Rheological models for fluid mixtures: Theoretical foundation and linear viscoelasticity

Various rheological models such as the Palierne, Gramespacher-Meissner, and Doi-Ohta models have been developed to study the immiscible blend of fluids. In this study, we compared the three models based on irreversible thermodynamics. Although these models have different origins, we found that the thermodynamic aspect allows us to express the dynamic modulus of all the models as a sum of the polymer modulus and interfacial modulus. The polymer modulus represents a mixing rule of the moduli of ingredient fluids, and the interfacial modulus represents the relaxation of interface. In addition, we showed that the interfacial modulus of the three models can be expressed as a single-mode Maxwell model. Based on the comparison of experimental data with a full range of composition with the models, we concluded that the thermodynamic model with the linearized Doi-Ohta equation is more robust for the given experimental data than the other models.