Rheological Analysis of Elongational Flows
Abstract
The objective of this paper is to analyze the fluid element under the elongational deformation and to explain the origin of the rheology functions of shear free flows. The analysis’s shown that flow kinematics of the uniaxial and biaxial elongations are rotational, while those of the planar elongation are irrotational. From force balances of the free body diagram of a fluid element in an uniaxial elongational flow experiment, the stretching force is related to the elongational viscosity and the Young’s elastic modulus . Moreover, the force balances of the fluid element give the biaxial elongational viscosity and the Young’s elastic modulus in biaxial flow. Last, the rheology functions of planar elongational flow are examined. The first and second planar elongational viscosities, and , and the first and second planar elongational moduli, and , are exploded. Moreover, the relationships between shear viscosity and extensional parameters are determined. These elongational rheology functions are standardized by the American the Society of Rheology to be commonly used worldwide. Keywords : rheology of elongational flow ; elongational viscosity ; uniaxial flow ; biaxial flow ; planar flowReferences
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Kolitawong, C. (2018). Rheology Property Testing of Shear Flow, Journal of Science Ladkrabang, 27(2), 44-64. ISSN 0857-9512. (in Thai)
Kolitawong, C. (2019a). Rheology Properties of Elongational Flow Experiments, The Journal of Applied Science, 18(2), pp.1-19. ISSN 2586-9663. doi:10.14416/j.appsci.2019.09.002 (in Thai).
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Kolitawong, C. (2020), Rheology behavior identification of materials from oscillatory shear, The Journal of Industrial Technology, 16(3), 96-115. (in Thai)
Kolitawong, C. and A.J. Giacomin (2009). Sliding Plate Rheometer and its Applications, Journal of King Mongkut’s University of Technology North Bangkok, 19(1), pp. 109-115. ISSN: 2465-4698.
Menard, Hevin P (2008), Dynamic Mechanical Analysis, A Practical Introduction, 2nd ed., CRC Press, Taylor & Francis Group, Boca Raton, FL, USA.
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Sharma, R.K., K. Furusawa, A. Fukui, and N. Sasaki (2014). Effects of a flow field on amyloid fibrillogenesis in a B-lactoglobulin solution, International Journal of Biological Macromolecules, 70, 490-497.
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Tanner, R.I. (2002). Engineering Rheology, 2nd. ed., Oxford Engineering Science Series, Oxford University Press.
Taylor, G.I. (1934). The Formation of Emulsions in Definable Fields of Flow, Proc. R. Soc. (Lond.) A, 146, 501–523.
Trouton, F. T. (1906). On the Coefficient of Viscous Traction and Its Relation to that of Viscosity, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 77(519), 426–440.
Wangchai, S (2005). Finite Element Analysis of Heat Generation in Particle Filled Natural Rubber Valcanizates During Cyclic Deformation, Master Thesis, Department of Mechanical Engineering, King Mongkut’s Institute of Technology North Bangkok, Thailand. (in Thai)
Wangchai, S., C. Kolitawong, and A. Chaikittiratna (2008). Finite Element Simulation for Heat Built-up in Vulcanized Natural Rubber Subjected to Dynamic Load, Journal of King Mongkut’s University of Technology North Bangkok, 18(3), pp.49-61. ISSN: 2465-4698 (in Thai)
Wangchai, S., C. Kolitawong, and A. Chaikittiratna (2011), Finite Element Analysis of Heat Generation in Particle Filled Natural rubber Valcanizates During Cyclic Deformation, Journal of King Mongkut’s University of Technology North Bangkok, 21(1), pp.754-762. ISSN: 2465-4698. (in Thai)
White, F. M. (2003). Fluid Mechanics, 4th ed., McGraw Hill, New York.
ASTM D412-98a (2003). “Standard Test Methods for Vulcanized Rubber and Thermoplastic Elastomers-Tension,” ASTM International, West Conshohocken, PA, United States.
Barroso, V. C., Ribeiro, S. P. and Maia, J. M. (2003). Stress relaxation after a step strain in uniaxial extension of polyisobutylene and polyethylene, Rheologica Acta, 42(4), 345–354.
Bird, R.B., Stewart, W.E., Lightfoot, E.N., Klingenberg, D.J. (2015), Introductory Transport Phenomena, Wiley.
Bird, R.B., Armstrong R.C., and Hassager O. (1987). Dynamics of Polymeric Liquids: Volume 1 Fluid Mechanics, 2nd ed., John Wiley and Sons, New York.
Brimmo, A.T., and M.A. Qasaimeh (2017). Stagnation point flows in analytical chemistry and life sciences, Royal Society of Chemistry Advances, 7, 51206.
Callister W.D., Jr. and Rethwisch, D.G. (2015). Fundamentals of Materials Science and Engineering, An Integrated Approach, 5th ed., John Wiley & Sons, Inc., Hoboken, NJ, USA.
Cengel, Y. A. and J. M. Cimbala (2006). Fluid Mechanics, Fundamentals and Applications, International Edition, McGraw Hill, New York.
Dealy, John M. (1984). Official Nomenclature for Material Functions Describing the Response of a Viscoelastic Fluid to Various Shearing and Extensional Deformations. Journal of Rheology, 28, 181.
