(352a) Estimation of the First Normal Stress Difference From Shear Viscosity Data for Polymer Melts and Solutions

The relevant stress distribution for Non-Newtonian fluids in response to a steady simple shear flow is expressed using three viscometric measures; the shear stress and two normal stress differences. The normal stress differences are associated with nonlinear viscoelastic effects, and become vanishingly small in linear viscoelastic measurements. Normal stress measurements are relatively difficult to perform and require specialized equipment; by contrast, measurements of the complex viscosity/modulus (in oscillatory shear) or steady flow curves are relatively straightforward and far more accurate. The Cox-Merz rule and Laun's rule are two empirical relations that somewhat intriguingly allow the estimation of steady shear viscosity and first normal stress difference (nonlinear response), respectively, using small amplitude oscillatory shear measurements (of the linear viscoelastic response). Recently, by using a lesser known relationship also proposed by Cox and Merz, in conjunction with Laun's rule, Sharma and McKinley deduced an empirical relationship between the rate-dependent steady shear viscosity and the first normal stress difference. The new rule enables a priori estimation of the first normal stress difference using only the steady shear viscosity vs shear rate data of entangled polymeric solutions and melts. In this talk, we rigorously examine the dissipative and recoverable contributions to the measured nonlinear rate-dependent shear viscosity response, in pursuit of a self-consistent physical description of the correlation between the three viscometric functions.