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Linear viscoelastic model for different flows based on control theory

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Original languageEnglish
Article number64304
JournalApplied Rheology
Issue number6
Publication statusPublished - 2015
Publication typeA1 Journal article-refereed


Traditional Maxwell-type models have limitations when applied to the flows of real polymers containing macromolecules and complex microstructures. The main weakness of Maxwell models is the use of relaxation-time spectra that conducts to illposed problems in integral functions, and shear-induced relaxation spectrum transformations may lead to non-linearity. In contrast, control theory, which has apparently not been applied in rheology so far, enables modelling without knowledge of relaxation times. This study used viscoelastic constitutive equations derived from control theory and a new polymer fingerprint, which we call the rheologically effective distribution (RED). The study shows that a relaxation-time scheme is not essential to describe viscoelasticity, and applying the RED to computational modelling provides many theoretical and practical benefits, including giving higher accuracy. The proposed model is versatile and presents viscoelastic formulas for shear viscosity and other types of flow. Furthermore, the new model provides explanations for the empirical Cox-Merz rule and a power law behavior, the origin of which is frequently disputed in rheology.


  • Control theory, Empirical rules, Rheologically effective distribution (RED), Shear and dynamic viscosity, Viscoelasticity

Publication forum classification

Field of science, Statistics Finland