Integration approach to solve the Couette inverse problem based on nonlinear rheological models in a coaxial cylinder rheometer

Abstract

The Couette inverse problem of how the relationships between shear stress and shear strain rate based on rheological models are transformed into the relationships between torque and rotational speed is one of the most important theoretical problems for selecting a suitable rheological model for a fluid and correctly calculating the rheological parameters of the fluid. To date, however, great errors have been made in previous studies on the Couette inverse problem based on some nonlinear rheological models, especially for the modified Bingham model and Herschel–Bulkley model, which are widely used in shear-thickening or shear-thinning fluids with yield stress, such as fresh cementitious materials. In this paper, the detailed steps of establishing an integral approach are shown to solve the Couette inverse problem in a coaxial cylinder rheometer. The correctness of the integral approach has been verified by comparing the Reiner–Riwlin equation and the relationship between torque and rotational speed obtained by the integral approach based on the Bingham model. To show the process of solving the Couette inverse problem using the integral approach, the detailed calculation process of the relationships between torque and rotational speed based on some nonlinear rheological models of a fluid, such as the non-Newtonian fluid model, Casson model, Parabolic model, and Robertson–Stiff model, has been shown. According to the integral approach, errors in the relationships between torque and rotational speed based on the modified Bingham model and Herschel–Bulkley model in a coaxial cylinder rheometer have been corrected.