Whereas devices for measuring the interfacial shear and dilatational rheology are readily available, extensional rheometry at interfaces remains essentially unexplored. However, a setup mimicking a 2D filament stretching rheometer, the Cambridge Interfacial Tensiometer, was proposed for this very purpose [Jones and Middelberg, Chem. Eng. Sci. 57, 1711–1722 (2002)]. In the present work, a framework is presented for analyzing the interfacial flow field in such device for Newtonian interfaces in the presence of Marangoni flows. Based on the dimensionless numbers that govern the interfacial flow field, different dominant flow types can be identified and the sensitivity of the device for measuring the extensional interfacial viscosity is determined. For the flow field to be dominated by extensional deformations, either the Marangoni number or the ratio of dilatational viscosity to shear viscosity should be at least an order of magnitude higher than the Trouton ratio. Using an analysis for Newtonian materials, the contribution to the overall force by the extensional stress can be determined. It should be noted that obtaining these viscosities from the Cambridge Interfacial Tensiometer also requires knowledge of the interfacial shear and dilatational rheology together with the surface pressure isotherm. To test the technique and evaluate the model, experiments on a dipalmitoylphosphatidylcholine monolayer at an air-water interface have been performed and analyzed.

1.
Alonso
,
C.
,
A.
Waring
, and
J. A.
Zasadzinski
, “
Keeping lung surfactant where it belongs: protein regulation of two-dimensional viscosity
,”
Biophys. J.
89
,
266
273
(
2005
).
2.
Batchelor
,
G. K.
, “
The stress generated in a non-dilute suspension of elongated particles by pure straining motion
,”
J. Fluid Mech.
46
,
813
829
(
1971
).
3.
Brooks
,
C. F.
,
G. G.
Fuller
,
C. W.
Frank
, and
C. R.
Robertson
, “
An interfacial stress rheometer to study rheological transitions in monolayers at the water-air interface
,”
Langmuir
15
,
2450
2458
(
1999
).
5.
Cicuta
,
P.
, and
E. M.
Terentjev
, “
Viscoelasticity of a protein monolayer from anisotropic surface pressure measurements
,”
Eur. Phys. J. E
16
,
147
158
(
2005
).
6.
Dickinson
,
E.
, “
Adsorbed protein layers at fluid interfaces: Interactions, structure and surface rheology
,”
Colloids Surf., B
15
,
161
176
(
1999
).
7.
Dimitrijev-Dwyer
,
M.
, and
A. P. J.
Middelberg
, “
The extensional viscoelasticity of protein-coated interfaces
,”
Soft Matter
7
,
7772
7781
(
2011
).
8.
Edwards
,
D. A.
,
H.
Brenner
, and
D. T.
Wasan
,
Interfacial Transport Processes and Rheology
(
Butterworth-Heinemann
,
Boston
,
1991
).
9.
Fischer
,
T. M.
, “
The drag on needles moving in a Langmuir monolayer
,”
J. Fluid Mech.
498
,
123
137
(
2004
).
10.
Gavranovic
,
G. T.
,
R. E.
Kurtz
,
K.
Golemanov
,
A.
Lange
, and
G. G.
Fuller
, “
Interfacial rheology and structure of straight-chain and branched hexadecanol mixtures
,”
Ind. Eng. Chem. Res.
45
,
6880
6884
(
2006
).
11.
Herzig
,
E. M.
,
K. A.
White
,
A. B.
Schofield
,
W. C. K.
Poon
, and
P. S.
Clegg
, “
Bicontinuous emulsions stabilized solely by colloidal particles
,”
Nature Mater.
6
,
966
971
(
2007
).
12.
Hoffman
,
B. D.
, and
E. S. G.
Shaqfeh
, “
The dynamics of the coil-stretch transition for long, flexible polymers in planar mixed flows
,”
J. Rheol.
51
,
947
969
(
2007
).
13.
Jones
,
D. B.
, and
A. P. J.
Middelberg
, “
Direct determination of the mechanical properties of an interfacially adsorbed protein film
,”
Chem. Eng. Sci.
57
,
1711
1722
(
2002
).
14.
Krägel
,
J.
, and
S. R.
Derkatch
, “
Interfacial shear rheology
,”
Curr. Opin. Colloid Interface Sci.
15
,
246
255
(
2010
).
15.
Krägel
,
J.
,
G.
Kretzschmar
,
J.
Li
,
G.
Loglio
,
R.
Miller
, and
H.
Möhwald
, “
Surface rheology of monolayers
,”
Thin Solid Films
284
,
361
364
(
1996
).
16.
Langevin
,
D.
, “
Influence of interfacial rheology on foam and emulsion properties
,”
Adv. Colloid Interface Sci.
