Development of constitutive equations for polymeric melts and solutions

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Abstract
The importance and characteristics of viscoelastic fluid behavior are briefly reviewed, as are theoretical predictions of the relationships between the stresses developed in such a fluid and its deformation rate and history. It is seen that most of the equations available for the prediction of these stresses(variously termed “constitutive equations” or “rheological equations of state”) either do not predict the properties of real materials correctly or, alternately, are of such overriding complexity that they cannot be applied to the solution of any but the simplest real problems. A new constitutive equation in which all the significant parameters may be evaluated from only two sets of experiments is developed. Comparison with available experimental results, while not entirely conclusive, indicates that the equation may predict correctly the behavior of nonpolar solutions and polymeric melts and that it may work well on polar systems in the range of high deformation rates, i.e., the region of primary industrial interest. Several problems of interest to the plastics industry are worked to illustrate the use of this constitutive equation.

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