Advertisement

Korea-Australia Rheology Journal

, Volume 31, Issue 4, pp 267–284 | Cite as

Nonlinear material functions under medium amplitude oscillatory shear (MAOS) flow

  • Hyeong Yong Song
  • Kyu HyunEmail author
Article

Abstract

Dynamic oscillatory shear flow has been widely used to investigate viscoelastic material functions. In particular, small amplitude oscillatory shear (SAOS) tests have become the canonical method for characterizing the linear viscoelastic properties of complex fluids based on strong theoretical background and plenty of experimental results. Recently, there has been increasing interest in the use of large amplitude oscillatory shear (LAOS) tests for the characterization of complex fluids. However, it is difficult to define material functions in LAOS regime due to an infinite number of higher harmonic contributions. For this reason, many recent studies have focused on intrinsic nonlinearities obtained in medium amplitude oscillatory shear (MAOS) regime, which is a subdivision of the full LAOS regime. In this study, we reviewed recent experimental and theoretical results of nonlinear material functions in the MAOS regime, which contain four MAOS moduli (two first-harmonic moduli and two third-harmonic moduli) from Fourier and power series of shear stress, and a nonlinear material function Q0 and its elastic and viscous parts from Fourier-transform rheology (FT rheology). Furthermore, to identify linear-to-nonlinear transitions in stress response of model polystyrene (PS) solutions, we presented Pipkin diagrams in frequency ranges from the rubbery plateau region to the terminal region.

Keywords

medium amplitude oscillatory shear MAOS moduli FT rheology material functions nonlinear rheology 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgments

This work was supported by a 2-Year Research Grant of Pusan National University.

