Orthogonal versus parallel superposition measurements

Abstract

The non-linear flow behaviour of viscoelastic fluids can be studied in detail by means of a perturbation analysis. For that purpose small amplitude oscillations can be superimposed on the steady-state shear flow. In this manner, detailed information about the spectral content of the material under the non-linear steady flow is obtained. The oscillatory flow can be either parallel or perpendicular to the main shear flow. Devices for both types are becoming readily available and apparently are being used without realizing the intricate nature of these flows. An analysis shows that linear superposition moduli do not obey the basic rules of linear viscoelasticity. This includes deviations from the Kramers–Kronig relation and from the usual relation between steady-state and dynamic viscosities. This is demonstrated on the basis of a Wagner I model for which analytical solutions of the superposition moduli can be derived. Other models give different results, consequently superposition flows could be used for the critical evaluation of rheological models. Preliminary data for both parallel and orthogonal superposition flows on a polyisobutene solution illustrate the potential of this technique. The relation between parallel and orthogonal superposition moduli derived by Bernstein for the K-BKZ model seems to be in agreement with the data. The results offer a potential for further theoretical work. The data also suggest that a physical interpretation of superposition moduli is not straightforward.