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A revisit of strain-rate frequency superposition of dense colloidal suspensions under oscillatory shears

  • Materials, Metallurgy, Chemical and Environmental Engineering
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Abstract

Strain-rate frequency superposition (SRFS) is often employed to probe the low-frequency behavior of soft solids under oscillatory shear in anticipated linear response. However, physical interpretation of an apparently well-overlapped master curve generated by SRFS has to combine with nonlinear analysis techniques such as Fourier transform rheology and stress decomposition method. The benefit of SRFS is discarded when some inconsistencies of the shifted master curves with the canonical linear response are observed. In this work, instead of evaluating the SRFS in full master curves, two criteria were proposed to decompose the original SRFS data and to delete the bad experimental data. Application to Carabopol suspensions indicates that good master curves could be constructed based upon the modified data and the high-frequency deviations often observed in original SRFS master curves are eliminated. The modified SRFS data also enable a better quantitative description and the evaluation of the apparent structural relaxation time by the two-mode fractional Maxwell model.

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References

  1. HYUN K, WILHELM M, KLEIN C O, CHO K S, NAM J G, AHN K H, LEE S J, EWOLDT R H, MCKINLEY G H. A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS) [J]. Progress in Polymer Science, 2011, 36(12): 1697–1753.

    Article  Google Scholar 

  2. KALELKAR C, LELE A, KAMBLE S. Strain-rate frequency superposition in large-amplitude oscillatory shear [J]. Physical Review E, 2010, 81: 031401.

    Article  Google Scholar 

  3. TSCHOEGL N W, TSCHOEGL N W. The phenomenological theory of linear viscoelastic behavior: An introduction [M]. New York: Springer-Verlag Berlin, 1989: 35–68.

    Book  MATH  Google Scholar 

  4. FERRY J D. Viscoelastic properties of polymers [M]. New York: John Wiley & Sons, 1980: 234–237.

    Google Scholar 

  5. WYSS H M, MIYAZAKI K, MATTSSON J, HU Z, REICHMAN D R, WEITZ D A. Strain-rate frequency superposition: A rheological probe of structural relaxation in soft materials [J]. Physical Review Letters, 2007, 98: 238303.

    Article  Google Scholar 

  6. DEALY J, PLAZEK D. Time-temperature superposition—A users guide [J]. Rheology Bulletin, 2009, 78(2): 16–31.

    Google Scholar 

  7. ROULEAU L, DEÜ J F, LEGAY A, LE L F. Application of Kramers–Kronig relations to time–temperature superposition for viscoelastic materials [J]. Mechanics of Materials, 2013, 65: 66–75.

    Article  Google Scholar 

  8. EWOLDT R, BHARADWAJ N A. Low-dimensional intrinsic material functions for nonlinear viscoelasticity [J]. Rheologica Acta, 2013, 52(3): 201–219.

    Article  Google Scholar 

  9. KALELKAR C, LELE A, KAMBLE S. Strain-rate frequency superposition in large-amplitude oscillatory shear [J]. Physical Review E, 2010, 81(3): 031401.

    Article  Google Scholar 

  10. HESS A, AKSEL N. Yielding and structural relaxation in soft materials: Evaluation of strain-rate frequency superposition data by the stress decomposition method [J]. Physical Review E, 2011, 84(5): 051502.

    Article  Google Scholar 

  11. CHO K S, HYUN K, AHN K H, LEE S J. A geometrical interpretation of large amplitude oscillatory shear response [J]. Journal of Rheology, 2005, 49(3): 747–758.

    Article  Google Scholar 

  12. EWOLDT R H, HOSOI A E, MCKINLEY G H. New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear [J]. Journal of Rheology, 2008, 52(6): 1427–1458.

    Article  Google Scholar 

  13. DIMITRIOU C J, EWOLDT R H, MCKINLEY G H. Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress) [J]. Journal of Rheology, 2013, 57(1): 27–70.

    Article  Google Scholar 

  14. ERWIN B M, ROGERS S A, CLOITRE M, VLASSOPOULOS D. Examining the validity of strain-rate frequency superposition when measuring the linear viscoelastic properties of soft materials [J]. Journal of Rheology, 2010, 54(2): 187–195.

    Article  Google Scholar 

  15. BIRD R B, ARMSTRONG R C, HASSAGER O. Dynamics of polymeric liquids. Volume 1: fluid mechanics [M]. New York: John Wiley & Sons, 1987: 455–459.

    Google Scholar 

  16. WILHELM M, MARING D, SPIESS H W. Fourier-transform rheology [J]. Rheologica Acta, 1998, 37(4): 399–405.

    Article  Google Scholar 

  17. PEARSON D S, ROCHEFORT W E. Behavior of concentrated polystyrene solutions in large-amplitude oscillating shear fields [J]. Journal of Polymer Science: Polymer Physics Edition, 1982, 20(1): 83–98.

    Google Scholar 

  18. DRAPACA C S, SIVALOGANATHAN S, TENTI G. Nonlinear constitutive laws in viscoelasticity [J]. Mathematics and Mechanics of Solids, 2007, 12(5): 475–501.

    Article  MathSciNet  MATH  Google Scholar 

  19. GANERIWALA S N, ROTZ C A. Fourier transform mechanical analysis for determining the nonlinear viscoelastic properties of polymers [J]. Polymer Engineering & Science, 1987, 27(2): 165–178.

    Article  Google Scholar 

  20. CHO K S, SONG K W, CHANG G S. Scaling relations in nonlinear viscoelastic behavior of aqueous PEO solutions under large amplitude oscillatory shear flow [J]. Journal of Rheology, 2010, 54(1): 27–63.

    Article  Google Scholar 

  21. BOOIJ H C, THOONE G P. Generalization of Kramers-Kronig transforms and some approximations of relations between viscoelastic quantities [J]. Rheologica Acta, 1982, 21(1): 15–24.

