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http://dx.doi.org/10.12772/TSE.2017.54.230

A Time-Strain Separable K-BKZ Constitutive Equation to Describe the Large Amplitude Oscillatory Shear (LAOS) Flow Behavior of Viscoelastic Polymer Liquids  

Ahn, Hye-Jin (Department of Organic Material Science and Engineering, Pusan National University)
Chang, Gap-Shik (Industrial Materials and Component Business Team, FITI Testing & Research Institute)
Song, Ki-Won (Department of Organic Material Science and Engineering, Pusan National University)
Publication Information
Textile Science and Engineering / v.54, no.4, 2017 , pp. 230-245 More about this Journal
Abstract
The present study has been designed to describe the nonlinear viscoelastic behavior of concentrated polymer systems in large amplitude oscillatory shear (LAOS) flow fields using a time-strain separable K-BKZ constitutive equation (i.e., Wagner model). Using an Advanced Rheometric Expansion System (ARES), the dynamic viscoelastic behavior of aqueous poly(ethylene oxide) (PEO) solutions with various molecular weights and different concentrations has been investigated with a various combination of several fixed strain amplitudes and constant angular frequencies. The linear dynamic data (storage modulus and loss modulus) over a wide range of angular frequencies were obtained to determine the relaxation spectrum parameters and the stress relaxation moduli at various deformation magnitudes were measured to determine the damping function. The effects of the number of relaxation spectrum parameters and damping functions on the prediction results of the Wagner model were examined in depth. The nonlinear viscoelastic functions were analyzed by the aid of 3D plots and predicted over a wide range of strain amplitudes to evaluate the overall predictability of the Wagner model. The main findings obtained from this study are summarized as follows : (1) The Lissajous patterns predicted by the Wagner model are in good coincidence with the experimentally obtained stress-strain rate hysteresis loops both in linear and nonlinear viscoelastic regions and are independent of the number of relaxation spectrum parameters used in the calculation of memory function. (2) The effect of damping function on the predictive ability of the Wagner model is more sensitive than that of memory function. When the damping function is smaller than that of the experimental data, the stress amplitude predicted by the Wagner model also becomes smaller. (3) The Wagner model predictions are closely coincident with the experimental results in the linear viscoelastic region. As the strain amplitude is increased, the predicted nonlinear viscoelastic functions are somewhat larger than that of the experimental data. Nevertheless, all trends of the nonlinear viscoelastic behavior are in good agreement with the experimental results in a qualitative sense. (4) The Wagner model predicts the first harmonic loss modulus more exactly than the first harmonic storage modulus. As the strain amplitude is increased, the first harmonic storage modulus is somewhat overpredicted. The third and fifth harmonic storage and loss moduli exhibit an overshoot or an undershoot at large strain amplitudes. This constitutive equation has an ability to qualitatively describe well such dramatic behavioral changes.
Keywords
viscoelastic polymer liquid; large amplitude oscillatory shear (LAOS); time-strain separable K-BKZ constitutive equation; Wagner model; discrete relaxation spectrum; memory function; damping function; nonlinear viscoelastic function;
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Times Cited By KSCI : 3  (Citation Analysis)
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1 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.
2 F. E. Bailey, Jr. and J. V. Koleske, "Poly(ethylene oxide)", Academic Press, New York, 1976.
3 K. R. Shah, S. A. Chaudhary, and T. A. Mehta, "Polyox (polyethylene oxide) Multifunctional Polymer in Novel Drug Delivery System", Int. J. Pharm. Sci. Drug Res., 2014, 6, 95-101.
4 S. Bekiranov, R. Bruinsma, and P. Pincus, "Solution Behavior of Poly(ethylene oxide) in Water as a Function of Temperature and Pressure", Phys. Rev. E., 1997, 55, 577-585.
5 S. Kawaguchi, G. Imai, J. Suzuki, A. Miyahara, T. Kitano, and K. Ito, "Aqueous Solution Properties of Oligo- and Poly(ethylene oxide) by Static Light Scattering and Intrinsic Viscosity", Polymer, 1997, 38, 2885-2891.   DOI
6 P. N. Georgelos and J. M. Torkelson, "The Role of Solution Structure in Apparent Thickening Behavior of Dilute PEO/Water Systems", J. Non-Newt. Fluid Mech., 1988. 27, 191-204.   DOI
7 C. L. Mallows, "Some Comments on Cp", Technometrics, 1973, 15, 661-675.
8 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.
