Abstract
It is herein shown that for separable integral constitutive equations with power-law distributions of relaxation times, the streamlines in creeping flow are independent of flow rate.
For planar flows of constant stretch history, the stress tensor is the sum of three terms, one proportional to the rate-of-deformation tensor, one to the square of this tensor, and the other to the Jaumann derivative of the rate-of-deformation tensor. The three tensors are the same as occur in the Criminale-Ericksen-Filbey Equation, but the coefficients of these tensors depend not only on the second invariant of the strain rate, but also on another invariant which is a measure of flow strength. With the power-law distribution of relaxation times, each coefficient is equal to the second invariant of the strain rate tensor raised to a power, times a function that depends only on strength of the flow. Axisymmetric flows of constant stretch history are more complicated than the planar flows, because three instead of two nonzero normal components appear in the velocity gradient tensor. For homogeneous axisymmetric flows of constant stretch history, the stress tensor is given by the sum of the same three terms. The coefficients of these terms again depend on the flow strength parameter, but in general the dependences are not the same as in planar flow.
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Larson RG (1985) Rheol Acta 24:30
Cox WP, Merz EH (1958) J Polym Sci 28:619
Bersted BH (1976) J Appl Polym. Sci 20:2705
Koyama K, Ishizuka O (1983) Polym Proc Eng 1:55
Wissler EH (1971) I & EC Fundamentals 10:411
Larson RG (1981) I & EC Fundamentals 20:132
Coleman BD (1962) Arch Rational Mech. Anal 9:273
Noll W (1962) Arch Rational Mech Anal 11:97
Astarita G, Marrucci G (1974) Principles of non-newtonian fluid mechanics. McGraw Hill, London
Wang CC (1965) Arch Rational Mech Anal 20:329
Noll W (1955) J Rational Mech Anal 4:3
Criminale WO Jr, Ericksen JL, Filbey GL Jr. (1958) Arch Rational Mech Anal 1:410
Bird RB, Armstrong RC, Hassager O (1977) Dynamics of polymer liquids, vol 1. John Wiley & Sons, New York
Tanner RI, Huigol RR (1975) Rheol Acta 14:959
Kim-E M (1984) PhD Thesis, Mass Inst Tech
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Larson, R.G. Flows of constant stretch history for polymeric materials with power-law distributions of relaxation times. Rheol Acta 24, 443–449 (1985). https://doi.org/10.1007/BF01462490
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DOI: https://doi.org/10.1007/BF01462490