Rheological constitutive equation development and evaluation for viscoelastic liquids

The formulation of constitutive equations capable of predicting the complex rheological behavior of viscoelastic fluids is important to the design and operation of polymer processing equipment. In this investigation, a new integral constitutive equation for polymeric liquids is derived based on simple fluid theory. The derivation is carried out so that strain coupling terms are included in the model in a relatively convenient form. Inclusion of strain coupling effects makes this constitutive equation considerably more general than the widely accepted K-BKZ integral model.; Simple shear flow rheological data on a concentrated polystyrene solution in a number deformation histories are presented. Steady, oscillatory, single-step strain, double-step strain, and initiation and cessation of steady flow experiments were performed. The Doi-Edwards and K-BKZ models were evaluated in an extensive series of double-step strain tests, and it is shown that neither is capable of providing an adequate description of observed behavior. For the double-step strain experiment, it is demonstrated that the strain coupling constitutive model is able to account for some of the deficiencies of the K-BKZ theory. Initiation and cessation of steady flow data were utilized in a number of consistency relations to evaluate the K-BKZ model, and it was found that strain coupling effects are not negligible for these deformations.; A number of new consistency relations for finite amplitude oscillatory flows have been formulated. Two of these relations were used to evaluate the K-BKZ model, and it was shown that this model was unable to describe observed behavior in this type of deformation. Also presented are four simple fluid consistency relations which can be used as a check of simple fluid theory or as a means to obtain linear and non-linear steady flow data from large amplitude oscillatory data.; Finally, an evaluation of the effects of using a sample reservoir on rotational rheometers is presented. This evaluation includes an exact analysis of parallel plate with sample cup flow, which provides a method for the accurate determination of viscosity data for Newtonian fluids in this geometry.