We study density-stable laminar miscible displacement flow of two iso-viscous Newtonian fluids in an inclined pipe (diameter

$\hat{D}$
D̂⁠). We present a wide range of novel experimental results. We illustrate the non-monotone relation in displacement efficiency at the density difference moves from positive (density unstable) to negative (density stable), the efficiency being minimal for iso-dense fluids. The density stable configuration has been found to produce highly efficient displacements, with the bulk of the interface moving steadily at the mean velocity. The streamwise length of the stretched interface, or stretch length 
$\hat{L}$
L̂⁠, is measured over a wide range of parameters. The stretch length increases with the mean flow velocity, increases with inclination β from vertical, decreases with density difference, and increases with viscosity. Our data are well represented by the scaled expression L − tan β = −3680/χ, where χ is the ratio of buoyancy and viscous stresses.

Topics
Transport properties, Acoustic noise measurement, Optical imaging, Thin films, Interpolation, Newtonian fluids, Hydrostatics, Laminar flows, Buoyancy, Viscosity
1.
G. I.
 
Taylor
, “
Dispersion of soluble matter in a solvent flowing slowly through a tube
,”
Proc. R. Soc. London, Ser. A
 
219
,
186
(
1953
).
https://doi.org/10.1098/rspa.1953.0139
Google Scholar
Crossref
Search ADS
 
2.
R.
 
Aris
, “
On the dispersion of a solute in a fluid flowing through a tube
,”
Proc. R. Soc. London, Ser. A
 
235
,
67
(
1956
).
https://doi.org/10.1098/rspa.1956.0065
Google Scholar
Crossref
Search ADS
 
3.
P.
 
Petitjeans
 and
T.
 
Maxworthy
, “
Miscible displacements in capillary tubes. Part 1. Experiments
,”
J. Fluid Mech.
 
326
,
37
(
1996
).
https://doi.org/10.1017/S0022112096008233
Google Scholar
Crossref
Search ADS
 
4.
J.
 
Scoffoni
,
E.
 
Lajeunesse
, and
G. M.
 
Homsy
, “
Interface instabilities during displacements of two miscible fluids in a vertical pipe
,”
Phys. Fluids
 
13
,
553
(
2001
).
https://doi.org/10.1063/1.1343907
Google Scholar
Crossref
Search ADS
 
5.
J.
 
Kuang
,
T.
 
Maxworthy
, and
P.
 
Petitjeans
, “
Miscible displacements between silicone oils in capillary tubes
,”
Eur. J. Mech. B/Fluids
 
22
,
271
(
2003
).
https://doi.org/10.1016/S0997-7546(03)00035-9
Google Scholar
Crossref
Search ADS
 
6.
R.
 
Balasubramaniam
,
N.
 
Rashidnia
,
T.
 
Maxworthy
, and
J.
 
Kuang
, “
Instability of miscible interfaces in a cylindrical tube
,”
Phys. Fluids
 
17
,
052103
(
2005
).
https://doi.org/10.1063/1.1884645
Google Scholar
Crossref
Search ADS
 
7.
E.
 
Lajeunesse
,
J.
 
Martin
,
N.
 
Rakotomalala
,
D.
 
Salin
, and
Y. C.
 
Yortsos
, “
Miscible displacement in a Hele-Shaw cell at high rates
,”
J. Fluid Mech.
 
398
,
299
(
1999
).
https://doi.org/10.1017/S0022112099006357
Google Scholar
Crossref
Search ADS
 
8.
J.
 
Fernandez
,
P.
 
Kurowski
,
P.
 
Petitjeans
, and
E.
 
Meiburg
, “
Density-driven unstable flows of miscible fluids in a Hele-Shaw cell
,”
J. Fluid Mech.
 
451
,
239
(
2002
).
https://doi.org/10.1017/S0022112001006504
Google Scholar
Crossref
Search ADS
 
9.
C.
 
Jiao
 and
T.
 
Maxworthy
, “
An experimental study of miscible displacement with gravity-override and viscosity-contrast in a Hele Shaw cell
,”
Exp. Fluids
 
44
,
781
(
2008
).
https://doi.org/10.1007/s00348-007-0434-8
Google Scholar
Crossref
Search ADS
 
10.
C.-Y.
 
Chen
 and
E.
 
Meiburg
, “
Miscible displacements in capillary tubes. Part 2. numerical simulations
,”
J. Fluid Mech.
 
326
,
57
(
1996
).
https://doi.org/10.1017/S0022112096008245
Google Scholar
Crossref
Search ADS
 
11.
N.
 
Rakotomalala
,
D.
 
Salin
, and
P.
 
Watzky
, “
Miscible displacement between two parallel plates: BGK lattice gas simulations
,”
J. Fluid Mech.
 
338
,
277
(
1997
).
https://doi.org/10.1017/S0022112097004928
Google Scholar
Crossref
Search ADS
 
12.
K. C.
 
Sahu
,
H.
 
Ding
,
P.
 
Valluri
, and
O. K.
 
Matar
, “
Pressure-driven miscible two-fluid channel flow with density gradients
,”
Phys. Fluids
 
21
,
043603
(
2009
).
https://doi.org/10.1063/1.3122779
Google Scholar
Crossref
Search ADS
 
13.
S. M.
 
Taghavi
,
T.
 
Seon
,
K.
 
Wielage-Burchard
,
D. M.
 
Martinez
, and
I. A.
 
Frigaard
, “
Stationary residual layers in buoyant Newtonian displacement flows
,”
Phys. Fluids
 
23
,
044105
(
2011
).
https://doi.org/10.1063/1.3581063
Google Scholar
Crossref
Search ADS
 
14.
S. M.
 
Taghavi
,
K.
 
Alba
,
T.
 
Seon
,
K.
 
Wielage-Burchard
,
D. M.
 
Martinez
, and
I. A.
 
Frigaard
, “
Miscible displacement flows in near-horizontal ducts at low Atwood number
,”
J. Fluid Mech.
 
696
,
175
(
2012
).
https://doi.org/10.1017/jfm.2012.26
Google Scholar
Crossref
Search ADS
 
15.
R. M.
 
Oliveira
 and
E.
 
Meiburg
, “
Miscible displacements in Hele-Shaw cells: Three-dimensional Navier-Stokes simulations
,”
J. Fluid Mech.
 
687
,
431
(
2011
).
https://doi.org/10.1017/jfm.2011.367
Google Scholar
Crossref
Search ADS
 
16.
S. M.
 
Taghavi
,
T.
 
Seon
,
D. M.
 
Martinez
, and
I. A.
 
Frigaard
, “
Influence of an imposed flow on the stability of a gravity current in a near horizontal duct
,”
Phys. Fluids
 
22
,
031702
(
2010
).
https://doi.org/10.1063/1.3326074
Google Scholar
Crossref
Search ADS
 
17.
S. M.
 
Taghavi
,
T.
 
Seon
,
D. M.
 
Martinez
, and
I. A.
 
Frigaard
, “
Buoyancy-dominated displacement flows in near-horizontal channels: the viscous limit
,”
J. Fluid Mech.
 
639
,
1
(
2009
).
https://doi.org/10.1017/S0022112009990620
Google Scholar
Crossref
Search ADS
 
© 2012 American Institute of Physics.
2012
American Institute of Physics
You do not currently have access to this content.