Textile Science and Engineering (한국섬유공학회지)

The Korean Fiber Society (한국섬유공학회)
권호 표지
DOI QR코드

DOI QR Code

Relationships between Steady and Transient Flow Functions for Viscoelastic Polymer Liquids: Experimental and Theoretical Examination of the Gleissle Mirror Relations

점탄성 고분자 액체의 정상유동함수와 과도적 유동함수의 상관관계 연구: Gleissle 밀러 관계식들의 실험적 검증 및 이론적 고찰

  • Kwak, Yun-Jeong (Department of Organic Material Science and Engineering, Pusan National University) ;
  • Ahn, Hye-Jin (Department of Organic Material Science and Engineering, Pusan National University) ;
  • Song, Ki-Won (Department of Organic Material Science and Engineering, Pusan National University)
  • 곽윤정 (부산대학교 공과대학 유기소재시스템공학과) ;
  • 안혜진 (부산대학교 공과대학 유기소재시스템공학과) ;
  • 송기원 (부산대학교 공과대학 유기소재시스템공학과)
  • Received : 2015.04.21
  • Accepted : 2015.06.01
  • Published : 2015.06.30
⟨ Previous Next ⟩

Abstract

The objective of this study is to systematically investigate the relationships between steady flow functions and transient flow functions for viscoelastic polymer liquids. Using a strain-controlled rheometer (Advanced Rheometric Expansion System (ARES)), the steady shear flow properties and the transient shear flow properties of concentrated poly(ethylene oxide) (PEO) solutions have been measured over a wide range of shear rates and times. The validity of the three forms of the Gleissle mirror relations was examined by comparing them with the experimentally obtained results. In addition, the effect of nonlinearity on the applicability of these Gleissle mirror relations was discussed from a theoretical view-point by introducing the concept of a nonlinear strain measure. The main findings obtained from this study can be summarized as follows: (1) A nonlinear strain measure is decreased with an increase in strain magnitude, after reaching the maximum value at small strain range. This behavior is quite different from the theoretical prediction to satisfy the conditions of the Gleissle mirror relations. (2) The first mirror relation describing the equivalence between steady shear flow viscosity and shear stress growth coefficient is valid over a wide range of shear rates and is hardly affected by the nonlinearity of polymer solutions. (3) The second mirror relation expressing the equivalence between first normal stress coefficient and first normal stress growth coefficient is also applicable over a wide range of shear rates. This relation is, however, significantly influenced by the degree of nonlinearity (i.e., shape of a nonlinear strain measure) of polymer solutions. (4) The third mirror relation can be regarded as a very useful empirical model to predict the first normal stress coefficient from steady shear flow viscosity data, provided that an appropriate value of a shift factor is given.

