We report on shear startup data for two wormlike micellar solutions, differing only in concentration and type of two binding aromatic sodium salts. The surfactant molecule is cetylpiridinium chloride at a fixed concentration (100 mM). Sodium salicylate (NaSal) and diclofenac sodium (Diclo) are used as binding salts at concentrations 68 mM NaSal and 52 mM Diclo such that both systems are fully entangled and their linear viscoelastic response is essentially identical. Both systems show the linear response typical of a wormlike micellar solution, with terminal behavior at low frequencies, a well-defined moduli crossover, and a plateau modulus. In the nonlinear regime, however, the behavior of the two systems is totally different, suggesting that the molecular structure difference of the salts and their binding activity to the surfactant molecule are both crucial to determine the fast flow behavior. The NaSal solution shows a very complex rheological response, with strain hardening and very sharp stress peaks, whereas the solution containing Diclo behaves much like ordinary linear polymers, exhibiting pronounced overshoots as well as moderate undershoots in the transient shear viscosity, before approaching the steady state. This polymerlike behavior has also been proved by successfully comparing data with predictions of a constitutive equation recently adopted for both entangled polymers and linear wormlike micelles. As far as NaSal is concerned, a phenomenological model based on rubber network theory is developed, which describes the flow singularities. A physical interpretation of the different behavior in the nonlinear regime is also suggested.

1.
Larson
,
R. G.
,
The Structure and Rheology of Complex Fluids
(
Oxford University
,
New York
,
1999
), Vol. 150.
2.
Ito
,
T. H.
,
P. C.
Miranda
,
N. H.
Morgon
,
G.
Heerdt
,
C. A.
Dreiss
, and
E.
Sabadini
, “
Molecular variations in aromatic cosolutes: Critical role in the rheology of cationic wormlike micelles
,”
Langmuir
30
,
11535
11542
(
2014
).
3.
Sullivan
,
P. F.
,
M. K.
Panga
, and
V.
Lafitte
, “
Applications of wormlike micelles in the oilfield industry
,”
RSC Soft Matter
2017
,
330
352
(
2017
).
4.
Yang
,
J.
, “
Viscoelastic wormlike micelles and their applications
,”
Curr. Opin. Colloid Interface Sci.
7
,
276
281
(
2002
).
5.
Kang
,
W.
,
S. J.
Mushi
,
H.
Yang
,
P.
Wang
, and
X.
Hou
, “
Development of smart viscoelastic surfactants and its applications in fracturing fluid: A review
,”
J. Pet. Sci. Eng.
190
,
107107
(
2020
).
6.
Cates
,
M. E.
, and
S. M.
Fielding
, “
Rheology of giant micelles
,”
Adv. Phys.
55
,
799
879
(
2006
).
7.
Rothstein
,
J. P.
, and
H.
Mohammadigoushki
, “
Complex flows of viscoelastic wormlike micelle solutions
,”
J. Non-Newtonian Fluid Mech.
285
,
104382
(
2020
).
8.
Berret
,
J. F.
,
J.
Appell
, and
G.
Porte
, “
Linear rheology of entangled wormlike micelles
,”
Langmuir
9
,
2851
2854
(
1993
).
9.
Danino
,
D.
,
Y.
Talmon
,
H.
Levy
,
G.
Beinert
, and
R.
Zana
, “
Branched threadlike micelles in an aqueous solution of a trimeric surfactant
,”
Science
269
,
1420
1421
(
1995
).
10.
Danino
,
D.
, “
Cryo-TEM of soft molecular assemblies
,”
Curr. Opin. Colloid Interface Sci.
17
,
316
329
(
2012
).
11.
Kesselman
,
E.
, and
D.
Danino
, “Direct-imaging cryo-transmission electron microscopy of wormlike micelles,” in Wormlike Micelles: Advances in Systems, Characterisation and Applications (The Royal Society of Chemistry, Cambridge, UK, 2017), Chap. 7, pp. 171–192.
12.
González
,
Y. I.
, and
E. W.
Kaler
, “
Cryo-TEM studies of worm-like micellar solutions
,”
Curr. Opin. Colloid Interface Sci.