323
,
209
222
(
2000
).
17.
Leiske
,
D. L.
,
C.
Monteux
,
M.
Senchyna
,
H. A.
Ketelson
, and
G. G.
Fuller
, “
Influence of surface rheology on dynamic wetting of droplets coated with insoluble surfactants
,”
Soft Matter
7
,
7747
7753
(
2011
).
18.
Macosko
,
C. W.
,
Rheology: Principles, Measurements and Applications
(
Wiley
,
New York
,
1994
).
19.
Madivala
,
B.
,
S.
Vandebril
,
J.
Fransaer
, and
J.
Vermant
, “
Exploiting particle shape in solid stabilized emulsions
,”
Soft Matter
5
,
1717
1727
(
2009
).
20.
McKinley
,
G. H.
, and
T.
Sridhar
, “
Filament-stretching rheometry of complex fluids
,”
Annu. Rev. Fluid Mech.
34
,
375
415
(
2002
).
21.
Mewis
,
J.
, and
A. B.
Metzner
, “
Rheological properties of suspensions of fibers in Newtonian fluids subjected to extensional deformations
,”
J. Fluid Mech.
62
,
593
600
(
1974
).
22.
Muradoglu
,
M.
, and
G.
Tryggvason
, “
A front-tracking method for computation of interfacial flows with soluble surfactants
,”
J. Comput. Phys.
227
,
2238
2262
(
2008
).
23.
Powell
,
R. L.
, “
Rheology of suspensions of rodlike particles
,”
J. Stat. Phys.
62
,
1073
1094
(
1991
).
24.
Ravera
,
F.
,
G.
Loglio
, and
V. I.
Kovalchuk
, “
Interfacial dilational rheology by oscillating bubble/drop methods
,”
Curr. Opin. Colloid Interface Sci.
15
,
217
228
(
2010
).
25.
Reynaert
,
S.
,
C. F.
Brooks
,
P.
Moldenaers
,
J.
Vermant
, and
G. G.
Fuller
, “
Analysis of the magnetic rod interfacial stress rheometer
,”
J. Rheol.
52
,
261
285
(
2008
).
26.
Russev
,
S. C.
,
N.
Alexandrov
,
K. G.
Marinova
,
K. D.
Danov
,
N. D.
Denkov
,
L.
Lyutov
,
V.
Vulchev
, and
C.
Bilke-Krause
, “
Instrument and methods for surface dilatational rheology measurements
,”
Rev. Sci. Instrum.
79
,
104102
(
2008
).
27.
Scriven
,
L. E.
, “
Dynamics of a fluid interface—Equation of motion for Newtonian surface fluids
,”
Chem. Eng. Sci.
12
,
98
108
(
1960
).
28.
Stepanova
,
M.
, “
Reversible formation of nanodomains in monolayers of DPPC studied by kinetic modeling
,”
Biophys. J.
96
,
4896
4905
(
2009
).
29.
Stone
,
H. A.
, “
A simple derivation of the time-dependent convective-diffusion equation for surfactant transport along a deforming interface
,”
Phys. Fluids A
2
,
111
112
(
1990
).
30.
Stone
,
H. A.
, and
A.
Ajdari
, “
Hydrodynamics of particles embedded in a flat surfactant layer overlying a subphase of finite depth
,”
J. Fluid Mech.
369
,
151
173
(
1998
).
31.
Sun
,
H.
,
L.
Zhang
,
Z.
Li
,
L.
Luo
, and
S.
Zhao
, “
Interfacial dilational rheology related to enhance oil recovery
,”
Soft Matter
7
,
7601
7611
(
2011
).
32.
Tirtaatmadja
,
V.
, and
T.
Sridhar
, “
A filament stretching device for measurement of extensional viscosity
,”
J. Rheol.
37
,
1081
1102
(
1993
).
33.
Vandebril
,
S.
,
A.
Franck
,
G. G.
Fuller
,
P.
Moldenaers
, and
J.
Vermant
, “
A double wall-ring geometry for interfacial shear rheometry
,”
Rheol. Acta
49
,
131
144
(
2009
).
34.
Verwijlen
,
T.
,
P.
Moldenaers
,
H. A.
Stone
, and
J.
Vermant
, “
Study of the flow field in the magnetic rod interfacial stress rheometer
,”
Langmuir
27
,
9345
9358
(
2011
).
35.
Wüstneck
,
N.
,
R.
Wüstneck
,
V. B.
Fainerman
,
R.
Miller
, and
U.
Pison
, “
Interfacial behaviour and mechanical properties of spread lung surfactant protein/lipid layers
,”
Colloids Surf., B
21
,
191
205
(
2001
).
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