Dealy, John M. (1995). Official Nomenclature for Material Functions Describing the Response of a Viscoelastic Fluid to Various Shearing and Extensional Deformations. Journal of Rheology, 39, 253.
Khan, S. A. & Larson, R. G. (1987). Comparison of Simple Constitutive Equations for Polymer Melts in Shear and Biaxial and Uniaxial Extensions. Journal of Rheology, 31(3), 207–234. doi: 10.1122/1.549922
Khan, S. A. & Larson, R. G. (1990). Erratum: Comparison of simple constitutive equations for polymer melts in shear, and biaxial and uniaxial extensions [J. Rheol. 31, 207 (1987)]. Journal of Rheology, 34(1), 137–138. doi: 10.1122/1.550119
Khan, S. A. & Larson, R. G. (1991). Step planar extension of polymer melts using a lubricated channel. Rheologica Acta, 30(1), 1-6. doi: 10.1007/bf00366788
Kolitawong, C. (2003), A Sliding Plate Rheometer for Large Deformation Viscoelastic Measurements, The 17th Conference of Mechanical Engineering Network of Thailand, Prachinburi, Thailand, (October 15-17, 2003), pp.841-844, MM036.
Kolitawong, C. (2018). Rheology Property Testing of Shear Flow, Journal of Science Ladkrabang, 27(2), 44-64. ISSN 0857-9512. (in Thai)
Kolitawong, C. (2019a). Rheology Properties of Elongational Flow Experiments, The Journal of Applied Science, 18(2), pp.1-19. ISSN 2586-9663. doi:10.14416/j.appsci.2019.09.002 (in Thai).
Kolitawong, C. (2019b), Rheology of Generalized Newtonian Fluids, KKU Science Journal, 47(3), 392-401. (in Thai)
Kolitawong, C. (2020), Rheology behavior identification of materials from oscillatory shear, The Journal of Industrial Technology, 16(3), 96-115. (in Thai)
Kolitawong, C. and A.J. Giacomin (2009). Sliding Plate Rheometer and its Applications, Journal of King Mongkut’s University of Technology North Bangkok, 19(1), pp. 109-115. ISSN: 2465-4698.
Menard, Hevin P (2008), Dynamic Mechanical Analysis, A Practical Introduction, 2nd ed., CRC Press, Taylor & Francis Group, Boca Raton, FL, USA.
Messner, J., (1985). Experimental Aspects in Polymer Melt Elongational Rheometry. Chemical Engineering Communications, 33, 159-180.
Morrison, F. A. (2001). Understanding Rheology, Oxford University Press, New York.
Munson, B. R., D. F. Young, and T. H. Okiishi (2002). Fundamentals of Fluid Mechanics, 4th ed, John Wiley and Sons.
Münstedt, H., (1980). Dependence of the Elongational Behavior of Polystyrene Melts on Molecular Weight and Molecular Weight Distribution. J. Rheol., 24, 847-867.
Pritchard, Philip J. (2011). Fox and McDonald’s Introduction to Fluid Mechanics, 8th ed., John Wiley & Sons, Inc.
Song, Y., Q. Zheng, and Z. Wang (2007), Equibiaxial extensional flow of wheat gluten plasticized with glycerol, Food Hydrocolloids, 21, 1290-1295.
Soskey, P. R. and Winter, H. H. (1985). Equibiaxial Extension of Two Polymer Melts: Polystyrene and Low Density Polyethylene. Journal of Rheology, 29(5), 493-517.
Sharma, R.K., K. Furusawa, A. Fukui, and N. Sasaki (2014). Effects of a flow field on amyloid fibrillogenesis in a B-lactoglobulin solution, International Journal of Biological Macromolecules, 70, 490-497.
Shaw, M.T, and MacKnight (2005), W.J., Introduction to Polymer Viscoelasticity, 3rd Ed., Wiley-Interscience, John Wiley & Sons, Inc., New Jersey.
Tanner, R.I. (2002). Engineering Rheology, 2nd. ed., Oxford Engineering Science Series, Oxford University Press.
Taylor, G.I. (1934). The Formation of Emulsions in Definable Fields of Flow, Proc. R. Soc. (Lond.) A, 146, 501–523.
Trouton, F. T. (1906). On the Coefficient of Viscous Traction and Its Relation to that of Viscosity, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 77(519), 426–440.
Wangchai, S (2005). Finite Element Analysis of Heat Generation in Particle Filled Natural Rubber Valcanizates During Cyclic Deformation, Master Thesis, Department of Mechanical Engineering, King Mongkut’s Institute of Technology North Bangkok, Thailand. (in Thai)
Wangchai, S., C. Kolitawong, and A. Chaikittiratna (2008). Finite Element Simulation for Heat Built-up in Vulcanized Natural Rubber Subjected to Dynamic Load, Journal of King Mongkut’s University of Technology North Bangkok, 18(3), pp.49-61. ISSN: 2465-4698 (in Thai)
Wangchai, S., C. Kolitawong, and A. Chaikittiratna (2011), Finite Element Analysis of Heat Generation in Particle Filled Natural rubber Valcanizates During Cyclic Deformation, Journal of King Mongkut’s University of Technology North Bangkok, 21(1), pp.754-762. ISSN: 2465-4698. (in Thai)
White, F. M. (2003). Fluid Mechanics, 4th ed., McGraw Hill, New York.
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2021-01-04
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