    Article  MATH  Google Scholar 

  22. DROZDOV A D. Constitutive models in linear viscoelasticity [M]. London: Academic Presss City, 1998: 25–106.

    Google Scholar 

  23. ANDERSSEN R S, LOY R J. Completely monotone fading memory relaxation modulii [J]. Bulletin of the Australian Mathematical Society, 2002, 65(3): 449–460.

    Article  MathSciNet  MATH  Google Scholar 

  24. ROBERT B. B, ROBERT C A, OLE H. Dynamics of polymeric liquids, kinetic theory [M]. New York: Wiley-Interscience, 1987: 112–120.

    Google Scholar 

  25. JOHN M D, RONALD G. Structure and rheology of molten polymers: from structure to flow behavior and back again [M]. Munich: Hanser Gardner Publications, 2006: 91–99.

    Google Scholar 

  26. JAISHANKAR A, MCKINLEY G H. Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2013, 469: 2149–2166.

    MathSciNet  Google Scholar 

  27. NIKIFOROV A F, UVAROV V B. Special functions of mathematical physics [M]. Boston: Springer, 1988: 2149–2166.

    Book  Google Scholar 

  28. WANG Bao, WANG Li-jun, LI Dong, WEI Qing, ADHIKARI B. The rheological behavior of native and high-pressure homogenized waxy maize starch pastes [J]. Carbohydrate Polymers, 2012, 88(2): 481–489.

    Article  Google Scholar 

  29. SHU Rui-wen, SUN Wei-xiang, WANG Tao, WANG Chao-yang, LIU Xin-xing, TONG Zhen. Linear and nonlinear viscoelasticity of water-in-oil emulsions: Effect of droplet elasticity [J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2013, 434: 220–228.

    Article  Google Scholar 

  30. van HORN, B L, WINTER H H. Dynamics of shear aligning of nematic liquid crystal monodomains [J]. Rheologica Acta, 2000, 39(3): 294–300.

    Article  Google Scholar 

  31. HOWARD A B, HUTTON J F. An introduction to rheology [M]. Elsevier, 1989: 46–50.

    Google Scholar 

  32. BRADER J M, SIEBENBÜRGER M, BALLAUFF M, REINHEIMER K, WILHELM M, FREY S J, WEYSSER F, FUCHS M. Nonlinear response of dense colloidal suspensions under oscillatory shear: Mode-coupling theory and Fourier transform rheology experiments [J]. Physical Review E, 2010, 82(6): 061401.

    Article  Google Scholar 

  33. HYUN K, WILHELM M. Establishing a new mechanical nonlinear coefficient Q from FT-Rheology: First investigation of entangled linear and comb polymer model systems [J]. Macromolecules, 2008, 42(1): 411–422.

    Article  Google Scholar 

  34. PIPKIN A C. Lectures on viscoelasticity theory [M]. Springer-Verlag, 1986: 132–135.

    Book  Google Scholar 

  35. EWOLDT R H, HOSOI A E, MCKINLEY G H. Rheological fingerprinting of complex fluids using large amplitude oscillatory shear (laos) flow [J]. Annual Transactions-Nordic Rheology Society, 2007, 15: 3–8.

    Google Scholar 

  36. MOLLER P C F, MEWIS J, BONN D. Yield stress and thixotropy: On the difficulty of measuring yield stresses in practice [J]. Soft Matter, 2006, 2(4): 274–283.

    Article  Google Scholar 

  37. MØLLER P C F, RODTS S, MICHELS M A J, BONN D. Shear banding and yield stress in soft glassy materials [J]. Physical Review E, 2008, 77(4): 041507.

    Article  Google Scholar 

  38. DAVIES A, ANDERSSEN R S. Sampling localization in determining the relaxation spectrum [J]. Journal of Non-Newtonian Fluid Mechanics, 1997, 73(1): 163–179.

    Article  Google Scholar 

  39. MUSTAPHA S S, PHILLIPS T. A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum [J]. Journal of Physics D: Applied Physics, 2000, 33(10): 1219.

    Article  Google Scholar 

  40. BAUMGAERTEL M, WINTER H H. Determination of discrete relaxation and retardation time spectra from dynamic mechanical data [J]. Rheologica Acta, 1989, 28(6): 511–519.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematic, Xiamen University, Xiamen, 361005, China

    Jun-jie Li  (李俊杰)

  2. Fujian Key Laboratory of Advanced Materials, Xiamen University, Xiamen, 361005, China

    Jun-jie Li  (李俊杰), Xuan Cheng  (程璇) & Ying Zhang  (张颖)

  3. Department of Materials Science and Engineering, College of Materials, Xiamen University, Xiamen, 361005, China

    Xuan Cheng  (程璇) & Ying Zhang  (张颖)

  4. Research Institute of Materials Science and State Key Laboratory of Luminescent Materials and Devices, South China University of Technology, Guangzhou, 510640, China

    Wei-xiang Sun  (孙尉翔)

Authors
  1. Jun-jie Li  (李俊杰)
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  2. Xuan Cheng  (程璇)
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  3. Ying Zhang  (张颖)
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  4. Wei-xiang Sun  (孙尉翔)
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Corresponding author

Correspondence to Ying Zhang  (张颖).

Additional information

Foundation item: Project(11372263) supported by the National Natural Science Foundation of China

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Li, Jj., Cheng, X., Zhang, Y. et al. A revisit of strain-rate frequency superposition of dense colloidal suspensions under oscillatory shears. J. Cent. South Univ. 23, 1873–1882 (2016). https://doi.org/10.1007/s11771-016-3242-6

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  • DOI: https://doi.org/10.1007/s11771-016-3242-6

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