Thixotropy, antithixotropy, and viscoelasticity are three types of time-dependent dynamics that involve fundamentally different underlying physical processes. Here, we show that the three dynamics exhibit different signatures in hysteresis by examining the fingerprints of the simplest thixotropic kinetic model, a new antithixotropic model that we introduce here, and the Giesekus model. We start by showing that a consistent protocol to generate hysteresis loops is a discrete shear-rate controlled ramp that begins and ends at high shear rates, rather than at low shear rates. Using this protocol, we identify two distinguishing features in the resulting stress versus shear rate loops. The first is the direction of the hysteresis loops: clockwise for thixotropy, but counterclockwise for viscoelasticity and antithixotropy. A second feature is achieved at high ramping rates where all responses lose hysteresis: the viscoelastic response shows a stress plateau at low shear rates due to lack of stress relaxation, whereas the thixotropic and antithixotropic responses are purely viscous with minimal shear thinning or thickening. We establish further evidence for these signatures by experimentally measuring the hysteresis of Laponite suspensions, carbon black suspensions, and poly(ethylene oxide) solutions, each representing a historically accepted example of each class of material behavior. The signatures measured in experiments are consistent with those predicted by the three models. This study reveals different fingerprints in hysteresis loops associated with thixotropy, antithixotropy, and viscoelasticity, which may be helpful in distinguishing the three time-dependent responses.
REFERENCES
1.
da Silva Leite Coelho
, P. H.
, V. A.
de Deus Armellini
, and A. R.
Morales
, “Assessment of percolation threshold simulation for individual and hybrid nanocomposites of carbon nanotubes and carbon black
,” Mater. Res.
20
(6
), 1638
–1649
(2017
). 2.
Richards
, J. J.
, J. B.
Hipp
, J. K.
Riley
, N. J.
Wagner
, and P. D.
Butler
, “Clustering and percolation in suspensions of carbon black
,” Langmuir
33
(43
), 12260
–12266
(2017
). 3.
Trappe
, V.
, and D. A.
Weitz
, “Scaling of the viscoelasticity of weakly attractive particles
,” Phys. Rev. Lett.
85
(2
), 449
–452
(2000
). 4.
Trappe
, V.
, V.
Prasad
, L.
Cipelletti
, P. N.
Segre
, and D. A.
Weitz
, “Jamming phase diagram for attractive particles
,” Nature
411
(6839
), 772
–775
(2001
). 5.
International Carbon Black Association. “Carbon black user's guide,” https://www.carbon-black.org/ (2016).
6.
Hipp
, J. B.
, J. J.
Richards
, and N. J.
Wagner
, “Structure-property relationships of sheared carbon black suspensions determined by simultaneous rheological and neutron scattering measurements
,” J. Rheol.
63
(3
), 423
–436
(2019
). 7.
Hipp
, J. B.
, J. J.
Richards
, and N. J.
Wagner
, “Direct measurements of the microstructural origin of shear-thinning in carbon black suspensions
,” J. Rheol.
65
(2
), 145
–157
(2021
). 8.
Ovarlez
, G.
, L.
Tocquer
, F.
Bertrand
, and P.
Coussot
, “Rheopexy and tunable yield stress of carbon black suspensions
,” Soft Matter
9
(23
), 5540
–5549
(2013
). 9.
Wang
, Y.
, and R. H.
Ewoldt
, “New insights on carbon black suspension rheology—Anisotropic thixotropy and anti-thixotropy
,” J. Rheol.
66
(5
), 937
–953
(2022
). 10.
Narayanan
, A.
, F.
Mugele
, and M. H. G.
Duits
, “Mechanical history dependence in carbon black suspensions for flow batteries: A rheo-impedance study
,” Langmuir
33
, 1629
–1638
(2017
). 11.
Nelson
, A. Z.
, and R. H.
Ewoldt
, “Design of yield-stress fluids: A rheology-to-structure inverse problem
,” Soft Matter
13
, 7578
–7594
(2017
). 12.
Ewoldt
, R. H.
, and C.
Saengow
, “Designing complex fluids
,” Annu. Rev. Fluid Mech.
54
, 413
–441
(2022
). 13.
Wang
, Q.
, L.
Wang
, M. S.
Detamore
, and C.
Berkland
, “Biodegradable colloidal gels as moldable tissue engineering scaffolds
,” Adv. Mater.
20
, 236
–239
(2008
). 14.
Corker
, A.
, H. C. H.
Ng
, R. J.
Poole
, and E.
