A rheological model for materials which support coexistent shear rates

In this work we study a version of the three constant differential-type Old royd constitutive relation which allows distinct objective time derivatives for the extra stress and the stretching. We integrate the constitutive equ ation and determine an equivalent history integral representation for this model for the general class of viscometric motions. For certain choices of the material parameters and initial conditions, we find that this model all ows for the development of shear rate discontinuities in the flow domain as a steady viscometric flow is achieved. Correspondingly, we also give evide nce that intense shear rate oscillations may occur during the transient per iod as an impulsively started viscometric flow in a channel tends to a stea dy state under a constant critical shear stress. This critical shear stress lies in an interval of values for which the material experiences the pheno menon of "flow yielding". A qualitative comparison with experimental data i s made for certain creams and greases. The material instabilities inherent in this constitutive theory for viscometric motions are suggestive of the i nstabilities that occur in many viscoelastic fluids such as sharkskin patte rns, wavy fracture, and spurt flow. (C) 2000 Elsevier Science Ltd. All righ ts reserved.