Abstract
It is shown that many present rheological models reduce to the form of the equations of a generalized Maxwellian liquid.
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B. M. Khusid, “Equivalence of some types of rheological equations of state of flowing polymer media. I. General analysis,” Inzh.-Fiz. Zh.,42, No. 4, 670–677 (1982).
J. Astarita and J. Marucci, Foundations of the Hydromechanics of Non-Newtonian Liquids [Russian translation], Mir, Moscow (1978).
G. V. Vinogradov and A. Ya. Malkin, Rheology of Polymers [in Russian], Khimiya, Moscow (1977).
Chang Dei Khan, Rheology in Polymer Reprocessing Processes [Russian translation], Khimiya, Moscow (1979).
R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Fluids, Vol. I, Wiley, New York (1977).
M. W. Johnson and D. Segalman, “A model for viscoelastic fluid behavior which allows nonaffine deformation,” J. Non-Newtonian Fluid Mech.,2, No. 3, 255–270 (1977).
A. S. Lodge, Elastic Liquids [in Russian], Nauka, Moscow (1968).
J. D. Goddard and C. Miller, “An inverse for the Jaumann derivative and some applications to the rheology of viscoelastic fluids,” Rheol. Acta,5, No. 3, 177–184 (1966).
V. P. Gorodtsov and A. I. Leonov, “Kinematics, nonequilibrium thermodynamics, and rheological relations in the nonlinear theory of viscoelasticity,” Prikl. Mat. Mekh.,32, No. 1, 70–94 (1968).
D. Acierno, F. P. La Mantia, G. Marrucci, and G. Titomanlio, “A nonlinear viscoelastic model with structure-dependent relaxation times. I. Basic formulation,” J. Non-Newtonian Fluid Mech.,1, 125–146 (1976).
V. N. Pokrovskii and N. P. Kruchinin, “Nonlinear effects accompanying flow of linear polymers,” Vysokomolekul. Soed. Kratkie Soobshch.,22, No. 5, 335–338 (1980).
F. P. La Mantia, “Nonlinear viscoelasticity of polymeric liquids interpreted by means of a stress-dependent free volume,” Rheol. Acta,16, No. 3, 302–308 (1977).
F. P. La Mantia and G. Titomanlio, “Testing of a constitutive equation with free volume dependent relaxation spectrum,” Rheol. Acta,18, No. 4, 469–477 (1979).
N. Phan-Thien, “A nonlinear network viscoelastic model,” J. Rheology,22, No. 3, 259–283 (1978).
F. M. Wiegel, “A network model for viscoelastic fluids,” Physica,42, No. 1, 156–164 (1969).
A. Kaye, “An equation of state for non-Newtonian fluids,” Brit. J. Appl. Phys.,17, No. 6, 803–806 (1966).
M. Takahashi, T. Masuda, and S. Onogi, “New critical tests for integral constitutive equations,” Trans. Soc. Rheology,21, No. 3, 337–354 (1977).
M. Takahashi, T. Masuda, and S. Onogi, “A stress dependent constitutive equation,” J. Rheology,22, 285–291 (1978).
R. B. Bird, O. Hassager, R. C. Armstrong, and C. C. Curtiss, Dynamics of Polymeric Fluids, Vol. II, Wiley, New York (1977).
R. I. Tanner, “Stresses in dilute solutions of bead-nonlinear-spring macromolecules, III. Friction coefficient varying with dumbell extension,” Trans. Soc. Rheology,19, No. 4, 557–582 (1975).
N. Phan-Thien and R. I. Tanner, “Langevin analysis of dumbbells with hydrodynamic interaction,” Rheol. Acta,17, No. 6, 568–577 (1978).
E. J. Hinch, “Mechanical models of dilute polymer solutions in strong flows,” Phys. Fluids,20, No. 10, Pt. II, 22–30 (1977).
R. C. Armstrong and S. Ishikawa, “A rheological equation of state for dilute solutions of nearly Hookean dumbells,” J. Rheology,24, 143–165 (1980).
A. I. Leonov, “Nonequilibrium thermodynamics and rheology of viscoelastic polymer media,” Rheol. Acta,15, No. 2, 85–98 (1976).
C. Pearson and S. Middleman, “An empirical constitutive model for polymer solutions,” Trans. Soc. Rheol.,20, No. 4, 559–573 (1976).
J. David, “On some integral viscoelastic fluid models with the rate-of-strain dependent function,” Rheol. Acta,11, No. 3/4, 333–340 (1972).
C. J. S. Petrie, “Measure of deformation and convected derivatives,” J. Non-Newtonian Fluid Mech.,5, 147–176 (1979).
J. D. Goddard, “Polymeric fluid mechanics,” Adv. Appl. Mech.,19, 143–219 (1979).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 5, pp. 779–786, May, 1982.
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Khusid, B.M. Equivalence of certain types of rheological equations of state of flowing polymer media. II. Analysis of specific models. Journal of Engineering Physics 42, 538–543 (1982). https://doi.org/10.1007/BF00824947
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DOI: https://doi.org/10.1007/BF00824947