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Due to evergrowing importance of understanding flow of bio-fluids in Lab-on-CD based systems, we investigate the flow behaviour of power-law fluids in the rotating electroosmotic flow through a polyelectrolyte grafted (soft) narrow channel. We use a in-house numerical code to solve the governing transport equations for the velocities and flow rates in a rotating channel subjected to an applied external electric field. We show the strong effect of polyelectrolyte layer on the flow behaviour and find an increase in flow rate as we increase the size of the polyelectrolyte layer. We also show that rheology strongly influences the interplay of the Coriolis forces due to rotation and electrical body force due to the applied electric field. We show that the velocities are generally higher for shear thinning fluids as compared to shear thickening fluids. We also show that presence of polymer brushes in the polyelectrolyte layer creates a drag on the fluid which reduces velocities. We elaborate that the flow rates are strongly altered by the effect of rotation and that shear thickening fluids have lower flow rates than shear thinning fluids. We believe that studying effect of fluid rheology becomes very important for designing soft channel based Lab-on-CD systems driven by electroosmotic forcing and dealing with rheologically complex bio-fluids such as blood, saliva or mucus.