10
,
256
260
(
2005
).
13.
Rogers
,
S. A.
,
M. A.
Calabrese
, and
N. J.
Wagner
, “
Rheology of branched wormlike micelles
,”
Curr. Opin. Colloid Interface Sci.
19
,
530
535
(
2014
).
14.
Croce
,
V.
,
T.
Cosgrove
,
C. A.
Dreiss
,
S.
King
,
G.
Maitland
, and
T.
Hughes
, “
Giant micellar worms under shear: A rheological study using SANS
,”
Langmuir
21
,
6762
6768
(
2005
).
15.
Wu
,
S.
, and
H.
Mohammadigoushki
, “
Linear versus branched: Flow of a wormlike micellar fluid past a falling sphere
,”
Soft Matter
17
,
4395
4406
(
2021
).
16.
Gaudino
,
D.
,
R.
Pasquino
, and
N.
Grizzuti
, “
Adding salt to a surfactant solution: Linear rheological response of the resulting morphologies
,”
J. Rheol.
59
,
1363
1375
(
2015
).
17.
Oelschlaeger
,
C.
,
M.
Schopferer
,
F.
Scheffold
, and
N.
Willenbacher
, “
Linear-to-branched micelles transition: A rheometry and diffusing wave spectroscopy (DWS) study
,”
Langmuir
25
,
716
723
(
2009
).
18.
Gaudino
,
D.
,
S.
Costanzo
,
G.
Ianniruberto
,
N.
Grizzuti
, and
R.
Pasquino
, “
Linear wormlike micelles behave similarly to entangled linear polymers in fast shear flows
,”
J. Rheol.
64
,
879
888
(
2020
).
19.
Lequeux
,
F.
, “
Structure and rheology of wormlike micelles
,”
Curr. Opin. Colloid Interface Sci.
1
,
341
344
(
1996
).
20.
Rehage
,
H.
, and
H.
Hoffmann
, “
Viscoelastic surfactant solutions: Model systems for rheological research
,”
Mol. Phys.
74
,
933
973
(
1991
).
21.
Thurn
,
H.
, and
H.
Hoffmann
, “
Evidence of sticky contacts between wormlike micelles in viscoelastic surfactant solutions
,”
Langmuir
35
,
12192
12204
(
2019
).
22.
Majumdar
,
S.
, and
A.
Sood
, “
Nonlinear viscoelasticity of entangled wormlike micellar fluid under large-amplitude oscillatory shear: Role of elastic Taylor-Couette instability
,”
Phys. Rev. E
89
,
062314
(
2014
).
23.
Das
,
M.
,
R.
Bandyopadhyay
,
B.
Chakrabarti
,
S.
Ramaswamy
,
C.
Dasgupta
, and
A.
Sood
, “Rheological chaos in wormlike micelles and nematic hydrodynamics,” in Molecular Gels (Springer, Dordrecht, Netherlands, 2006), pp. 193–221.
24.
Calabrese
,
M. A.
,
S. A.
Rogers
,
R. P.
Murphy
, and
N. J.
Wagner
, “
The rheology and microstructure of branched micelles under shear
,”
J. Rheol.
59
,
1299
1328
(
2015
).
25.
Cates
,
M.
, “
Nonlinear viscoelasticity of wormlike micelles (and other reversibly breakable polymers)
,”
J. Phys. Chem.
94
,
371
375
(
1990
).
26.
Berret
,
J.-F.
, “
Transient rheology of wormlike micelles
,”
Langmuir
13
,
2227
2234
(
1997
).
27.
Saengow
,
C.
,
A. J.
Giacomin
,
N.
Grizzuti
, and
R.
Pasquino
, “
Startup steady shear flow from the Oldroyd 8-constant framework
,”
Phys. Fluids
31
,
063101
(
2019
).
28.
Costanzo
,
S.
,
Q.
Huang
,
G.
Ianniruberto
,
G.
Marrucci
,
O.
Hassager
, and
D.
