An Insight into Parameter Identifiability Issues in the Carreau-Yasuda Model: a More Consistent Rheological Formulation for Shear-thinning non-Newtonian Inelastic Fluids

Abstract

The Carreau-Yasuda rheological model is widely employed in both research and industrial applications to describe the shear-thinning behaviour of non-Newtonian inelastic fluids. However, the model parameter traditionally employed to characterize the shear thinning response exhibits only a weak correlation with the actual shear thinning rate observed in experimental data. This limitation leads to intrinsic identifiability issues, which may result in misleading physical interpretations of the model parameters and unreliable flow predictions. Aiming to contribute to overcoming these issues, this paper introduces a novel heuristic rheological formulation for shear-thinning non-Newtonian inelastic fluids, as an alternative to the Carreau-Yasuda model. Analytical results and exemplary numerical case studies demonstrate that the proposed formulation is based on physically meaningful model parameters, whose identifiability is not compromised by the key limitations of the Carreau-Yasuda model. The new approach allows for effective parameter estimation through a straightforward direct identification strategy, eliminating the need for inverse identification procedures based on nonlinear regression techniques. Moreover, the proposed formulation naturally enables the identication of two Carreau numbers based on the two characteristic shear rates of the fluid.