The understanding of the mechanical behaviour and rheology of suspensions is crucial to many research and application fields. The utilisation of experiments in this field can often not provide an insight into the flow behaviour and the interaction on the micro scale, or if so, only in a very complicated way. Therefore, we employ a Direct Numerical Simulation of suspended aggregates immersed in a fluid monolithically modelled with Smoothed Particle Hydrodynamics (SPH) particles. For the carrier fluid, we can use Newtonian or non-Newtonian rheology to include effects below the resolution of our characteristic aggregate size. Our Lagrangian simulation enables us to follow the trajectories of the immersed aggregates and to fully map the near field in the vicinity of the solid aggregates discretised by rigid bound SPH particles. We validate the near field solution of our simulation with the analytical solution for an accelerated sphere moving through a viscous fluid in a Stokes’ regime. To discuss near field phenomena in the vicinity of suspended aggregates, we investigate a boundary value problem with two slightly shifted spheres immersed in a body force driven flow between two parallel plates in a Newtonian and non-Newtonian fluid.