairbrother
,
F.
, and
Stubbs
,
A. E.
,
1935
, “
Studies in Electroendosmosis. Part VI. The Bubble-Tube Methods of Measurement
,”
J. Chem. Soc.
,
1
, pp.
527
529
.
8.
Taylor
,
G. I.
,
1961
, “
Deposition of a Viscous Fluid on the Wall of a Tube
,”
J. Fluid Mech.
,
10
, pp.
161
165
.
9.
Cox
,
B. G.
,
1962
, “
On Driving a Viscous Fluid Out of a Tube
,”
J. Fluid Mech.
,
14
, pp.
81
96
.
10.
Bretherton
,
F. P.
,
1961
, “
The Motion of Long Bubbles in Tubes
,”
J. Fluid Mech.
,
10
, pp.
166
188
.
11.
Giavedoni
,
M. D.
, and
Saita
,
F. A.
,
1997
, “
The Axisymmetric and Plane Cases of a Gas Phase Steadily Displacing a Newtonian Liquid: A Simultaneous Solution of the Governing Equations
,”
Phys. Fluids
,
9
, pp.
2420
2428
.
12.
Lee
,
A. G.
,
Shaqfeh
,
E. S. G.
, and
Khomami
,
B.
,
2002
, “
A Study of Viscoelastic Free Surface Flows by the Finite Element Method: Hele-Shaw and Slot Coating Flows
,”
J. Non-Newtonian Fluid Mech.
,
108
, pp.
327
362
.
13.
Goldsmith
,
H. L.
, and
Mason
,
S. G.
,
1963
, “
The Flow of Suspensions Through Tubes
,”
J. Colloid Sci.
,
18
, pp.
237
261
.
14.
Teletzke
,
G. F.
,
Davis
,
H. T.
, and
Scriven
,
L. E.
,
1988
, “
Wetting Hydrodynamics
,”
Rev. Phys. Appl.
,
23
, pp.
989
1007
.
15.
Petitjeans
,
P.
, and
Maxworthy
,
T.
,
1996
, “
Miscible Displacements in Capillary Tubes
,”
J. Fluid Mech.
,
326
, pp.
37
56
.
16.
de Santos, J. M., 1991, Two-Phase Cocurrent Downflow Through Constricted Pas-Sages, PhD thesis, University of Minnesota.
17.
Chen
,
C.
, and
Meiburg
,
E.
,
1996
, “
Miscible Displacements in Capillary Tubes. Part 2. Numerical Simulation
,”
J. Fluid Mech.
,
326
, pp.
57
90
.
18.
Cox
,
B. G.
,
1964
, “
An Experimental Investigation of the Streamlines in Viscous Fluid Expelled From a Tube
,”
J. Fluid Mech.
,
20
, pp.
193
200
.
19.
Schwartz
,
L. W.
,
Princen
,
H.
, and
Kiss
,
A.
,
1986
, “
On the Motion of Bubbles in Capillary Tubes
,”
J. Fluid Mech.
,
172
, pp.
259
275
.
You do not currently have access to this content.