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The Goddard memory‐integral expansion for the stress tensor of viscoelastic fluids differs from previous expansions in that it uses a deformation rate referred to a co‐rotating reference frame. It is shown how to get the kernel functions in the Goddard series in terms of the structural parameters occurring in the kinetic theory of macromolecular solutions. That the series has much better convergence properties than previously used expansions is demonstrated by comparison with exact kinetic theory results for steady‐state shear flow and elongational flow.

A simple method for predicting the primary normal stress function, θ, from viscosity data is proposed. A relation between θ and the viscosity function, θ, based on the Goddard-Miller rheological equation of state, is given. An easy-to-use generalized chart for estimating θ from θ is presented; in order to use this chart, viscosity data must be available from the zero-shear-rate value of the “power law region.” The method was applied to six polymer melts, three polymer solutions, and an aluminum soap solution for which θ had been measured experimentally. Even though θ varied by a factor of 103 over the examined range of shear rate, the theory and experiment seldom differed by more than a factor of 2. The generalized chart for θ was combined with Tanner's theory to prepare a graph which may be used to estimate jet swell from viscosity data. Comparison with experimental data of jet swell for 4 polymer melts shows good agreement.

A survey is given of co-rotational rheological equations suitable for describing the flow of viscoelastic liquids such as polymer solutions and melts. Comparisons are given with experimental data and molecular theories. An introduction to kinematical descriptions in co-rotating reference frames is included.