Polyethylene oxide solutions have a behavioral flexibility that provides researchers with the opportunity to use constitutive law models in a variety of ways for their MRI characterization. Our results obtained in numerical simulation carried out in 2D and 3D for speed profiles of a solution of PEO deployed by the simple method of the cylindrical Couette geometry considering the fluid Newtonian defect, allowed to identify the behavior of fluid complex (rheo-fluidifying threshold fluid). The relevance and the interest of the method are examined by analyzing these results generated by the numerical data obtained, since these profiles depend on the non-Newtonian properties of the fluid which one does not know a priori and which one seeks to measure by postulating first to the power law of Ostwald, then to the truncated power law.