Keywords

Acknowledgement

Supported by : 부산대학교

References

  1. J. M. Dealy and K. F. Wissbrun, "Melt Rheology and Its Role in Plastics Processing : Theory and Applications", Van Nostrand Reinhold, New York, 1990.
  2. R. I. Tanner, "Engineering Rheology", 2nd Ed., Oxford University Press, New York, 2000.
  3. R. B. Bird, R. C. Armstrong, and O. Hassager, "Dynamics of Polymeric Liquids", 2nd Ed., Vol. 1, John Wiley & Sons, New York, 1987.
  4. P. J. Carreau, D. C. R. De Kee, and R. P. Chhabra, "Rheology of Polymeric Systems : Principles and Applications", Carl Hanser Verlag, Munich, 1997.
  5. F. J. Padden and T. W. DeWitt, "Some Rheological Properties of Concentrated Polyisobutylene Solutions", J. Appl. Phys., 1954, 25, 1086-1091. https://doi.org/10.1063/1.1721819
  6. T. S. R. Al-Hadithi, H. A. Barnes, and K. Walters, "The Relationship between the Linear (Oscillatory) and Nonlinear (Steady-State) Flow Properties of a Series of Polymer and Colloidal Systems", Colloid. Polym. Sci., 1992, 270, 40-46. https://doi.org/10.1007/BF00656927
  7. K. W. Song, G. S. Chang, C. B. Kim, J. O. Lee, and J. S. Paik, "Rheological Characterization of Aqueous Poly(Ethylene Oxide) Solutions (II) : Comparison of Steady Flow Viscosity with Dynamic and Complex Viscosities", J. Kor. Fiber Soc., 1998, 35, 480-489.
  8. K. W. Song, D. S. Kim, and G. S. Chang, "Relationship between Steady Flow and Dynamic Rheological Properties for Viscoelastic Polymer Solutions : Examination of the Cox-Merz Rule Using a Nonlinear Strain Measure", Kor. J. Rheol., 1998, 10, 234-246.
  9. W. P. Cox and E. H. Merz, "Correlation of Dynamic and Steady Flow Viscosities", J. Polym. Sci., 1958, 28, 619-622. https://doi.org/10.1002/pol.1958.1202811812
  10. H. M. Laun, "Prediction of Elastic Strains of Polymer Melts in Shear and Elongation", J. Rheol., 1986, 30, 459-501. https://doi.org/10.1122/1.549855
  11. R. G. Larson, "The Structure and Rheology of Complex Fluids", Oxford University Press, New York, 1999.
  12. Y. H. Wen, H. C. Lin, C. H. Li, and C. C. Hua, "An Empirical Appraisal of the Cox-Merz Rule and Laun's Rule Based on Bidisperse Entangled Polystyrene Solutions", Polymer, 2004, 45, 8551-8559. https://doi.org/10.1016/j.polymer.2004.10.012
  13. J. M. Dealy and R. G. Larson, "Structure and Rheology of Molten Polymers", Gardner, Cincinnati, 2006.
  14. H. H. Winter, "Three Views of Viscoelasticity for Cox-Merz Materials", Rheol. Acta, 2009, 48, 241-243. https://doi.org/10.1007/s00397-008-0329-5
  15. V. Sharma and G. H. McKinley, "An Intriguing Empirical Rule for Computing the First Normal Stress Difference from Steady Shear Viscosity Data for Concentrated Polymer Solutions and Melts", Rheol. Acta, 2012, 51, 487-495. https://doi.org/10.1007/s00397-011-0612-8
  16. M. Yamamoto, "Rate-Dependent Relaxation Spectra and Their Determination", Trans. Soc. Rheol., 1971, 15, 331-344. https://doi.org/10.1122/1.549213
  17. G. Gleissle in "Rheology", (Proc. 8th. Int. Congr. Rheol.) (G. Astarita, G. Marruci, and L. Nicolais Eds.), Vol. 2, Plenum Press, New York, 1980.
  18. W. Gleissle, "The Mirror Relation for Viscoelastic Liquids", Proc. AIChE. Symp., New Orleans, 1981, 48, 59-65.
  19. A. S. Lodge, "Elastic Liquids", Academic Press, New York, 1964.
  20. P. M. Wood-Adams, "The Effect of Long Chain Branches on the Shear Flow Behavior of Polyethylene", J. Rheol., 2001, 45, 203-210. https://doi.org/10.1122/1.1332785
  21. C. Friedrich, "Einige Bemerkungen zum Spiegelverhalten viskoelastischer Flussigkeiten", Plaste und Kautschulk, 1984, 31, 12-15.
  22. P. J. Carreau, "Rheological Equations from Molecular Network Theories", Trans. Soc. Rheol., 1972, 16, 99-127. https://doi.org/10.1122/1.549276
