A microstructure model to describe the viscoelasticity and thixotropy properties of complex fluids is proposed. The model is based on the Lodge–Yamamoto network theory and is an extension of the Phan-Thien–Tanner model, with a kinetic process in which specific forms of creation and destruction rates are assumed. The final equation is simple with a small number of empirical parameters required and can be conveniently employed in engineering simulations. The predictions based on the model in a variety of shear and oscillatory shear flows are given. The stress response obtained from the model prediction agrees well with experiments on both shear and oscillatory flow histories.
REFERENCES
1.
H. D.
Weymann
, M. C.
Chuang
, and R. A.
Ross
, “Structure of thixotropic suspensions in shear flow: I. Mechanical properties
,” Phys. Fluids
16
, 775
(1973
).2.
R. A.
Ross
, H. D.
Weymann
, and M. C.
Chuang
, “Structure of thixotropic suspensions in shear flow: II. Optical properties
,” Phys. Fluids
16
, 784
(1973
).3.
C. F.
Goodeve
, “A general theory of thixotropy and viscosity
,” Trans. Faraday Soc.
35
, 342
–358
(1939
).4.
K.
Le-Cao
, N.
Phan-Thien
, B. C.
Khoo
, and N.
Mai-Duy
, “A dissipative particle dynamics model for thixotropic materials exhibiting pseudo-yield stress behaviour
,” J. Non-Newtonian Fluid Mech.
241
, 1
–13
(2017
).5.
A.
Mujumdar
, A. N.
Beris
, and A. B.
Metzner
, “Transient phenomena in thixotropic systems
,” J. Non-Newtonian Fluid Mech.
102
, 157
–178
(2002
).6.
H. A.
Barnes
, “Thixotropy—A review
,” J. Non-Newtonian Fluid Mech.
70
(1
), 1
–33
(1997
).7.
J.
Mewis
and N. J.
Wagner
, “Thixotropy
,” Adv. Colloid Interface Sci.
147-148
, 214
–227
(2009
).8.
R. G.
Larson
and Y.
Wei
, “A review of thixotropy and its rheological modeling
,” J. Rheol.
63
, 477
(2019
).9.
B. T.
Storey
and E. W.
Merrill
, “The rheology of aqueous solutions of amylose and amylopectin with reference to molecular configuration and intermolecular association
,” J. Polym. Sci.
33
, 361
–375
(1958
).10.
T. Y.
Liu
, D. S.
Soong
, and M. C.
Williams
, “Time-dependent rheological properties and transient structural states of entangled polymeric liquids—A kinetic network model
,” Polym. Eng. Sci.
21
, 675
(1981
).11.
D.
De Kee
and C. F.
Chan Man Fong
, “Rheological properties of structured fluids
,” Polym. Eng. Sci.
34
, 438
(1994
).12.
C. F.
Chan Man Fong
and D.
De Kee
, “Yield stress and small amplitude oscillatory flow in transient networks
,” Ind. Eng. Chem. Res.
33
, 2374
–2376
(1994
).13.
D.
Soong
and M.
Shen
, “Kinetic network model for nonlinear viscoelastic properties of entangled monodisperse polymers. I. Steady-state flow
,” J. Rheol.
25
, 259
(1981
).14.
F.
Moore
, “The rheology of ceramic slips and bodies
,” Trans. Br. Ceram. Soc.
58
, 470
–492
(1959
).15.
D. C.-H.
Cheng
and F.
Evans
, “Phenomenological characterization of the rheological behaviour of inelastic reversible thixotropic and antithixotropic fluids
,” Br. J. Appl. Phys.
16
, 1599
(1965
).16.
C.
Tiu
and D. V.
Boger
, “Complete rheological characterization of time-dependent food products
,” J. Texture Stud.
5
, 329
–338
(1974
).17.
C. J.
Dimitriou
and G. H.
McKinley
, “A comprehensive constitutive law for waxy crude oil: A thixotropic yield stress fluid
,” Soft Matter
10
, 6619
(2014
).18.
P. R.
de Souza Mendes
, “Modeling the thixotropic behavior of structured fluids
,” J. Non-Newtonian Fluid Mech.
164
, 66
–75
(2009
).19.
E. A.
Toorman
, “Modelling the thixotropic behaviour of dense cohesive sediment suspensions
,” Rheol. Acta
36
, 56
–65
(1997
).20.
P.
Coussot
, Q. D.
Nguyen
, H. T.
Huynh
, and D.
Bonn
, “Avalanche behavior in yield stress fluids
,” Phys. Rev. Lett.