García-Tuñón
, “3D printing with 2D colloids: Designing rheology protocols to predict ‘printability’ of soft-materials
,” Soft Matter
15
, 1444
–1456
(2019
). 15.
Smay
, J. E.
, G. M.
Gratson
, R. F.
Shepherd
, J.
Cesarano III
, and J. A.
Lewis
, “Directed colloidal assembly of 3D periodic structures
,” Adv. Mater.
14
, 1279
–1283
(2002
). 16.
Youssry
, M.
, L.
Madec
, P.
Soudan
, M.
Cerbelaud
, D.
Guyomard
, and B.
Lestriez
, “Non-aqueous carbon black suspensions for lithium-based redox flow batteries: Rheology and simultaneous rheo-electrical behavior
,” Phys. Chem. Chem. Phys.
15
(34
), 14476
–14486
(2013
). 17.
Duduta
, M.
, B.
Ho
, V. C.
Wood
, P.
Limthongkul
, V. E.
Brunini
, W. C.
Carter
, and Y.-M.
Chiang
, “Semi-solid lithium rechargeable flow battery
,” Adv. Energy Mater.
1
(4
), 511
–516
(2011
). 18.
Fan
, F. Y.
, W. H.
Woodford
, Z.
Li
, N.
Baram
, K. C.
Smith
, A.
Helal
, G. H.
McKinley
, W. C.
Carter
, and Y.-M.
Chiang
, “Polysulfide flow batteries enabled by percolating nanoscale conductor networks
,” Nano Lett.
14
(4
), 2210
–2218
(2014
). 19.
Wei
, T.-S.
, F. Y.
Fan
, A.
Helal
, K. C.
Smith
, G. H.
McKinley
, Y.-M.
Chiang
, and J. A.
Lewis
, “Biphasic electrode suspensions for Li-ion semi-solid flow cells with high energy density, fast charge transport, and low-dissipation flow
,” Adv. Energy Mater.
5
(15
), 1500535
(2015
). 20.
Sen
, S.
, A. G.
Morales
, and R. H.
Ewoldt
, “Thixotropy in viscoplastic drop impact on thin films
,” Phys. Rev. Fluids
6
, 043301
(2021
). 21.
Larson
, R. G.
, “Constitutive equations for thixotropic fluids
,” J. Rheol.
59
(3
), 595
–611
(2015
). 22.
Bird
, R. B.
, R. C.
Armstrong
, and O.
Hassager
, Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics
, 2nd ed.
(Wiley
, New York
, 1987
).23.
Bauer
, W. H.
, and E. A.
Collins
, Chapter 8—Thixotropy and Dilatancy, in Rheology
(Academic Press
, New York
, 1967
).24.
Barnes
, H. A.
, “Thixotropy: A review
,” J. Non-Newton. Fluid Mech.
70
, 1
–33
(1997
). 25.
IUPAC
, Compendium of Chemical Terminology: The Gold Book
, 2nd ed.
(Blackwell Science
, Oxford
, 1997
).26.
Mewis
, J.
, and N. J.
Wagner
, “Thixotropy
,” Adv. Colloid Interface Sci.
147–148
, 214
–227
(2009
). 27.
Larson
, R. G.
, and Y.
Wei
, “A review of thixotropy and its rheological modeling
,” J. Rheol.
63
, 477
–501
(2019
). 28.
Yearsley
, K. M.
, M. R.
Mackley
, F.
Chinesta
, and A.
Leygue
, “The rheology of multiwalled carbon nanotube and carbon black suspensions
,” J. Rheol.
56
(6
), 1465
–1490
(2012
). 29.
Horner
, J. S.
, M. J.
Armstrong
, N. J.
Wagner
, and A. N.
Beris
, “Measurements of human blood viscoelasticity and thixotropy under steady and transient shear and constitutive modeling thereof
,” J. Rheol.
63
, 799
–813
(2019
). 30.
Ran
, R.
, S.
Pradeep
, S. K.
Acharige
, B. C.
Blackwell
, C.
Kammer
, D. J.
Jerolmack
, and P. E.
Arratia
, “Understanding the rheology of kaolinite clay suspensions using Bayesian inference
,” J. Rheol.
67
, 241
–252
(2023
). 31.
Dullaert
, K.
, and J.
Mewis
, “A model system for thixotropy studies
,” Rheol. Acta
45
, 23
–32
(2005
). 32.
Dullaert
, K.
, and J.
Mewis
, “Stress jumps on weakly flocculated dispersions: Steady state and transient results
,” J. Colloid Interface Sci.
287
(2
), 542
–551
(2005
). 33.
Dullaert
, K.
, and J.
