This work is an attempt to study the behaviour of fluid in the mixing vessel with a two-bladed or four-bladed impeller. The working fluid is complex, of a shear-thinning type and the Oswald model is used to describe the fluid viscosity. The study was accomplishedby numerically solving the governing equations of momentum and continuity. These equations were solved for the following range of conditions: 50–1000 for the Reynolds number, 0–0.15 for the baffle length ratio, and the number of impeller blades 2 and 4. The simulations were done for the steady state and laminar regime. The results show that the increase in baffle length (by increasing the ratio baffle length ratio) decreases the fluid velocity in the vessel. Increasing the speed of rotation of the impeller and/or increasing the number of blades improves the mixing process. Also, the length of the baffles does not affect the consumed power.