9 R. I. Tanner, "Engineering Rheology", 2nd Ed., Oxford University Press, New York, 2000.
10 J. M. Dealy and K. F. Wissbrun, "Melt Rheology and Its Role in Plastics Processing : Theory and Applications", Van Nostrand Reinhold, New York, 1990.
11 M. R. B. Mermet-Guyennet, J. G. de Castro, M. Habibi, N. Martel, M. M. Denn, and D. Bonn, "LAOS : The Strain Softening/Strain Hardening Paradox", J. Rheol., 2015, 59, 21-32.   DOI
12 K. Hyun, S. H. Kim, K. H. Ahn, and S. J. Lee, "Large Amplitude Oscillatory Shear as a Way to Classify the Complex Fluids", J. Non-Newt. Fluid Mech., 2002, 107, 51-65.   DOI
13 K. S. Cho, K. Hyun, K. H. Ahn, and S. J. Lee, "A Geometrical Interpretation of Large Amplitude Oscillatory Shear Response", J.Rheol., 2005, 49, 747-758.   DOI
14 P. R. de Souza Mendes, R. L. Thompson, A. A. Alicke, and R. T. Leite, "The Quasilinear Large-Amplitude Viscoelastic Regime and Its Significance in the Rheological Characterization of Soft Matter", J. Rheol., 2014, 58, 537-561.   DOI
15 X. Li, S. Q. Wang, and X. Wang, "Nonlinearity in Large Amplitude Oscillatory Shear (LAOS) of Different Viscoelastic Materials", J. Rheol., 2009, 53, 1255-1274.   DOI
16 S. A. Rogers and M. P. Lettinga, "A Sequence of Physical Processes Determined and Quantified in Large-Amplitude Oscillatory Shear (LAOS) : Application to Theoretical Nonlinear Models", J. Rheol., 2012, 56, 1-25.   DOI
17 A. S. Lodge, "Elastic Liquids", Academic Press, New York, 1964.
18 A. Kaye, "Non-Newtonian Flow in Incompressible Fluids", Note No. 134, College of Aeronautics, Cranford, UK, 1962.
19 B. Bernstein, E. A. Kearsley, and L. J. Zapas, "A Study of Stress Relaxation with Finite Strain", Trans. Soc. Rheol., 1963, 7, 391-410.   DOI
20 M. H. Wagner, "Analysis of Time-Dependent Nonlinear Stress Growth Data for Shear and Elongational Flow of a Low- Density Branched Polyethylene Melt", Rheol. Acta, 1976, 15, 136-142.   DOI
21 C. Valencia, M. C. Sanchez, A. Ciruelos, A. Latorre, J. M. Madiedo, and C. Gallegos, "Nonlinear Viscoelasticity Modeling of Tomato Paste Products", Food Res. Int., 2003, 36, 911-919.   DOI
22 A. J. Giacomin, R. S. Jeyaseelan, T. Samurkas, and J. M. Dealy, "Validity of Separable BKZ Model for Large Amplitude Oscillatory Shear", J. Rheol., 1993, 37, 811-826.   DOI
23 M. J. Reimers and J. M. Dealy, "Sliding Plate Rheometer Studies of Concentrated Polystyrene Solutions : Large Amplitude Oscillatory Shear of a Very High Molecular Weight Polymer in Diethyl Phthalate", J. Rheol., 1996, 40, 167-186.   DOI
24 C. Gallegos, M. Berjano, A. Guerrero, J. Munoz, and V. Flores, "Transient Flow of Mayonnaise Described by A Nonlinear Viscoelasticity Model", J. Texture Stud., 1992, 23, 153-168.   DOI
25 P. Partal, A. Guerrero, M. Berjano, and C. Gallegos, "Transient Flow of O/W Sucrose Palmitate Emulsions", J. Food Eng., 1999, 41, 33-41.   DOI
26 J. M. Madiedo, J. M. Franco, C. Valencia, and C. Gallegos, "Modeling of the Nonlinear Rheological Behavior of a Lubricating Greese at Low Shear Rates", J. Tribol. (Trans. ASME), 2000, 122, 590-596.   DOI
27 C. Bengoechea, M. C. Puppo, A. Romero, F. Cordobes, and A. Guerrero, "Linear and Nonlinear Viscoelasticity of Emulsions Containing Carob Protein as Emulsifier", J. Food Eng., 2008, 87, 124-135.   DOI
28 C. J. Carriere, A. J. Thomas, and G. E. Inglett, "Prediction of the Nonlinear Transient and Oscillatory Rheological Behavior of Flour Suspensions Using a Strain-Separable Integral Constitutive Equation", Carbohydr. Polym., 2002, 47, 219-231.   DOI
29 M. R. Mackley, R. T. J. Marshall, J. B. A. F. Smeulders, and F. D. Zhao, "The Rheological Characterization of Polymeric and Colloidal Fluids", Chem. Eng. Sci., 1994, 49, 2551-2565.   DOI
30 E. Behzadfar and S. G. Hatzikiriakos, "Viscoelastic Properties and Constitutive Modeling of Bitumen", Fuel, 2013, 108, 391-399.   DOI
31 J. Ren and R. Krishnamoorti, "Nonlinear Viscoelastic Properties of Layered-Silicate-Based Intercalated Nanocomposites", Macromolecules, 2003, 36, 4443-4451.   DOI
32 S. H. Lee and J. R. Youn, "Experimental and Theoretical Study on Shear Flow Behavior of Polypropylene/Layered Silicate Nanocomposites", Adv. Comp. Mat., 2008, 17, 191-214.   DOI