88
, 175501
(2002
).21.
H. T.
Huynh
, N.
Roussel
, and P.
Coussot
, “Aging and free surface flow of a thixotropic fluid
,” Phys. Fluids
17
, 033101
(2005
).22.
N.
Roussel
, R. L.
Roy
, and P.
Coussot
, “Thixotropy modelling at local and macroscopic scales
,” J. Non-Newtonian Fluid Mech.
117
(2
), 85
(2004
).23.
K.
Bekkour
, M.
Leyama
, A.
Benchabane
, and O.
Scrivener
, “Time-dependent rheological behavior of bentonite suspensions: An experimental study
,” J. Rheol.
49
(6
), 1329
(2005
).24.
E. W.
Billington
, “Some measurements of the time dependence of the viscosity of thixotropic fluids
,” Proc. Phys. Soc.
75
, 40
–50
(1960
).25.
D. C.-H.
Cheng
, “Yield stress: A time-dependent property and how to measure it
,” Rheol. Acta
25
(5
), 542
(1986
).26.
J. J.
Derksen
, “Drag on random assemblies of spheres in shear-thinning and thixotropic liquids
,” Phys. Fluids
21
, 083302
(2009
).27.
A.
Syrakos
, G. C.
Georgiou
, and A. N.
Alexandrou
, “Thixotropic flow past a cylinder
,” J. Non-Newtonian Fluid Mech.
220
, 44
(2015
).28.
H. A.
Ardakani
, E.
Mitsoulis
, and S. G.
Hatzikiriakos
, “Thixotropic flow of toothpaste through extrusion dies
,” J. Non-Newtonian Fluid Mech.
166
(21
), 1262
(2011
).29.
A.
Potanin
, “3D simulations of the flow of thixotropic fluids, in large-gap Couette and vane-cup geometries
,” J. Non-Newtonian Fluid Mech.
165
(5
), 299
(2010
).30.
M. M.
Gumulya
, R. R.
Horsley
, and V.
Pareek
, “Numerical simulation of the settling behaviour of particles in thixotropic fluids
,” Phys. Fluids
26
, 023102
(2014
).31.
A. I.
Croudace
, D.
Pritchard
, and S. K.
Wilson
, “Unsteady flow of a thixotropic fluid in a slowly varying pipe
,” Phys. Fluids
29
, 083103
(2017
).32.
D.
Acierno
, F. P.
La Mantia
, G.
Marrucci
, and G.
Titomanlio
, “A non-linear viscoelastic model with structure-dependent relaxation times: I. Basic formulation
,” J. Non-Newtonian Fluid Mech.
1
(2
), 125
–146
(1976
).33.
P.
Coussot
, A. I.
Leonov
, and J. M.
Piau
, “Rheology of concentrated dispersed systems in a low molecular weight matrix
,” J. Non-Newtonian Fluid Mech.
46
(2
), 179
–217
(1993
).34.
K.
Dullaert
and J.
Mewis
, “A model system for thixotropy studies
,” Rheol. Acta
45
, 23
–32
(2005
).35.
K.
Dullaert
and J.
Mewis
, “A structural kinetics model for thixotropy
,” J. Non-Newtonian Fluid Mech.
139
, 21
–30
(2006
).36.
M. J.
Armstrong
, A. N.
Beris
, S. A.
Rogers
, and N. J.
Wagner
, “Dynamic shear rheology of a thixotropic suspension: Comparison of an improved structure-based model with large amplitude oscillatory shear experiments
,” J. Rheol.
60
, 433
(2016
).37.
N.
Hermidas
, R. S.
Jacinto
, J. T.
Eggenhuisenc
, and S. M.
Luthi
, “A new rheological model for thixoelastic materials in subaqueous gravity driven flows
,” J. Non-Newtonian Fluid Mech.
266
, 102
–117
(2019
).38.
F.
Yziquel
, P. J.
Carreau
, M.
Moan
, and P. A.
Tanguy
, “Rheological modeling of concentrated colloidal suspensions
,” J. Non-Newtonian Fluid Mech.
86
, 133
–155
(1999
).39.
K. A.
Ramya
, R.
Srinivasan
, and A. P.
Deshpande
, “Time dependent response of thixotropic systems: Insights from small amplitude oscillatory shear
,” Phys. Fluids
32
, 013109
(2020
).40.
M. M.
Cross
, “Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems
,” J. Colloid Sci.
20
, 417
–437
(1965
).41.
P.
Doremus
and J. M.
Piau
, “Yield stress fluid. Structural model and transient shear flow behaviour
,” J. Non-Newtonian Fluid Mech.
