In the present study, we introduce a robust modified Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method in order to examine miscible mixing within a two-blade paddle mixer. Since it has a Lagrangian nature and it is based on particles, Smoothed Particle Hydrodynamics (SPH) is an appropriate and convenient method for simulating the moving boundary problems and tracking the particles in the mixing process. The present study thus introduces a convenient SPH method for modelling the mixing process for the power-law fluids. Two geometries for the mixer are examined and the effects of the power-law index on the fluid mixing are investigated. The results show that the geometric change from circular chamber to twin chamber considerably increases the mixing rate (by at least 49%). The results also indicate that the twin chamber mixer is more efficient for the fluids with higher power-law index.