Vlassopoulos
, “
Shear and extensional rheology of polystyrene melts and solutions with the same number of entanglements
,”
Macromolecules
49
,
3925
3935
(
2016
).
29.
Gaudino
,
D.
,
R.
Pasquino
,
J.
Stellbrink
,
N.
Szekely
,
M.
Krutyeva
,
A.
Radulescu
,
W.
Pyckhout-Hintzen
, and
N.
Grizzuti
, “
The role of the binding salt sodium salicylate in semidilute ionic cetylpyridinium chloride micellar solutions: A rheological and scattering study
,”
Phys. Chem. Chem. Phys.
19
,
782
790
(
2017
).
30.
Mohammadigoushki
,
H.
,
A.
Dalili
,
L.
Zhou
, and
P.
Cook
, “
Transient evolution of flow profiles in a shear banding wormlike micellar solution: Experimental results and a comparison with the VCM model
,”
Soft Matter
15
,
5483
5494
(
2019
).
31.
Shikata
,
T.
,
H.
Hirata
,
E.
Takatori
, and
K.
Osaki
, “
Nonlinear viscoelastic behavior of aqueous detergent solutions
,”
J. Non-Newtonian Fluid Mech.
28
,
171
182
(
1988
).
32.
Brown
,
E. F.
,
W. R.
Burghardt
, and
D. C.
Venerus
, “
Tests of the Lodge-Meissner relation in anomalous nonlinear step strain of an entangled wormlike micelle solution
,”
Langmuir
13
,
3902
3904
(
1997
).
33.
Inoue
,
T.
,
Y.
Inoue
, and
H.
Watanabe
, “
Nonlinear rheology of CTAB/NaSal aqueous solutions: Finite extensibility of a network of wormlike micelles
,”
Langmuir
21
,
1201
1208
(
2005
).
34.
Wang
,
M. C.
, and
E.
Guth
, “
Statistical theory of networks of non-Gaussian flexible chains
,”
J. Chem. Phys.
20
,
1144
1157
(
1952
).
35.
Shikata
,
T.
,
H.
Hirata
, and
T.
Kotaka
, “
Micelle formation of detergent molecules in aqueous media. 2. Role of free salicylate ions on viscoelastic properties of aqueous cetyltrimethylammonium bromide-sodium salicylate solutions
,”
Langmuir
4
,
354
359
(
1988
).
36.
Danino
,
D.
,
A.
Bernheim-Groswasser
, and
Y.
Talmon
, “
Digital cryogenic transmission electron microscopy: An advanced tool for direct imaging of complex fluids
,”
Colloids Surf., A
183
,
113
122
(
2001
).
37.
Pasquino
,
R.
,
B.
De Gennaro
,
D.
Gaudino
, and
N.
Grizzuti
, “
On the use of nonsteroidal anti-inflammatory drugs as rheology modifiers for surfactant solutions
,”
J. Pharm. Sci.
106
,
3410
3412
(
2017
).
38.
Danino
,
D.
,
Y.
Talmon
, and
R.
Zana
, “
Cryo-tem of thread-like micelles: On-the-grid microstructural transformations induced during specimen preparation
,”
Colloids Surf., A
169
,
67
73
(
2000
).
39.
Larson
,
R. G.
, “
The lengths of thread-like micelles inferred from rheology
,”
J. Rheol.
56
,
1363
1374
(
2012
).
40.
Cates
,
M.
, “
Reptation of living polymers: Dynamics of entangled polymers in the presence of reversible chain-scission reactions
,”
Macromolecules
20
,
2289
2296
(
1987
).
41.
Winter
,
H. H.
, and
M.
Mours
, “
The cyber infrastructure initiative for rheology
,”
Rheol. Acta
45
,
331
338
(
2006
).
42.
Tan
,
G.
, and
R.
Larson
, “
Quantitative modeling of threadlike micellar solution rheology
,”
Rheol. Acta
61
,
443
457
(
2022
).
43.
Bautista
,
F.
,
J.
De Santos
,
J.
Puig
, and
O.