References

  1. Abbasi, M., N.G. Ebrahimi, and M. Wilhelm, 2013, Investigation of the rheological behavior of industrial tubular and autoclave LDPEs under SAOS, LAOS, transient shear, and elongational flows compared with predictions from the MSF theory, J. Rheol.57, 1693–1714.CrossRefGoogle Scholar
  2. Astarita, G. and R.J.J. Jongschaap, 1978, The maximum amplitude of strain for the validity of linear viscoelasticity, J. Non-Newton. Fluid Mech.3, 281–287.CrossRefGoogle Scholar
  3. Bae, J.E. and K.S. Cho, 2017, Analytical studies on the LAOS behaviors of some popularly used viscoelastic constitutive equations with a new insight on stress decomposition of normal stresses, Phys. Fluids29, 093103.CrossRefGoogle Scholar
  4. Bharadwaj, N.A. and R.H. Ewoldt, 2014, The general low-frequency prediction for asymptotically nonlinear material functions in oscillatory shear, J. Rheol.58, 891–910.CrossRefGoogle Scholar
  5. Bharadwaj, N.A. and R.H. Ewoldt, 2015, Constitutive model fingerprints in medium-amplitude oscillatory shear, J. Rheol.59, 557–592.CrossRefGoogle Scholar
  6. Bharadwaj, N.A., K.S. Schweizer, and R.H. Ewoldt, 2017, A strain stiffening theory for transient polymer networks under asymptotically nonlinear oscillatory shear, J. Rheol.61, 643–665.CrossRefGoogle Scholar
  7. Bird, R.B., A.J. Giacomin, A.M. Schmalzer, and C. Aumnate, 2014, Dilute rigid dumbbell suspensions in large-amplitude oscillatory shear flow: Shear stress response, J. Chem. Phys.140, 074904.CrossRefGoogle Scholar
  8. Bird, R.B., R.C. Armstrong, and O. Hassager, 1987, Dynamics of polymeric liquids. Vol. 1: Fluid Mechanics, 2nd ed., John Wiley & Sons, New York.Google Scholar
  9. Bozorgi, Y. and P.T. Underhill, 2014, Large-amplitude oscillatory shear rheology of dilute active suspensions, Rheol. Acta53, 899–909.CrossRefGoogle Scholar
  10. Chang, G.S., H.J. Ahn, and K.W. Song, 2015, A simple analysis method to predict the large amplitude oscillatory shear (LAOS) flow behavior of viscoelastic polymer liquids, Text. Sci. Eng.52, 159–166.CrossRefGoogle Scholar
  11. Chang, G.S., H.J. Ahn, and K.W. Song, 2016, Discrete Fourier transform analysis to characterize the large amplitude oscillatory shear (LAOS) flow behavior of viscoelastic polymer liquids, Text. Sci. Eng.53, 317–327.CrossRefGoogle Scholar
  12. Cho, K.S., K. Hyun, K.H. Ahn, and S.J. Lee, 2005, A geometrical interpretation of large amplitude oscillatory shear response, J. Rheol.49, 747–758.CrossRefGoogle Scholar
  13. Cho, K.S., K.W. Song, and G.S. Chang, 2010, Scaling relations in nonlinear viscoelastic behavior of aqueous PEO solutions under large amplitude oscillatory shear flow, J. Rheol.54, 27–63.CrossRefGoogle Scholar
  14. Costanzo, S., Q. Huang, G. Ianniruberto, G. Marrucci, O. Hassager, and D. Vlassopoulos, 2016, Shear and extensional rheology of polystyrene melts and solutions with the same number of entanglements, Macromolecules49, 3925–3935.CrossRefGoogle Scholar
  15. Cziep, M.A., M. Abbasi, M. Heck, L. Arens, and M. Wilhelm, 2016, Effect of molecular weight, polydispersity, and monomer of linear homopolymer melts on the intrinsic mechanical nonlinearity 3Q 0(ω) in MAOS, Macromolecules49, 3566–3579.CrossRefGoogle Scholar
  16. Davis, W.M. and C.W. Macosko, 1978, Nonlinear dynamic mechanical moduli for polycarbonate and PMMA, J. Rheol.22, 53–71.CrossRefGoogle Scholar
  17. Ewoldt, R.H. and N.A. Bharadwaj, 2013, Low-dimensional intrinsic material functions for nonlinear viscoelasticity, Rheol. Acta52, 201–219.CrossRefGoogle Scholar
  18. Ewoldt, R.H., A. Hosoi, and G.H. McKinley, 2008, New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear, J. Rheol.52, 1427–1458.CrossRefGoogle Scholar
  19. Fan, X.J. and R.B. Bird, 1984, A kinetic theory for polymer melts VI. Calculation of additional material functions, J. Non-Newton. Fluid Mech.15, 341–373.CrossRefGoogle Scholar
  20. Ferry, J.D., 1980, Viscoelastic Properties of Polymers, 3rd ed., John Wiley & Sons, New York.Google Scholar
  21. Giacomin, A.J. and J.M. Dealy, 1993, Large-amplitude oscillatory shear, In: Collyer, A.A., eds., Techniques in Rheological Measurement, Chapman & Hall, Dordrecht, 99–121.CrossRefGoogle Scholar
  22. Giacomin, A.J., R.B. Bird, L.M. Johnson, and A.W. Mix, 2011, Large-amplitude oscillatory shear flow from the corotational Maxwell model, J. Non-Newton. Fluid Mech.166, 1081–1099.CrossRefGoogle Scholar
  23. Giacomin, A.J., R.S. Jeyaseelan, T. Samurkas, and J.M. Dealy, 1993, Validity of separable BKZ model for large amplitude oscillatory shear, J. Rheol.37, 811–826.CrossRefGoogle Scholar