Mewis
, “Thixotropy: Build-up and breakdown curves during flow
,” J. Rheol.
49
, 1213
–1230
(2005
). 34.
Dullaert
, K.
, and J.
Mewis
, “A structural kinetics model for thixotropy
,” J. Non-Newton. Fluid Mech.
139
, 21
–30
(2006
). 35.
Chang
, C.
, Q. D.
Nguyen
, and H. P.
Rønningsen
, “Isothermal start-up of pipeline transporting waxy crude oil
,” J. Non-Newton. Fluid Mech.
87
, 127
–154
(1999
). 36.
Toorman
, E. A.
, “Modelling the thixotropic behaviour of dense cohesive sediment suspensions
,” Rheol. Acta
36
, 56
–65
(1997
). 37.
Sen
, S.
, and R. H.
Ewoldt
, “Thixotropic spectra and Ashby-style charts for thixotropy
,” J. Rheol.
66
(5
), 1041
–1053
(2022
). 38.
Sudreau
, I.
, M.
Auxois
, M.
Servel
, S.
Manneville
, and T.
Divoux
, “Residual stresses and shear-induced overaging in boehmite gels
,” Phys. Rev. Mater.
6
, L042601
(2022
). 39.
Agarwal
, M.
, M.
Kaushal
, and Y. M.
Joshi
, “Signatures of overaging in an aqueous dispersion of carbopol
,” Langmuir
36
, 14849
–14863
(2020
). 40.
Viasnoff
, V.
, and F.
Lequeux
, “Rejuvenation and overaging in a colloidal glass under shear
,” Phys. Rev. Lett.
89
(6
), 065701
(2002
). 41.
Keller
, D. S.
, and D. V.
Keller
, “The effect of particle size distribution on the antithixotropic and shear thickening properties of coal–water dispersions
,” J. Rheol.
35
, 1583
–1607
(1991
). 42.
Chang
, C.
, P. A.
Smith
, C.
Chang
, and P. A.
Smith
, “Flow-induced structure in a system of nuclear waste simulant slurries
,” Rheol. Acta
35
, 382
–389
(1996
). 43.
Vermant
, J.
, and M. J.
Solomon
, “Flow-induced structure in colloidal suspensions
,” J. Phys.: Condens. Matter
17
(4
), R187
–R216
(2005
). 44.
Hoekstra
, H.
, J.
Vermant
, J.
Mewis
, and G. G.
Fuller
, “Flow-induced anisotropy and reversible aggregation in two-dimensional suspensions
,” Langmuir
19
, 9134
–9141
(2003
). 45.
Varadan
, P.
, and M. J.
Solomon
, “Shear-induced microstructural evolution of thermoreversible colloidal gel
,” Langmuir
17
, 2918
–2929
(2001
). 46.
Macosko
, C. W.
, Rheology: Principles, Measurements, and Applications
(VCH Publishers. Inc.
, New York
, 1994
).47.
Divoux
, T.
, V.
Grenard
, and S.
Manneville
, “Rheological hysteresis in soft glassy materials
,” Phys. Rev. Lett.
110
, 1
–5
(2013
). 48.
Sharma
, S.
, V.
Shankar
, and Y. M.
Joshi
, “Viscoelasticity and rheological hysteresis
,” J. Rheol.
67
, 139
–155
(2023
). 49.
Wang
, Y.
, X.
Li
, X.
Zhu
, and S.
Wang
, “Characterizing state of chain entanglement in entangled polymer solutions during and after large shear deformation
,” Macromolecules
45
(5
), 2514
–2521
(2012
). 50.
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
). 51.
Agarwal
, M.
, S.
Sharma
, V.
Shankar
, and Y. M.
Joshi
, “Distinguishing thixotropy from viscoelasticity
,” J. Rheol.
65
, 663
–680
(2021
). 52.
Green
, H.
, and R. N.
Weltmann
, “Analysis of thixotropy of pigment-vehicle suspensions—Basic principles of the hysteresis loop
,” Ind. Eng. Chem. Anal. Ed.
15
, 201
–206
(1943
). 53.
Green
, H.
, and R. N.
Weltmann
, “The effect of thixotropy on plasticity measurements
,” J. Appl. Phys.
15
, 414
–420
(1944
). 54.
Negi
, A. S.
, and C. O.
Osuji
, “New insights on fumed colloidal rheology—Shear thickening and vorticity-aligned structures in flocculating dispersions
,” Rheol. Acta
48
, 871
–881
(2009
). 55.
N’gouamba
, E.
, M.
Essadik
, J.
