We implicitly assess the distributive mixing of generalized Newtonian fluids with shear-thinning behavior in a journal bearing flow geometry. For this purpose, we firstly develop a finite element code to calculate the flow field parameters. Our numerical algorithm splits the viscous stress tensor into arbitrary Newtonian stress and a source term, which grows gradually during the iterative solution. Therefore, we get a better converging solution than the Picard method, especially for highly shear-thinning fluids. Secondly, considering two inert fluids in the mixing domain, we employ a Lagrangian-Eulerian approach to predict the shape of the interface between two fluids. The results of our numerical analysis provide us the required information to evaluate three implicit mixing criteria: the concentration variance, the striation thickness, and the mean strain function. Then we conduct a parametric study to investigate the effects of different parameters (geometry and rheology) on the distributive mixing state. In addition, we discuss which mixing criteria provide a better evaluation for distributive mixing.