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Rheologica Acta

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16-02-2024 | Original Contribution

Frequency response analysis of the Bautista-Manero-Puig model with normal stress: analytical and numerical solution for large amplitudes

Authors: E. Hernandez, F. Bautista, J. P. García-Sandoval, O. Manero

Published in: Rheologica Acta | Issue 3/2024

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Abstract

We derive explicit analytical expressions for the recurrence relations using the analytical matrix method for frequency response and the Bautista-Manero-Puig model for complex fluids. The BMP model is derived from the Extended Irreversible Thermodynamics formalism and has been shown to be useful in predicting the complex rheological behavior of self-associative systems. All harmonics of the alternating normal and shear stresses in oscillatory shear with various amplitude oscillatory regimes (AOS) can be calculated analytically, i.e., small amplitude oscillatory shear (SAOS), medium amplitude oscillatory shear (MAOS), and large amplitude oscillatory shear (LAOS). We show that incorporating the effects of the first and second normal stress differences for all AOS regimes leads to the emergence of higher harmonics. We establish the limits between the different AOS regimes based on criteria suggested by the analytical method. For some typical systems, such as CTAB-NaSal, we found a satisfactory quantitative agreement with the measured behavior of AOS.

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Here \(\tilde{\Sigma }_{zz}\left( \tau \right) \) has been dropped because at the invariant submanifold \(\tilde{\Sigma }_{zz}\left( \tau \right) =0\).

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Abdel-Khalik S, Hassager O, Bird R (1974) The goddard expansion and the kinetic theory for solutions of rodlike macromolecules. J Chem Phys 61(10):4312–4316. https://doi.org/10.1063/1.1681736ADSCrossRef

Akers LC, Williams MC (2003) Oscillatory normal stresses in dilute polymer solutions. J Chem Phys 51(9):3834–3841. https://doi.org/10.1063/1.1672599ADSCrossRef

Bautista F, Hernandez E, Manero O et al (2023) The global rheological diagram and critical phenomena beyond equilibrium for self-associative fluids. J Nonnewton Fluid Mech 317:105045. https://doi.org/10.1016/j.jnnfm.2023.105045MathSciNetCrossRef

Bharadwaj NA, Ewoldt RH (2014) The general low-frequency prediction for asymptotically nonlinear material functions in oscillatory shear. J Rheol 58(4):891–910. https://doi.org/10.1122/1.4874344ADSCrossRef

Bird R, Hassager O, Abdel-Khalik S (1974) Co-rotational rheological models and the goddard expansion. AIChE J 20(6):041–066. https://doi.org/10.1002/aic.690200602CrossRef

Bird RB, Warner HR, Evans DC (1971) Kinetic theory and rheology of dumbbell suspensions with brownian motion. In: Adv. Pol. Sci., vol 8. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 1–90

Bird RB, Giacomin AJ, Schmalzer AM et al (2014) Dilute rigid dumbbell suspensions in large-amplitude oscillatory shear flow: Shear stress response. J Chem Phys 140(7):074904. https://doi.org/10.1063/1.4862899ADSCrossRefPubMed

Bozorgi Y, Underhill PT (2014) Large-amplitude oscillatory shear rheology of dilute active suspensions. Rheol Acta 53(12):899–909. https://doi.org/10.1007/s00397-014-0806-yCrossRef

Carter KA, Girkin JM, Fielding SM (2016) Shear banding in large amplitude oscillatory shear (LAOStrain and LAOStress) of polymers and wormlike micelles. J Rheol 60(5):883–904. https://doi.org/10.1122/1.4960512ADSCrossRef

Cho KS, Song KW, Chang GS (2010) Scaling relations in nonlinear viscoelastic behavior of aqueous PEO solutions under large amplitude oscillatory shear flow. J Rheol 54(1):27–63. https://doi.org/10.1122/1.3258278ADSCrossRef

Fan XJ, Byron Bird R (1984) A kinetic theory for polymer melts vi. calculation of additional material functions. J Non-Newtonian Fluid Mech 15(3), 341-373. https://doi.org/10.1016/0377-0257(84)80018-X

Fardin MA, Perge C, Casanellas L et al (2014) Flow instabilities in large amplitude oscillatory shear: a cautionary tale. Rheol Acta 53(12):885–898. https://doi.org/10.1007/s00397-014-0818-7CrossRef

García-Sandoval JP, Martín del Campo A, Bautista F et al (2018) Nonhomogeneous flow of micellar solutions: A kinetic-network theory approach. AIChE J 64(6):2277–2292. https://doi.org/10.1002/aic.16079ADSCrossRef

