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Large-amplitude oscillatory shear flow simulation for a FENE fluid

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Abstract

In this work, the FENE dumbbell model under small- and large-amplitude oscillatory shear flows using a micro-macro approach is presented. This approach involves the evolution of an ensemble of Brownian Configuration Fields which describes the polymer dynamics of the microscopic scale and the momentum equation describes the macroscopic scale. The Lissajous curves for the shear stress and the first normal stress difference versus the instantaneous strain or strain rate for the elastic or viscous projection are shown. The influences of the solvent/polymer viscosity ratio, the maximum extension length, and the relation between strain rate and frequency are analyzed. An important finding is the self-intersection of the Lissajous curves, which forms secondary loops for short extension lengths and high Weissenberg/Deborah dimensionless numbers ratio.

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References

  • Adrian DW, Giacomin A (1992) The quasi-periodic nature of a polyurethane melt in oscillatory shear. J Rheol 36(7):1227–1243

    Article  CAS  Google Scholar 

  • Atalik K, Keunings R (2004a) On the occurrence of even harmonics in the shear stress response of viscoelastic fluids in large amplitude oscillatory shear. J Non-Newtonian Fluid Mech 122(2):107–116

    Article  CAS  Google Scholar 

  • Atalik K, Keunings R (2004b) On the occurrence of even harmonics in the shear stress response of viscoelastic fluids in large amplitude oscillatory shear. J Non-Newtonian Fluid Mech 122:107–116

    Article  CAS  Google Scholar 

  • Bharadwaj NA, Ewoldt RH (2014) The general low-frequency prediction for asymptotically nonlinear material functions in oscillatory shear. J Rheol 58(4):891–910

    Article  CAS  Google Scholar 

  • Bird RB, Hassager O, Armstrong RC, Curtiss CF (1977) Dynamics of polymeric liquids vol.2. Kinetic theory. Wiley, New York

    Google Scholar 

  • Bird RB, Giacomin AJ, Schmalzer AM, Aumnate C (2014) Dilute rigid dumbbell suspensions in large-amplitude oscillatory shear flow: Shear stress response. J Chem Phys 140(7):074,904–1–074,904–16

    Article  CAS  Google Scholar 

  • Blawzdziewicz Vlahovska JP aand, Loewenberg M (2002) Nonlinear rheology of a dilute emulsion of surfactant-covered spherical drops in time-dependent flows. J Fluid Mech 463:1–24

    Article  CAS  Google Scholar 

  • Deshpande AP (2010) Rheology of complex fluids. Springer, New York

    Google Scholar 

  • de Souza-Mendes PR, Thompson RL (2013) A unified approach to model elasto-viscoplastic thixotropic yield-stress materials and apparent yield-stress fluids. Rheol Acta 52(7):673–694

    Article  CAS  Google Scholar 

  • Ewoldt RH, McKinley GH (2010) On secondary loops in Laos via self-intersection of lissajous–bowditch curves. Rheol Acta 49(6):213–219

    Article  CAS  Google Scholar 

  • Ewoldt RH, Hosoi AE, McKinley GH (2008) New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J Rheol 52(6):1427–1458

    Article  CAS  Google Scholar 

  • Ferrer V, Gómez A, Ortega J, Manero O, Rincón E, López-Serrano F, Vargas RO (2017) Modeling of complex fluids using micro-macro approach with transient network dynamics. Rheol Acta 56(5):445–459

    Article  CAS  Google Scholar 

  • Giacomin AJ (1987) A sliding plate melt rheometer incorporating a shear stress transducer. McGill University, PhD Thesis

    Google Scholar 

  • Giacomin AJ, Dealy JM (1986) A new rheometer for mmolten plastics. SPE Tech Pappers 32(8):711–714

    Google Scholar 

  • Giacomin AJ, Samurkas T, Dealy JM (1989) A novel sliding plate rheometer for molten plastics. Polym Eng Sci 29(8):499–504

    Article  CAS  Google Scholar 

  • Giacomin AJ, Bird RB, Johnson LM, Mix AW (2011) Large-amplitude oscillatory shear flow from the corotational maxwell model. J Non-Newtonian Fluid Mech 166:1081–1099

    Article  CAS  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Halin P, Lielens G, Keunings R, Legat V (1998) The lagrangian particle method for macroscopic and micro-macro viscoelastic flow computations. J Non-Newtonian Fluid Mech 79(2):387–403

    Article  CAS  Google Scholar 

  • Hatzikiriakos SG, Dealy JM (1991) Wall slip of molten high density polyethylene. i. sliding plate rheometer studies. J Rheol 35(4):497–523

