Flow Properties of Polymer Solutions. II. Phenomenological Relation for the Stress Following Sudden Start of Steady Shear Flow

Abstract

The stress development at the start of steady shear flow was calculated from experimental data for the strain-dependent relaxation modulus of a concentrated polymer solution with the use of a constitutive equation based on the strain-dependent relaxation spectrum. Calculated results were in close agreement with those observed in the range of relatively low rate of shear, where no stress overshoot at the start of steady shear flow was observed. When stress overshoot was present, the calculated result was in close agreement with the observed up to the time at which the stress reached its maximum value. This time corresponded to a certain value sB of the shear strain, irrespective of the rate of shear, and was accurately predicted from the relaxation modulus using the strain-dependent constitutive model. At longer times the calculated result for the rate of decrease of the stress was too small, compared with the observed, so that the predicted peak of the stress overshoot was too broad. It was concluded that the strain-dependent constitutive model may be applied to polymer solutions when the shear strain is smaller than sB or when the rate of shear is smaller than sB/τm, where τm is the maximum relaxation time of the polymer solution.