Producing nanoparticles in dense suspensions can be achieved in a stirred media mill. However the mechanisms of fragmentation in the mill are still not fully understood and the process remains laborious because of the large amount of supplied energy. We focus on the numerical analysis of the local hydrodynamics in the mill. Based on the flow simulations we determine the parameters which control the efficiency of the collisions between grinding beads (impact velocities and orientation of the collisions). The suspension flow (grinding beads, particles, carrying fluid) is modelled with effective physical properties. We solve directly the continuity and Navier–Stokes equations for the equivalent fluid assuming that the flow is two-dimensional and steady. Depending on the Reynolds number and the non-Newtonian behaviour of the fluid, we found that the flow is composed of several toroidal vortices. The most energetic collisions are driven by the strong shear experienced by the suspension within the gap between the disc tip and the wall chamber.