  24. Gilbert, P.H. and A.J. Giacomin, 2016, Molecular origins of higher harmonics in large-amplitude oscillatory shear flow: Shear stress response, Phys. Fluids28, 103101.CrossRefGoogle Scholar
  25. Gross, L.H. and B. Maxwell, 1972, The limit of linear viscoelastic response in polymer melts as measured in the maxwell orthogonal rheometer, Trans. Soc. Rheol.16, 577–601.CrossRefGoogle Scholar
  26. Gurnon, A.K. and N.J. Wagner, 2012, Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: Giesekus model of banding and nonbanding wormlike micelles, J. Rheol.56, 333–351.CrossRefGoogle Scholar
  27. Helfand, E. and D.S. Pearson, 1982, Calculation of the nonlinear stress of polymers in oscillatory shear fields, J. Polym. Sci. Pt. B-Polym. Phys.20, 1249–1258.CrossRefGoogle Scholar
  28. Hershey, C. and K. Jayaraman, 2019, Dynamics of entangled polymer chains with nanoparticle attachment under large amplitude oscillatory shear, J. Polym. Sci. Pt. B-Polym. Phys.57, 62–76.CrossRefGoogle Scholar
  29. Hoyle, D.M., D. Auhl, O.G. Harlen, V.C. Barroso, M. Wilhelm, and T.C.B. McLeish, 2014, Large amplitude oscillatory shear and Fourier transform rheology analysis of branched polymer melts, J. Rheol.58, 969–997.CrossRefGoogle Scholar
  30. Hyun, K. and M. Wilhelm, 2009, Establishing a new mechanical nonlinear coefficient Q from FT-rheology: First investigation of entangled linear and comb polymer model systems, Macromolecules42, 411–422.CrossRefGoogle Scholar
  31. Hyun, K. and M. Wilhelm, 2018, Nonlinear oscillatory shear mechanical responses, In: Richert, R., eds., Nonlinear Dielectric Spectroscopy, Springer International Publishing, Cham, 321–368.CrossRefGoogle Scholar
  32. Hyun, K., E.S. Baik, K.H. Ahn, S.J. Lee, M. Sugimoto, and K. Koyama, 2007, Fourier-transform rheology under medium amplitude oscillatory shear for linear and branched polymer melts, J. Rheol.51, 1319–1342.CrossRefGoogle Scholar
  33. Hyun, K., H.T. Lim, and K.H. Ahn, 2012, Nonlinear response of polypropylene (PP)/clay nanocomposites under dynamic oscillatory shear flow, Korea-Aust. Rheol. J.24, 113–120.CrossRefGoogle Scholar
  34. Hyun, K., M. Wilhelm, C.O. Klein, K.S. Cho, J.G. Nam, K.H. Ahn, S.J. Lee, R.H. Ewoldt, and G.H. McKinley, 2011, A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS), Prog. Polym. Sci.36, 1697–1753.CrossRefGoogle Scholar
  35. Hyun, K., S.H. Kim, K.H. Ahn, and S.J. Lee, 2002, Large amplitude oscillatory shear as a way to classify the complex fluids, J. Non-Newton. Fluid Mech.107, 51–65.CrossRefGoogle Scholar
  36. Jongschaap, R.J.J., K.H. Knapper, and J.S. Lopulissa, 1978, On the limit of linear viscoelastic response in the flow between eccentric rotating disks, Polym. Eng. Sci.18, 788–792.CrossRefGoogle Scholar
  37. Kempf, M., D. Ahirwal, M. Cziep, and M. Wilhelm, 2013, Synthesis and linear and nonlinear melt rheology of well-defined comb architectures of PS and PpMS with a low and controlled degree of long-chain branching, Macromolecules46, 4978–4994.CrossRefGoogle Scholar
  38. Kirkwood, J.G. and R.J. Plock, 1956, Non-Newtonian viscoelastic properties of rod-like macromolecules in solution, J. Chem. Phys.24, 665–669.CrossRefGoogle Scholar
  39. Kumar, M.A., R.H. Ewoldt, and C.F. Zukoski, 2016, Intrinsic nonlinearities in the mechanics of hard sphere suspensions, Soft Matter12, 7655–7662.CrossRefGoogle Scholar
  40. Larson, R.G., 1988, Constitutive Equations for Polymer Melts and Solutions, Butterworth-Heinemann, Boston.Google Scholar
  41. Likhtman, A.E. and T.C.B. McLeish, 2002, Quantitative theory for linear dynamics of linear entangled polymers, Macromolecules35, 6332–6343.CrossRefGoogle Scholar
  42. Lim, H.T., K.H. Ahn, J.S. Hong, and K. Hyun, 2013, Nonlinear viscoelasticity of polymer nanocomposites under large amplitude oscillatory shear flow, J. Rheol.57, 767–789.CrossRefGoogle Scholar
  43. Martinetti, L. and R.H. Ewoldt, 2019, Time-strain separability in medium-amplitude oscillatory shear, Phys. Fluids31, 021213.CrossRefGoogle Scholar
  44. Martinetti, L., O. Carey-De La Torre, K.S. Schweizer, and R.H. Ewoldt, 2018, Inferring the nonlinear mechanisms of a reversible network, Macromolecules51, 8772–8789.CrossRefGoogle Scholar
  45. Merger, D., M. Abbasi, J. Merger, A.J. Giacomin, C. Saengow, and M. Wilhelm, 2016, Simple scalar model and analysis for large amplitude oscillatory shear, Appl. Rheol.26, 53809.Google Scholar
  46. Nie, Z., W. Yu, and C. Zhou, 2016, Nonlinear rheological behavior of multiblock copolymers under large amplitude oscillatory shear, J. Rheol.60, 1161–1179.CrossRefGoogle Scholar
