Determination of nonlinear viscoelastic properties of dilute drag reducing polymer solutions by a transient response method

Abstract

Viscous and elastic rheological properties of three very dilute polymer solutions (100 to 500 parts per million) of a polyacrylamide in distilled water have been determined. By using the Weissenberg Rheogoniometer, both the apparent viscosity and first normal stress difference were obtained over a shear rate range from about 10⁻² to 1500 sec⁻¹. The transient response characteristics w ere determined by a specially designed transient rheometer with modification for increased resolution. A simple 5-parameter nonlinear constitutive equation was used to correlate the data and compare the transient response with that predicted by Carreau's 7-parameter model B. A modified Marquardt's method was used to estimate the model parameters and a differential approximation technique was developed to evaluate the nonlinear convolution integral encountered in Carreau 's model B for arbitrarily time varying shear rate flow . A generalization of a scaling method for solving the system equation is also presented. The results indicate that the relative elastic influence upon the transient behavior of the polymer solutions is more important at lower concentrations than at higher concentration. The shear modulus parameter of the simple constitutive equation is the most sensitive parameter with respect to the viscosity and first norm al stress difference functions. The values of this parameter obtained from first normal stress difference data ranged from 6 to 9 times as large a s those from viscosity data, depending on the concentration of the solution..