There are several mathematical models used to describe the rheology of non-Newtonian fluids, but these are not limited to the following models; Power Law, Bingham, Hershel-Buckley, and Casson. Selecting the best rheological model that accurately represents the shear rate analysis with the shear stress is one of the rheology's wishes. Therefore, this study proposes a new rheological model which can be called (Casson-Stanciu) and that it extends the usual Casson expression and accurately represents the rheology of soybean oil. Moreover, with its additional corrective parameter (δ), this model can show the amount and sign of the deviation to the Casson linearity expressing in term of square root, the shear stress-shear rate dependence and classifying then the nature of the non-Newtonian fluid, according to the temperature value, as a type of super Casson or sub-Casson behavior in all the studied range of temperatures characterized by a sign-change temperature revealing, then an interesting overturning temperature (Tcs) which can be called Casson-Stanciu temperature characterizing the studied fluid and it will be an excellent criterion of discussion, interpretation, and classification of rheological fluid behavior.