Goyon
, T.
Oerther
, and P.
Coussot
, “Yielding and rheopexy of aqueous xanthan gum solutions
,” Rheol. Acta
60
(11
), 653
–660
(2021
). 56.
Bird
, R. B.
, and B. D.
Marsh
, “Viscoelastic hysteresis. Part I. Model predictions
,” J. Rheol.
12
, 479
–488
(1968
). 57.
Marsh
, B. D.
, “Viscoelastic hysteresis. Part II. Numerical and experimental examples
,” J. Rheol.
12
, 489
–510
(1968
). 58.
Rubio-Hernández
, F. J.
, and A. I.
Gómez-Merino
, “Time dependent mechanical behavior: The viscoelastic loop
,” Mech. Time-Depend. Mater.
12
, 357
–364
(2008
). 59.
Jamali
, S.
, and G. H.
McKinley
, “The Mnemosyne number and the rheology of remembrance
,” J. Rheol.
66
(5
), 1027
–1039
(2022
). 60.
See the supplementary material for the protorheology estimate of the yield stress of Laponite and CB suspensions and the relaxation time of the PEO solution, and other hysteresis protocols and results. All the data shown in the Experimental Results section are available within the supplementary material.
61.
MATLAB. R2021a (9.10.0.1602886). The MathWorks, Inc., 2021.
62.
Xu
, M.
, S.
Roig-Sanchez
, A.
Riseman
, and J. M.
Frostad
, “Influence of pH, salt ions, and binary mixtures of different molecular weights on the extensional rheology of polyethylene oxide
,” J. Rheol.
66
(5
), 881
–893
(2022
). 63.
Odell
, J. A.
, A.
Keller
, and Y.
Rabin
, “Flow-induced scission of isolated macromolecules
,” J. Chem. Phys.
88
(6
), 4022
–4028
(1988
). 64.
Odell
, J. A.
, A. J.
Muller
, K. A.
Narh
, and A.
Keller
, “Degradation of polymer solutions in extensional flows
,” Macromolecules
23
(12
), 3092
–3103
(1990
). 65.
Goodeve
, C. F.
, and G. W.
Whitfield
, “The measurement of thixotropy in absolute units
,” Trans. Faraday Soc.
34
, 511
–520
(1938
). 66.
Moore
, F.
, “The rheology of ceramic slips and bodies
,” Trans. Br. Ceram. Soc.
58
, 470
–494
(1959
).67.
Wei
, Y.
, M. J.
Solomon
, and R. G.
Larson
, “Quantitative nonlinear thixotropic model with stretched exponential response in transient shear flows
,” J. Rheol.
60
, 1301
–1315
(2016
). 68.
Wei
, Y.
, M. J.
Solomon
, and R. G.
Larson
, “A multimode structural kinetics constitutive equation for the transient rheology of thixotropic elasto-viscoplastic fluids
,” J. Rheol.
62
, 321
–342
(2018
). 69.
Wei
, Y.
, M. J.
Solomon
, and R. G.
Larson
, “Time-dependent shear rate inhomogeneities and shear bands in a thixotropic yield-stress fluid under transient shear
,” Soft Matter
15
, 7956
–7967
(2019
). 70.
Blackwell
, B. C.
, and R. H.
Ewoldt
, “A simple thixotropic-viscoelastic constitutive model produces unique signatures in large-amplitude oscillatory shear (LAOS)
,” J. Non-Newton. Fluid Mech.
208–209
, 27
–41
(2014
). 71.
Varchanis
, S.
, G.
Makrigiorgos
, P.
Moschopoulos
, Y.
Dimakopoulos
, and J.
Tsamopoulos
, “Modeling the rheology of thixotropic elasto-visco-plastic materials
,” J. Rheol.
63
, 609
–639
(2019
). 72.
Ewoldt
, R. H.
, and G. H.
McKinley
, “Mapping thixo-elasto-visco-plastic behavior
,” Rheol. Acta
56
, 195
–210
(2017
). 73.
Dealy
, J. M.
, “Weissenberg and Deborah numbers—Their definition and use
,” Rheol. Bull.
79
(2
), 14
–18
(2010
).74.
Buitenhuis
, J.
, and M.
Pönitsch
, “Negative thixotropy of polymer solutions. I. A model explaining time-dependent viscosity
,” Colloid Polym. Sci.
281
(3
), 253
–259
(2003
). 75.
Buckingham
, E.
, “On physically similar systems: Illustrations of the use of dimensional equations
,” Phys. Rev.
4
(4
), 345
–376
(1914
). 76.