  47. Onogi, S., T. Masuda, and K. Kitagawa, 1970, Rheological properties of anionic polystyrenes. I. Dynamic viscoelasticity of narrow-distribution polystyrenes, Macromolecules3, 109–116.CrossRefGoogle Scholar
  48. Paul, E. and R.M. Mazo, 1969, Hydrodynamic properties of a plane-polygonal polymer, according to Kirkwood-Riseman theory, J. Chem. Phys.51, 1102–1107.CrossRefGoogle Scholar
  49. Paul, E., 1969, Non-Newtonian viscoelastic properties of rodlike molecules in solution: Comment on a paper by Kirkwood and Plock, J. Chem. Phys.51, 1271–1272.CrossRefGoogle Scholar
  50. Pearson, D.S. and W.E. Rochefort, 1982, Behavior of concentrated polystyrene solutions in large-amplitude oscillating shear fields, J. Polym. Sci. Pt. B-Polym. Phys.20, 83–98.CrossRefGoogle Scholar
  51. Pipkin, A.C., 1986, Slow viscoelastic flow, In: Pipkin, A.C., eds., Lectures on Viscoelasticity Theory, Springer, New York, 131–156.CrossRefGoogle Scholar
  52. Poungthong, P., A.J. Giacomin, C. Saengow, and C. Kolitawong, 2019, Exact solution for intrinsic nonlinearity in oscillatory shear from the corotational Maxwell fluid, J. Non-Newton. Fluid Mech.265, 53–65.CrossRefGoogle Scholar
  53. Poungthong, P., C. Saengow, A.J. Giacomin, and C. Kolitawong, 2018, Power series for shear stress of polymeric liquid in largeamplitude oscillatory shear flow, Korea-Aust. Rheol. J.30, 169–178.CrossRefGoogle Scholar
  54. Saengow, C. and A.J. Giacomin, 2018, Exact solutions for oscillatory shear sweep behaviors of complex fluids from the Oldroyd 8-constant framework, Phys. Fluids30, 030703.CrossRefGoogle Scholar
  55. Saengow, C., A.J. Giacomin, and C. Kolitawong, 2017, Exact analytical solution for large-amplitude oscillatory shear flow from Oldroyd 8-constant framework: Shear stress, Phys. Fluids29, 043101.CrossRefGoogle Scholar
  56. Salehiyan, R., H.Y. Song, M. Kim, W.J. Choi, and K. Hyun, 2016, Morphological evaluation of PP/PS blends filled with different types of clays by nonlinear rheological analysis, Macromolecules49, 3148–3160.CrossRefGoogle Scholar
  57. Salehiyan, R., H.Y. Song, W.J. Choi, and K. Hyun, 2015, Characterization of effects of silica nanoparticles on (80/20) PP/PS blends via nonlinear rheological properties from Fourier transform rheology, Macromolecules48, 4669–4679.CrossRefGoogle Scholar
  58. Shahid, T., Q. Huang, F. Oosterlinck, C. Clasen, and E. van Ruymbeke, 2017, Dynamic dilution exponent in monodisperse entangled polymer solutions, Soft Matter13, 269–282.CrossRefGoogle Scholar
  59. Song, H.Y. and K. Hyun, 2018, Decomposition of Q 0 from FTrheology into elastic and viscous parts: Intrinsic-nonlinear master curves for polymer solutions, J. Rheol.62, 919–939.CrossRefGoogle Scholar
  60. Song, H.Y. and K. Hyun, 2019, First-harmonic intrinsic nonlinearity of model polymer solutions in medium amplitude oscillatory shear (MAOS), Korea-Aust. Rheol. J.31, 1–13.CrossRefGoogle Scholar
  61. Song, H.Y., O.S. Nnyigide, R. Salehiyan, and K. Hyun, 2016, Investigation of nonlinear rheological behavior of linear and 3-arm star 1,4-cis-polyisoprene (PI) under medium amplitude oscillatory shear (MAOS) flow via FT-rheology, Polymer104, 268–278.CrossRefGoogle Scholar
  62. Song, H.Y., S.J. Park, and K. Hyun, 2017a, Characterization of dilution effect of semidilute polymer solution on intrinsic nonlinearity Q 0 via FT rheology, Macromolecules50, 6238–6254.CrossRefGoogle Scholar
  63. Song, H.Y., R. Salehiyan, X. Li, S.H. Lee, and K. Hyun, 2017b, A comparative study of the effects of cone-plate and parallelplate geometries on rheological properties under oscillatory shear flow, Korea-Aust. Rheol. J.29, 281–294.CrossRefGoogle Scholar
  64. Wagner, M.H., V.H. Rolón-Garrido, K. Hyun, and M. Wilhelm, 2011, Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers, J. Rheol.55, 495–516.CrossRefGoogle Scholar
  65. Wilhelm, M., 2002, Fourier-transform rheology, Macromol. Mater. Eng.287, 83–105.CrossRefGoogle Scholar
  66. Wilhelm, M., K. Reinheimer, and J. Kübel, 2012, Optimizing the sensitivity of FT-rheology to quantify and differentiate for the first time the nonlinear mechanical response of dispersed beer foams of light and dark beer, Z. Phys. Chemie-Int. J. Res. Phys. Chem. Chem. Phys.226, 547–567.Google Scholar

Copyright information

© The Korean Society of Rheology and Springer 2019

Authors and Affiliations

  1. 1.School of Chemical and Biomolecular EngineeringPusan National UniversityBusanRepublic of Korea

Personalised recommendations