Rheology of Linear Viscoelastic Materials
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Abstract
This article shows how to derive a generalized linear viscoelastic model. We start with the Maxwell constitute equation, a model that contains a spring and a dashpot connected in series. The Maxwell model is further generalized by improving the model spectrums to infinity series paralleled to each other. Furthermore, Jefferys model is also mentioned. During the derivation, their solutions are also provided. Spriggs theorem is also introduced to improve the model spectrums to infinity; however, the model parameters is still minimized to a single spectrum plus a Spriggs coefficient . Finally, limitations of the linear viscoelastic models are discussed.
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References
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Kolitawong, C. Rheology of Generalized Newtonian Fluids. KKU Science Journal, Accepted Jan 16, 2019. in Thai.
. Bird, R.B., R.C. Armstrong, O. Hassager. Dynamics of Polymeric Liquids: Volume 1 Fluid Mechanics, 2nd ed. John Wiley and Sons, New York, 1987.
. Bird, R. B., Warren E. Stewart, Edwin N. Lightfoot. Transport Phenomena. John Wiley and Son, New York, 1960.
. Morrison, F. A. Understanding Rheology. Oxford University Press, New York, 2001.
. Bird, R.B., Stewaet, W.E., Lightfoot, E.N., Klingenberg, D.J. Introductory Transport Phenomena. Wiley, 2015.
. Shaw, M.T, and MacKnight, W.J. Introduction to Polymer Viscoelasticity, 3rd Ed. Wiley-Interscience, John Wiley & Sons, Inc., New Jersey, 2005.
. Abramowitz, M. and I. A. Stegun. Handbook of Mathematical Functions. National Bureau of Standards, Applied Math. Series No. 55. U.S. Govt. Printing Office, Washington, D.C., 1964.
. Abramowitz, M. and I. A. Stegun. Handbook of Mathematical Functions, 9th printing. Dover, New York, 1972.
. Bird, R.B., R.C. Armstrong, O. Hassager. Dynamics of Polymeric Liquids: Volume 1 Fluid Mechanics, 1st ed. John Wiley and Sons, New York, 1977.
. Murphy, G. M. Ordinary Differential Equations and Their Solutions. Van Nostrand, Princeton, NJ, 1960.
. Tuma, J. J. Engineering Mathematics Handbook, 3rd ed. McGraw-Hill, New York, 1987.
. Lighthill, M.J. An Introduction to Fourier Analysis and Generalized Functions. Cambridge University Press, 1964.
. Korn, G.A. and T.M. Korn. Mathematical Handbook for Scientists and Engineers. McGraw-Hill, New York, 1968.
. Saengow, C. and A.J. Giacomin. Exact Solution for Oscillatory Shear Sweep Behaviors of Complex Fluids from the Oldroyd 8-Constant Framework. Physics of Fluids, 2018; 30, 030703.
. Christopher W. Macosko. Rheology Principles, Measurements and Applications. Wiley-VCH, New Yorks, USA, 1994.