    Article  CAS  Google Scholar 

  • Hulsen MA, van Heel APG, van den Brule BHAA (1997) Simulation of viscoelastic flows using brownian configuration fields. J Non-Newtonian Fluid Mech 70(1):79–101

    Article  CAS  Google Scholar 

  • Hyun K, Kim SH, Kyung HA, Lee SJ (2002) Large amplitude oscillatory shear as a way to classify the complex fluids. J Non-Newtonian Fluid Mech 107(1):51–65

    Article  CAS  Google Scholar 

  • Hyun K, Wilhelm M, Klein CO, Cho KS, Nam JG, Ahn KH, Lee SJ, Ewoldt RH, McKinley GH (2011) A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (laos). Prog Polym Sci 36(12):1697–1753

    Article  CAS  Google Scholar 

  • Jeyaseelan RS, Giacomin AJ (2008) Network theory for polymer solutions in large amplitude oscillatory shear. J Non-Newtonian Fluid Mech 148(1-3):24–32

    Article  CAS  Google Scholar 

  • Khair AS (2016) Large amplitude oscillatory shear of the giesekus model. J Rheol 60(2):257–266

    Article  CAS  Google Scholar 

  • Kim J, Merger D, Wilhelm M, Helgeson ME (2014) Microstructure and nonlinear signa- tures of yielding in a heterogeneous colloidal gel under large amplitude oscillatory shear. J Rheol 58(5):1359–1390

    Article  CAS  Google Scholar 

  • Kornfield JA (1989) Measurement and theory of the dynamics of polydisperse polymer melts. Stanford University, PhD Thesis

    Google Scholar 

  • Kornfield JA, Fuller GG, Pearson DS (1991) Third normal stress difference and component relaxation spectra for bidisperse melts under oscillatory shear. Macromolecules 24(19):5429–5441

    Article  CAS  Google Scholar 

  • Laso M, Öttinger HC (1993) Calculation of viscoelastic flow using molecular models: the connffessit approach. J Non-Newtonian Fluid Mech 47:1–20

    Article  CAS  Google Scholar 

  • Lozinski A, Chauviere C (2003) A fast solver for fokker-planck equation applied to viscoelastic flows calculations: 2d fene model. J Comput Phys 189(2):607–625

    Article  Google Scholar 

  • Mas R, Magnin A (1997) Experimental validation of steady shear and dynamic viscosity relation for yield stress fluids. Rheol Acta 36(1):49–55

    Article  CAS  Google Scholar 

  • Melchior M, Öttinger HC (1995) Variance reduced simulations of stochastic differential equations. J Chem Phys 103(21):9506

    Article  CAS  Google Scholar 

  • Oakley J, Giacomin A, Yosick J (1999) Molecular origins of nonlinear viscoelasticity. Microchim Acta 130(1/2):1

    Google Scholar 

  • Öttinger HC (1995) Stochastic processes in polymeric fluids : tools and examples for developing simulation algorithms. Springer Verlag, Berlin, p 1995

    Google Scholar 

  • Öttinger HC, van den Brule BHAA, Hulsen MA (1997) Brownian configuration fields and variance reduced connffessit. J Non-Newtonian Fluid Mech 70(3):255–261

    Article  Google Scholar 

  • Owens RG, Phillips TN (2002) Computational rheology. Imperial College Press, London

    Book  Google Scholar 

  • Phillips TN, Smith KD (2006) A spectral element approach to the simulation of viscoelastic flows using brownian configuration fields. J Non-Newtonian Fluid Mech 138(2):98–110

    Article  CAS  Google Scholar 

  • Reimers MJ (1989) Sliding plate rheometer studies of concentrated polystyrene solutions. McGill University, PhD Thesis

    Google Scholar 

  • RM J, Dealy JM (1996) Sliding plate rheometer studies of concentrated polystyrene solutions: Large amplitude oscillatory shear of a very high molecular weight polymer in diethyl phthalate. J Rheol 40(1):167–186

    Article  Google Scholar 

  • Rogers SA, Lettinga MP (2012) A sequence of physical processes determined and quantified in large-amplitude oscillatory shear (laos): Application to theoretical nonlinear models. J Rheol 56(1):1–25

    Article  CAS  Google Scholar 

  • Saengow C, Giacomin AJ, Kolitawong C (2015) Exact analytical solution for large-amplitude oscillatory shear flow. Macromol Theory Simul 24(4):352–392

    Article  CAS  Google Scholar 

  • Schmalzer AM, Bird RB, Giacomin AJ (2015) Normal stress differences in large-amplitude oscillatory shear flow for dilute rigid dumbbell suspensions. J Non-Newtonian Fluid Mech 222:56–71

