Nonlinear viscoelasticity of polystyrene solutions. III. Stress development at the start of steady shear flow and an experimental check of some constitutive models

The development of the shear stress at the start of shear flow at constant rate of shear κ was measured for polystyrene solutions in diethyl phthalate with a cone-and-plate rheometer. Ranges of molecular weight M and concentration c were 3.10 × 10⁶?7.62 × 10⁶ and 0.112?0.329 g/cm³, respectively. The shear stress as a function of time t exhibited a marked maximum at large κ when either M or c was relatively low. When M and c were high, the maximum was broad and low. In a few extreme cases no maximum was observed in the range of κ studied. The constitutive model of Bernstein, Kearsley, and Zapas could describe approximately the shear stresses at a sudden start and on cessation of steady shear flow with a memory function evaluated from the strain-dependent relaxation modulus. The strain dependence of the memory function for solutions of low M or c was approximately expressed as exp{?α|s|} where α is a constant (ca. 0.37) and |s| is the absolute value of shear strain. When M and c were high, the strain dependence was found to be more diffuse and to require several terms if approximated by exponential functions of |s|. The Lodge model based on a strain-rate dependent relaxation spectrum was not able to describe the strain-dependent relaxation modulus as well as the interrelation between shear stresses at a sudden start and a cessation of steady shear flow.