39
, 335
–352
(1991
).42.
M.
Yamamoto
, “The visco-elastic properties of network structure I. General formalism
,” J. Phys. Soc. Jpn.
11
, 413
(1956
).43.
M.
Yamamoto
, “The visco-elastic properties of network structure III. Normal stress effect (Weissenberg effect)
,” J. Phys. Soc. Jpn.
13
, 1200
(1958
).44.
M.
Yamamoto
, “The visco-elastic properties of network structure II. Structural viscosity
,” J. Phys. Soc. Jpn.
12
(10
), 1148
–1158
(1957
).45.
D.
De Kee
and C. F.
Chan Man Fong
, “Modelling of complex suspensions
,” in Theoretical and Applied Rheology
, edited by P.
Moldenaers
and S.
Keunings
(Elsevier Science Publishers
, Oxford, Amsterdam
, 1992
), pp. 598
–600
.46.
R. S.
Jeyaseelan
and A. J.
Giacomin
, “Structural network theory for a filled polymer melt in large amplitude oscillatory shear
,” Polym. Gels Networks
3
, 117
–133
(1995
).47.
A.
Lodge
, “The isotropy of Gaussian molecular networks and the stress-birefringence relations for rubber-like materials cross-linked in stressed states
,” Kolloid-Z.
171
, 46
(1960
);A.
Lodge
, “Constitutive equations from molecular network theories for polymer solutions
,” Rheol. Acta
7
, 379
(1968
).48.
E.
Bertevas
, T.
Tran-Duc
, K.
Le-Cao
, B. C.
Khoo
, and N.
Phan-Thien
, “A smoothed particle hydrodynamics (SPH) formulation of a two-phase mixture model and its application to turbulent sediment transport
,” Phys. Fluids
31
, 103303
(2019
).49.
50.
F. W.
Wiegel
, “A network model for viscoelastic fluids
,” Physica
42
, 156
(1969
).51.
F. M.
Wiegel
and F. T.
de Bats
, “Rheological properties of a network model for macromolecular fluids
,” Physica
43
, 33
(1969
).52.
N.
Phan-Thien
and R. I.
Tanner
, “A new constitutive equation derived from network theory
,” J. Non-Newtonian Fluid Mech.
2
, 353
(1977
).53.
N.
Phan-Thien
, “A nonlinear network viscoelastic model
,” J. Rheol.
22
, 259
(1978
).54.
M. S.
Green
and A. V.
Tobolsky
, “A new approach to the theory of relaxing polymeric media
,” J. Chem. Phys.
14
, 80
(1946
).55.
R. B.
Bird
, C. F.
Curtiss
, R. C.
Armstrong
, and O.
Hassager
, Dynamics of Polymeric Liquids
, Kinetic Theory, 2nd ed. (John Wiley & Sons
, New York
, 1987
), Vol. 2.56.
Z.
Ouyang
, E.
Bertevas
, L.
Parc
, B. C.
Khoo
, N.
Phan-Thien
, J.
Ferec
, and G.
Ausias
, “A smoothed particle hydrodynamics simulation of fiber-filled composites in a non-isothermal three-dimensional printing process featured
,” Phys. Fluids
31
, 123102
(2019
).57.
J.
Férec
, E.
Bertevas
, B. C.
Khoo
, G.
Ausias
, and N.
Phan-Thien
, “A rheological constitutive model for semiconcentrated rod suspensions in Bingham fluids
,” Phys. Fluids
29
, 073103
(2017
).58.
N.
Phan-Thien
, in Rheology of Non-Spherical Particle Suspensions
, edited by F.
Chinesta
and G.
Ausias
(Wiley-ISTE
, London
, 2015
), pp. 2
–17
.59.
A.
Malkin
, V.
Kulichikhin
, and S.
Ilyin
, “A modern look on yield stress fluids
,” Rheol. Acta
56
, 177
–188
(2017
).60.
T. C.
Papanastasiou
, “Flows of materials with yield
,” J. Rheol.
31
(5
), 385
–404
(1987
).61.
P.
Coussot
, Q. D.
Nguyen
, H. T.
Huynh
, and D.
Bonn
, “Viscosity bifurcation in thixotropic, yielding fluids
,” J. Rheol.
46
(3
), 573
–589
(2002
).62.
P. R.
de Souza Mendes
and R. L.
Thompson
, “A critical overview of elasto-viscoplastic thixotropic modeling
,” J. Non-Newtonian Fluid Mech.
187-188
, 8
–15
(2012
).© 2020 Author(s).
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