Giacomin A, Bird R, Johnson L et al (2011) Large-amplitude oscillatory shear flow from the corotational maxwell model. J Nonnewton Fluid Mech 166(19):1081–1099. https://doi.org/10.1016/j.jnnfm.2011.04.002CrossRef

Gurnon AK, Wagner NJ (2012) Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: Giesekus model of banding and nonbanding wormlike micelles. J Rheol 56(2):333–351. https://doi.org/10.1122/1.3684751ADSCrossRef

Helfand E, Pearson DS (1982) Calculation of the nonlinear stress of polymers in oscillatory shear fields. J Polym Sci Polym Phys Ed 20(7):1249–1258. https://doi.org/10.1002/pol.1982.180200711CrossRef

Hernandez E, Manero O, Bautista F et al (2021) Analytic matrix method for frequency response techniques applied to nonlinear dynamical systems I: Small and Medium Amplitude Oscillations. Mathematics 9(24):3287–3307. https://doi.org/10.3390/math1485579CrossRef

Hernandez E, Manero O, Bautista F et al (2022) Analytic matrix method for frequency response techniques applied to nonlinear dynamical systems II: Large Amplitude Oscillations. Mathematics 10(15):2700. https://doi.org/10.3390/math10152700CrossRef

Hinch EJ, Leal LG (1975) Constitutive equations in suspension mechanics. Part 1. General formulation. J Fluid Mech 71(3):481–495. https://doi.org/10.1017/S0022112075002698ADSCrossRef

Hyun K, Wilhelm M (2009) Establishing a new mechanical nonlinear coefficient Q from FT-rheology: first investigation of entangled linear and comb polymer model systems. Macromolecules 42(1):411–422. https://doi.org/10.1021/ma8017266ADSCrossRef

Hyun K, Baik ES, Ahn KH et al (2007) Fourier-transform rheology under medium amplitude oscillatory shear for linear and branched polymer melts. J Rheol 51:1319–1342. https://doi.org/10.1122/1.2790072ADSCrossRef

Jeyaseelan RS, Giacomin AJ (2008) Network theory for polymer solutions in large amplitude oscillatory shear. J Nonnewton Fluid Mech 148(1):24–32. https://doi.org/10.1016/j.jnnfm.2007.04.012, the A.S. Lodge Commemorative Meeting on Rheometry

Jones TER, Walters K (1971) The behaviour of materials under combined steady and oscillatory shear. J Phys A: Gen Phys 4(1):85. https://doi.org/10.1088/0305-4470/4/1/012ADSCrossRef

Khair AS (2016) On a suspension of nearly spherical colloidal particles under large-amplitude oscillatory shear flow. J Fluid Mech 791:R5. https://doi.org/10.1017/jfm.2016.77ADSMathSciNetCrossRef

Kim SH, Sim HG, Ahn KH et al (2002) Large amplitude oscillatory shear behavior of the network model for associating polymeric systems. Korea-Australia Rheology Journal 14(2):49–55

Kirkwood JG, Plock RJ (1956) Non-newtonian viscoelastic properties of rod-like macromolecules in solution. J Chem Phys 24(4):665–669. https://doi.org/10.1063/1.1742594ADSCrossRef

Lodge A (1961) Rheological properties of concentrated polymer solutions i. growth of pressure fluctuations during prolonged shear flow. Polymer 2:195–201. https://doi.org/10.1016/0032-3861(61)90022-2CrossRef

MacDonald IF, Marsh B, Ashare E (1969) Rheological behavior for large amplitude oscillatory motion. Chem Eng Sci 24(10):1615–1625. https://doi.org/10.1016/0009-2509(69)80101-6CrossRef

Macosko C (1994) Rheology: Principles, Measurements, and Applications. Wiley-VCH, Canada

Manero O, Pérez-López J, Escalante J et al (2007) A thermodynamic approach to rheology of complex fluids: The generalized bmp model. J Nonnewton Fluid Mech 146(1):22–29. https://doi.org/10.1016/j.jnnfm.2007.02.012, 3rd Annual European Rheology Conference

Mou CY, Mazo RM (2008) Normal stress in a solution of a plane-polygonal polymer under oscillating shearing flow. J Chem Phys 67(12):5972–5973. https://doi.org/10.1063/1.434774ADSCrossRef

Onogi S, Masuda T, Matsumoto T (1970) Non-linear behavior of viscoelastic materials. I. Disperse systems of polystyrene solution and carbon black. Trans Soc Rheol 14:275–294. https://doi.org/10.1122/1.549190CrossRef

Paul E, Mazo RM (2003) Hydrodynamic properties of a plane-polygonal polymer, according to kirkwood-riseman theory. J Chem Phys 51(3):1102–1107. https://doi.org/10.1063/1.1672109ADSCrossRef