Manero
, “
Understanding thixotropic and antithixotropic behavior of viscoelastic micellar solutions and liquid crystalline dispersions. I. The model
,”
J. Non-Newtonian Fluid Mech.
80
,
93
113
(
1999
).
44.
Pipe
,
C.
,
N.
Kim
,
P.
Vasquez
,
L.
Cook
, and
G.
McKinley
, “
Wormlike micellar solutions: II. Comparison between experimental data and scission model predictions
,”
J. Rheol.
54
,
881
913
(
2010
).
45.
Pearson
,
D.
,
E.
Herbolzheimer
,
N.
Grizzuti
, and
G.
Marrucci
, “
Transient behavior of entangled polymers at high shear rates
,”
J. Polym. Sci., Part B: Polym. Phys.
29
,
1589
1597
(
1991
).
46.
Larson
,
R. G.
, in Constitutive Equations for Polymer Melts and Solutions, Butterworths Series in Chemical Engineering, edited by R. G. Larson (Butterworth-Heinemann, Oxford, UK, 1988).
47.
Divoux
,
T.
,
M. A.
Fardin
,
S.
Manneville
, and
S.
Lerouge
, “
Shear banding of complex fluids
,”
Annu. Rev. Fluid Mech.
48
,
81
103
(
2016
).
48.
Ruan
,
Y.
,
Y.
Lu
,
L.
An
, and
Z.-G.
Wang
, “
Shear banding in entangled polymers: Stress plateau, banding location, and lever rule
,”
ACS Macro Lett.
10
,
1517
1523
(
2021
).
49.
Snijkers
,
F.
,
D.
Vlassopoulos
,
H.
Lee
,
J.
Yang
,
T.
Chang
,
P.
Driva
, and
N.
Hadjichristidis
, “
Start-up and relaxation of well-characterized comb polymers in simple shear
,”
J. Rheol.
57
,
1079
1100
(
2013
).
50.
Nafar Sefiddashti
,
M. H.
,
B. J.
Edwards
, and
B.
Khomami
, “
Individual chain dynamics of a polyethylene melt undergoing steady shear flow
,”
J. Rheol.
59
,
119
153
(
2015
).
51.
Tanner
,
R. I.
, and
M.
Keentok
, “
Shear fracture in cone-plate rheometry
,”
J. Rheol.
27
,
47
57
(
1983
).
52.
Vasudevan
,
M.
,
A.
Shen
,
B.
Khomami
, and
R.
Sureshkumar
, “
Self-similar shear thickening behavior in CTAB/NaSal surfactant solutions
,”
J. Rheol.
52
,
527
550
(
2008
).
53.
Vasudevan
,
M.
,
E.
Buse
,
D.
Lu
,
H.
Krishna
,
R.
Kalyanaraman
,
A.
Shen
,
B.
Khomami
, and
R.
Sureshkumar
, “
Irreversible nanogel formation in surfactant solutions by microporous flow
,”
Nat. Mater.
9
,
436
441
(
2010
).
54.
Schweizer
,
T.
, and
A.
Bardow
, “
The role of instrument compliance in normal force measurements of polymer melts
,”
Rheol. Acta
45
,
393
402
(
2006
).
55.
Martinetti
,
L.
,
O.
Carey-De La Torre
,
K. S.
Schweizer
, and
R. H.
Ewoldt
, “
Inferring the nonlinear mechanisms of a reversible network
,”
Macromolecules
51
,
8772
8789
(
2018
).
56.
Louhichi
,
A.
,
A. R.
Jacob
,
L.
Bouteiller
, and
D.
Vlassopoulos
, “
Humidity affects the viscoelastic properties of supramolecular living polymers
,”
J. Rheol.
61
,
1173
1182
(
2017
).
57.
See the supplementary material at https://www.scitation.org/doi/suppl/10.1122/8.0000537 for the complete set on the first normal stress growth as a function of time at different Wi numbers for both samples (Fig. S1) and the comparison between steady and dynamic viscosities for both systems (Fig. S2).

Supplementary Material

You do not currently have access to this content.