    Article  CAS  Google Scholar 

  • Simon AR, Erwin BM, Vlassopoulos D, Cloitre M (2011) A sequence of physical processes determined and quantified in laos: Application to a yield stress fluid. J Rheol 55(2):435–458

    Article  CAS  Google Scholar 

  • Smith KD, Sequeira A (2011) Micro-macro simulations of a shear-thinning viscoelastic kinetic model: applications to blood flow. Appl Anal 90(1):227–252

    Article  Google Scholar 

  • Stadler FJ, Leygue A, Burhin H, Bailly C (2008) The potential of large amplitude oscillatory shear to gain an insight into the long-chain branching structure of polymers. In: The 235th ACS national meeting, polymer preprints ACS, New Orleans, LA, USA, vol 49, pp 121–122

  • 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(2):307–337

    Article  CAS  Google Scholar 

  • Tiu C, Guo J, Uhlherr H (2006) Yielding behaviour of viscoplastic materials. J Ind Eng Chem 12:653–662

    CAS  Google Scholar 

  • Townsend AK, Wilson HJ (2018) Small- and large-amplitude oscillatory rheometry with bead-spring dumbbells in stokesian dynamics to mimic viscoelasticity. J Non-Newtonian Fluid Mech 261:136–152

    Article  CAS  Google Scholar 

  • van den Brule BHAA (1993) Browian dynamics simulation of finitely extensible bead-spring chains. J Non-Newtonian Fluid Mech 47(C):357–378

    Article  Google Scholar 

  • van Heel APG, Hulsen MA, van den Brule BHAA (1998) On the selection of parameters in the FENE-P model. J Non-Newtonian Fluid Mech 75(2-3):253–271

    Article  Google Scholar 

  • vom Scheidt J (1989) Introduction to stochastic differential equations. J Appl Math Mech 69(8):258

    Google Scholar 

  • Vargas RO, Manero O, Phillips TN (2009) Viscoelastic flow past confined objects using a micro-macro approach. Rheol Acta 48(4):373–395

    Article  CAS  Google Scholar 

  • Warner HR (1972) Kinetic theory and rheology of dilute suspensions of finitely extendible dumbbells. Ind Eng Chem Fundam 11(3):379–387

    Article  CAS  Google Scholar 

  • Wendt JF, Anderson JD (2009) Computational fluid dynamics : an introduction. Springer Verlag, New York

    Book  Google Scholar 

  • Xi-Jun F, Bird RB (1984) A kinetic theory for polymer melts vi. calculation of additional material functions. J Non-Newtonian Fluid Mech 15(3):341–373

    Article  Google Scholar 

  • Yosick JA, Giacomin JA, Stewart WE, Ding F (1998) Fluid inertia in large amplitude oscillatory shear. Rheol Acta 37(4):365–373

    Article  CAS  Google Scholar 

Download references

Funding

The first author received financial support from the National Council for Science and Technology (CONACyT) of Mexico and the National Autonomous University of México (UNAM) through its postgraduate programs. R.O.V. received support with the project SIP-IPN 20196476.

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Authors and Affiliations

  1. Departamento de Termofluidos, Facultad de Ingeniería, Universidad Nacional Autónoma de México, Mexico City, 04510, Mexico

    Aldo Gómez-López

  2. ESIME-Zacatenco, Instituto Politécnico Nacional, Mexico City, 07738, Mexico

    Víctor H. Ferrer

  3. Dirección, Morelos Sociedad al Servicio de la niñez s.c., Morelos 11, Santa Fe, Ciudad de México, 01210, México

    Eduardo Rincón

  4. Instituto de Ciencias Aplicadas y Tecnología, Universidad Nacional Autónoma de México, Mexico City, 04510, Mexico

    Juan P. Aguayo

  5. Departamento de Ingenierá Química, Facultad de Química, Universidad Nacional Autónoma de México, Mexico City, 04510, Mexico

    Ángel E. Chávez

  6. ESIME Azcapotzalco, Instituto Politécnico Nacional, Av. de las Granjas 682, Col. Santa Catarina, Del. Azcapotzalco, Mexico City, 02250, Mexico

    René O. Vargas

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  1. Aldo Gómez-López
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Correspondence to René O. Vargas.

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Gómez-López, A., Ferrer, V.H., Rincón, E. et al. Large-amplitude oscillatory shear flow simulation for a FENE fluid. Rheol Acta 58, 241–260 (2019). https://doi.org/10.1007/s00397-019-01145-z

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  • DOI: https://doi.org/10.1007/s00397-019-01145-z

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