Pearson DS, Rochefort WE (1982) Behavior of concentrated polystyrene solutions in large-amplitude oscillating shear fields. J Polym Sci B 20(1):83–98. https://doi.org/10.1002/pol.1982.180200107CrossRef

Phan-Thien N, Newberry M, Tanner RI (2000) Non-linear oscillatory flow of a soft solid-like viscoelastic material. J Nonnewton Fluid Mech 92(1):67–80. https://doi.org/10.1016/S0377-0257(99)00110-XCrossRef

Rehage H, Fuchs R (2015) Experimental and numerical investigations of the non-linear rheological properties of viscoelastic surfactant solutions: application and failing of the one-mode Giesekus model. Colloid Polym Sci 293(11):3249–3265. https://doi.org/10.1007/s00396-015-3689-2

Rouyer F, Cohen-Addad S, Höhler R et al (2008) The large amplitude oscillatory strain response of aqueous foam: Strain localization and full stress Fourier spectrum. The European Physical Journal E 27(3):309–321. https://doi.org/10.1140/epje/i2008-10382-7CrossRef

Saengow C, Giacomin AJ, Kolitawong C (2015) Exact analytical solution for large-amplitude oscillatory shear flow. Macromol Theory Simul 24(4):352–392. https://doi.org/10.1002/mats.201400104CrossRef

Sim HG, Ahn KH, Lee SJ (2003) Three-dimensional dynamics simulation of electrorheological fluids under large amplitude oscillatory shear flow. J Rheol 47(4):879–895. https://doi.org/10.1122/1.1582854ADSCrossRef

Song HY, Hyun K (2019) First-harmonic intrinsic nonlinearity of model polymer solutions in medium amplitude oscillatory shear (MAOS). Korea-Aust Rheol J 31:1–13. https://doi.org/10.1007/s13367-019-0001-xCrossRef

Spriggs T (1965) A four-constant model for viscoelastic fluids. Chem Eng Sci 20(11):931–940. https://doi.org/10.1016/0009-2509(65)80091-4CrossRef

Swan JW, Furst EM, Wagner NJ (2014) The medium amplitude oscillatory shear of semi-dilute colloidal dispersions. Part I: Linear response and normal stress differences. J Rheol 58:307–337. https://doi.org/10.1122/1.4861071ADSCrossRef

Thompson RL, Alicke AA, de Souza Mendes PR (2015) Model-based material functions for saos and laos analyses. J Nonnewton Fluid Mech 215:19–30. https://doi.org/10.1016/j.jnnfm.2014.10.013MathSciNetCrossRef

Vishal B, Ghosh P (2018) Nonlinear viscoelastic behavior of aqueous foam under large amplitude oscillatory shear flow. Korea-Australia Rheology Journal 30(3):147–159. https://doi.org/10.1007/s13367-018-0015-9CrossRef

Wagner MH, Rolón-Garrido VH, Hyun K et al (2011) Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers. J Rheol 55(3):495–516. https://doi.org/10.1122/1.3553031ADSCrossRef

Wilhelm M (2002) Fourier-transform rheology. Macromol Mater Engng 287(2):83–105. https://doi.org/10.1002/1439-2054(20020201)287:2<83::aid-mame83>3.0.co;2-bCrossRef

Williams MC, Bird RB (1962) Three-constant oldroyd model for viscoelastic fluids. The Physics of Fluids 5(9):1126–1128. https://doi.org/10.1063/1.1724486ADSCrossRef

Yu W, Bousmina M, Grmela M et al (2002) Quantitative relationship between rheology and morphology in emulsions. J Rheol 46(6):1381–1399. https://doi.org/10.1122/1.1517302ADSCrossRef

Yu W, Bousmina M, Grmela M et al (2002) Modeling of oscillatory shear flow of emulsions under small and large deformation fields. J Rheol 46(6):1401–1418. https://doi.org/10.1122/1.1517303ADSCrossRef

Zhou L, Cook L, McKinley GH (2010) Probing shear-banding transitions of the vcm model for entangled wormlike micellar solutions using large amplitude oscillatory shear (laos) deformations. J Nonnewton Fluid Mech 165(21):1462–1472. https://doi.org/10.1016/j.jnnfm.2010.07.009CrossRef

Title: Frequency response analysis of the Bautista-Manero-Puig model with normal stress: analytical and numerical solution for large amplitudes
Authors: E. Hernandez
F. Bautista
J. P. García-Sandoval
O. Manero
Publication date: 16-02-2024
Publisher: Springer Berlin Heidelberg
Published in: Rheologica Acta / Issue 3/2024
Print ISSN: 0035-4511
Electronic ISSN: 1435-1528
DOI: https://doi.org/10.1007/s00397-024-01434-2

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