33 J. D. Ferry, "Viscoelastic Properties of Polymers", 3rd Ed., John Wiley & Sons, New York, 1980.
34 N. W. Tschoegl, "The Phenomenological Theory of Linear Viscoelastic Behavior", Springer-Verlag, Berlin, 1989.
35 H. M. Laun, "Prediction of Elastic Strains of Polymer Melts in Shear and Elongation", J. Rheol., 1986, 30, 459-501.   DOI
36 F. J. Stadler and C. Bailly, "A New Method for the Calculation of Continuous Relaxation Spectra from Dynamic-Mechanical Data", Rheol. Acta, 2009, 48, 33-49.   DOI
37 I. McDougall, N. Orbey, and J. M. Dealy, "Inferring Meaningful Relaxation Spectra from Experimental Data", J. Rheol., 2014, 58, 779-797.   DOI
38 H. M. Laun, "Description of the Nonlinear Shear Behavior of a Low-Density Polyethylene Melt by Means of an Experimentally Determined Strain-Dependent Memory Function", Rheol. Acta, 1978, 17, 1-15.   DOI
39 J. Honerkamp and J. Weese, "Determination of the Relaxation Spectrum by a Regularization Method", Macromolecules, 1989, 22, 4372-4377.   DOI
40 M. Baumgaertel and H. H. Winter, "Determination of Discrete Relaxation and Retardation Time Spectra from Dynamic Mechanical Data", Rheol, Acta, 1989, 28, 511-519.   DOI
41 L. J. Zapas, "Viscoelastic Behavior under Large Deformations", J. Res. NBS, 1966, 70A, 525-532.   DOI
42 F. A. Morrison and R. G. Larson, "A Study of Shear Stress Relaxation Anomalies in Binary of Monodisperse Polystyrenes", J. Polym. Sci. B: Polym. Phys., 1992, 30, 943-950.   DOI
43 A. C. Papanastasiou, L. E. Scriven, and C. W. Macosko, "An Integral Constitutive Equation for Mixed Flows : Viscoelastic Characterization", J. Rheol., 1983, 27, 387-410.   DOI
44 P. R. Soskey and H. H. Winter, "Large Step Shear Strain Experiments with Parallel-Disk Rotational Rheometers", J. Rheol., 1984, 28, 625-645.   DOI
45 K. Osaki, "On the Damping Function of Shear Relaxation Modulus for Entangled Polymers", Rheol. Acta, 1993, 32, 429-437.   DOI
46 K. Osaki, "Constitutive Equation and Damping Function for Entangled Polymers", Korea-Aust. Rheol. J., 1999, 11, 287-291.
47 V. H. Rolon-Garrido and M. H. Wagner, "The Damping Function in Rheology", Rheol. Acta, 2009, 48, 245-284.   DOI
48 M. Doi and S. F. Edwards, "The Theory of Polymer Dynamics", Oxford University Press, New York, 1986.
49 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.
50 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.   DOI
51 G. S. Chang, H. J. Ahn, and K. W. Song, "A Simple Analysis Method to Predict the Large Amplitude Oscillatory Shear (LAOS) Flow Behavior of Viscoelastic Polymer Liquids", Text. Sci. Eng., 2015, 52, 159-166.   DOI
52 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.
53 G. S. Chang, H. J. Ahn, and K. W. Song, "Discrete Fourier Transform Analysis to Characterize the Large Amplitude Oscillatory Shear (LAOS) Flow Behavior of Viscoelastic Polymer Liquids", Text. Sci. Eng., 2016, 53, 317-327.   DOI