This paper examines the pumping mechanisms generated by the Maxblend impeller. Simulation results obtained with the lattice Boltzmann method (LBM) are presented for Newtonian fluids (Re=2-140) and strongly shear-thinning fluids (Re-g=0.1-50) obeying the Carreau-Yasuda model with a very small power index (n=0.05). In the Newtonian case, the pumping numbers predicted by the LBM are shown to compare favourably to those obtained with the finite element (FEM) as well as to experimental data based on the decolourisation method. These results indicate a small pumping capacity in the deep laminar regime followed by its sharp increase in the transitional regime, a phenomenon which is explained by examining the flow field simulated with the LBM and the FEM and measured through PIV. In the case of the strongly shear thinning fluids, the impact of the rheology on pumping is investigated. The flow fields and so-called pumping volumes predicted with the LBM reveal, similarly to the Newtonian case, a change in the structure of the axial and (secondary) radial flow when the Reynolds number is increased. Viscosity contours suggest that this phenomenon is in fact related to the occurrence of zones with very different apparent viscosities, which explains the problematic flow patterns observed experimentally with the PIV.