  23. A. S. Lodge, "A Network Theory of Flow Birefringence and Stress in Concentrated Polymer Solutions", Trans. Faraday Soc., 1956, 52, 120-130. https://doi.org/10.1039/tf9565200120
  24. M. S. Green and A. V. Tobolsky, "A New Approach to the Theory of Relaxing Polymeric Media", J. Chem. Phys., 1946, 14, 80-92. https://doi.org/10.1063/1.1724109
  25. R. G. Larson, "Constitutive Equations for Polymer Melts and Solutions", Butterworth, Boston, 1988.
  26. A. S. Lodge and J. Meissner, "On the Use of Instantaneous Strains, Superposed on Shear and Elongational Flows of Polymeric Liquids, to Test the Gaussian Network Hypothesis and to Estimate the Segment Concentration and Its Variation during Flow", Rheol. Acta., 1972, 11, 351-352. https://doi.org/10.1007/BF01974779
  27. P. J. R. Leblans, J. Sampers, and H. C. Booij, "The Mirror Relations and Nonlinear Viscoelasticity of Polymer Melts", Rheol. Acta, 1985, 24, 152-158. https://doi.org/10.1007/BF01333243
  28. M. H. Wagner, "Analysis of Time-Dependent Non-Linear Stress Growth Data for Shear and Elongational Flow of a Low-Density Branched Polyethylene Melt", Rheol. Acta, 1976, 15, 136-142. https://doi.org/10.1007/BF01517505
  29. M. Ortiz, D. De Kee, and P. J. Carreau, "Rheology of Concentrated Poly(Ethylene Oxide) Solutions", J. Rheol., 1994, 38, 519-539. https://doi.org/10.1122/1.550472
  30. B. Briscoe, P. Luckham, and S. Zhu, "Rheological Study of Poly(Ethylene Oxide) in Aqueous Salt Solutions at High Temperature and Pressure", Macromolecules, 1996, 29, 6208-6211. https://doi.org/10.1021/ma960667z
  31. W. M. Kulicke, M. Kotter, and H. Grager, "Drag Reduction Phenomenon with Special Emphasis on Homogeneous Polymer Solutions", Adv. Polym. Sci., 1989, 89, 1-68. https://doi.org/10.1007/BFb0032288
  32. D. M. Yu, G. L. Amidon, N. D. Weiner, and A. G. Goldberg, "Viscoelastic Properties of Poly(Ethylene Oxide) Solutions", J. Pharm. Sci., 1994, 83, 1443-1449. https://doi.org/10.1002/jps.2600831016
  33. K. W. Song, G. S. Chang, C. B. Kim, J. O. Lee, and J. S. Paik, "Rheological Characterization of Aqueous Poly(Ethylene Oxide) Solutions (I) : Limits of Linear Viscoelastic Response and Nonlinear Behavior with Large Amplitude Oscillatory Shear Deformation", J. Kor. Fiber Soc., 1996, 33, 1083-1093.
  34. K. W. Song, D. H. Noh, and G. S. Chang, "Rheological Characterization of Aqueous Poly(Ethylene Oxide) Solutions (III) : Determination of Discrete Relaxation Spectrum and Relaxation Modulus from Linear Viscoelastic Functions", J. Kor. Fiber Soc., 1998, 35, 550-561.
  35. K. W. Song, S. H. Ye, and G. S. Chang, "Rheological Characterization of Aqueous Poly(Ethylene Oxide) Solutions (IV) : Nonlinear Stress Relaxation in Single-Step Large Shear Deformations", J. Kor. Fiber Soc., 1999, 36, 383-395.
  36. G. S. Chang, T. H. Kim, K. W. Song, and Y. H. Park, "Rheological Characterization of Aqueous Poly(Ethylene Oxide) Solutions (V) : Creep and Creep Recovery Behavior", J. Kor. Fiber Soc., 2002, 39, 660-670.
  37. K. W. Song, T. H. Kim, G. S. Chang, S. K. An, J. O. Lee, and C. H. Lee, "Steady Shear Flow Properties of Aqueous Poly (Ethylene Oxide) Solutions", J. Kor. Pharm. Sci., 1999, 29, 193-203.
  38. K. W. Song, J. W. Bae, G. S. Chang, D. H. Noh, Y. H. Park, and C. H. Lee, "Dynamic Viscoelastic Properties of Aqueous Poly(Ethylene Oxide) Solutions", J. Kor. Pharm. Sci., 1999, 29, 295-307.
  39. K. S. Cho, K. W. Song, and G. S. Chang, "Scaling Relations in Nonlinear Viscoelastic Behavior of Aqueous PEO Solutions under Large Amplitude Oscillatory Shear Flow", J. Rheol., 2010, 54, 27-63. https://doi.org/10.1122/1.3258278
  40. J. W. Bae, J. S. Lee, and K. W. Song, "Stress Growth Behavior of Aqueous Poly(Ethylene Oxide) Solutions at Start-up of Steady Shear Flow", Text. Sci. Eng., 2013, 50, 292-307. https://doi.org/10.12772/TSE.2013.50.292