Radhakrishnan
, R.
, T.
Divoux
, S.
Manneville
, and S. M.
Fielding
, “Understanding rheological hysteresis in soft glassy materials
,” Soft Matter
13
, 1834
–1852
(2017
). 77.
Acierno
, D.
, F. P.
La Mantia
, G.
Marrucci
, and G.
Titomanlio
, “A non-linear viscoelastic model with structure-dependent relaxation times. I. Basic formulation
,” J. Non-Newton. Fluid Mech.
1
(2
), 125
–146
(1976
). 78.
Jamali
, S.
, R. C.
Armstrong
, and G. H.
McKinley
, “Multiscale nature of thixotropy and rheological hysteresis in attractive colloidal suspensions under shear
,” Phys. Rev. Lett.
123
, 248003
(2019
). 79.
Puisto
, A.
, M.
Mohtaschemi
, M. J.
Alava
, and X.
Illa
, “Dynamic hysteresis in the rheology of complex fluids
,” Phys. Rev. E
91
, 042314
(2015
). 80.
Bonn
, D.
, H.
Kellay
, H.
Tanaka
, G.
Wegdam
, and J.
Meunier
, “Laponite: What is the difference between a gel and a glass?
,” Langmuir
15
(22
), 7534
–7536
(1999
). 81.
Cummins
, H. Z.
, “Liquid, glass, gel: The phases of colloidal laponite
,” J. Non-Cryst. Solids
353
(41–43
), 3891
–3905
(2007
). 82.
Tanaka
, H.
, J.
Meunier
, and D.
Bonn
, “Nonergodic states of charged colloidal suspensions: Repulsive and attractive glasses and gels
,” Phys. Rev. E
69
, 031304
(2004
).83.
Hossain
, T.
, and R. H.
Ewoldt
, “Protorheology,” J. Rheol. (unpublished).84.
Hossain
, T.
, and R. H.
Ewoldt
, “Do-it-yourself rheometry
,” Phys. Fluids
34
(5
), 053105
(2022
). 85.
Ebagninin
, K. W.
, A.
Benchabane
, and K.
Bekkour
, “Rheological characterization of poly(ethylene oxide) solutions of different molecular weights
,” J. Colloid Interface Sci.
336
(1
), 360
–367
(2009
). 86.
Yu
, D. M.
, G. L.
Amidon
, N. D.
Weiner
, and A. H.
Goldberg
, “Viscoelastic properties of poly(ethylene oxide) solution
,” J. Pharm. Sci.
83
(10
), 1443
–1449
(1994
). 87.
Bailey
, F. E.
, and J. V.
Koleske
, Solution Properties of Poly(ethylene Oxide), in Poly (Ethylene Oxide)
(Academic
, New York
, 1976
).88.
Grädel
, M.
, J. D.
Rathinaraj
, R.
More
, G.
Pagani
, J.
Vermant
, and G. H.
McKinley
, “Distinguishing thixotropy from viscoelasticity in complex fluids using gaborheometry and parallel superposition rheometry,” presented at the Institute of Non-Newtonian Fluid Mechanics–The British Society of Rheology Meeting, Lake Vyrnwy, Wales, 3–5 April 2023.89.
Vermant
, J.
, L.
Walker
, P.
Moldenaers
, and J.
Mewis
, “Orthogonal versus parallel superposition measurements
,” J. Non-Newton. Fluid Mech.
79
(2-3
), 173
–189
(1998
). 90.
Kim
, S.
, J.
Mewis
, C.
Clasen
, and J.
Vermant
, “Superposition rheometry of a wormlike micellar fluid
,” Rheol. Acta
52
, 727
–740
(2013
). 91.
Zhang
, J.
, A.
Jurzyk
, M. E.
Helgeson
, and L. G.
Leal
, “Modeling orthogonal superposition rheometry to probe nonequilibrium dynamics of entangled polymers
,” J. Rheol.
65
, 983
–998
(2021
). 92.
Lin
, N. Y. C.
, C.
Ness
, M. E.
Cates
, J.
Sun
, and I.
Cohen
, “Tunable shear thickening in suspensions
,” Proc. Natl. Acad. Sci. U.S.A.
113
(39
), 10774
–10778
(2016
). 93.
Ewoldt
, R. H.
, M. T.
Johnston
, and L. M.
Caretta
, “Experimental challenges of shear rheology: How to avoid bad data,” in Complex Fluids in Biological Systems, Springer Biological Engineering Series (Springer, New York, 2015).© 2023 The Society of Rheology.
2023
The Society of Rheology
You do not currently have access to this content.