In practice during polymer processing, we use branched polymeric materials with significant polydispersity quite often. This results in a necessity to take into account multiple relaxation processes for a description of the rheological equations of state. The aim of this contribution is to generalize the modified Pokrovskii and Vinogradov model for the case of multiple non-interacting modes. Each mode corresponds to a particular contribution of an individual polymer fraction to the stress tensor and is characterized by its corresponding relaxation time and viscosity. Simultaneously an internal friction notion is expressed by means of the parameters depending on the first invariant of the anisotropy tensor. Thus the generalized model can be applied to study polymeric materials at wider range of frequencies. Consequently, it implies a possibility to describe sufficiently slow flows of polydisperse polymers (both linear and branched) at a common theoretical approach. Theoretical modelling is compared with rheological characteristics measured for PE materials and there is a good agreement between the experiments and derived theoretical curves.
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