Magnetic resonance navigation (MRN) has become a significant method to steer magnetized particles in medical applications by using MRI scanners. Dedicated MRN sequences have been successfully developed to track and steer such particle aggregates for selective chemoembolization of liver tumors. Particle aggregation is however a complex process and a comprehensive study of its shape and motion is needed to avoid damaging healthy tissues. Previous computational studies have considered non-aggregating particles or aggregates in 2D simplified settings. In this study, we investigate the forces acting on such micro-particle aggregation including drag, gravity, pressure gradient, virtual mass, magnetic gradient, dipole and contact forces. The code is developed in the OpenFOAM framework. Primary results are compared with bifurcation in vitro experimental data. Different sizes of clusters, directions of the magnetic field and gradient can be investigated to optimize aggregation form. This research represents an initial step towards complex in-vitro phantoms and in-vivo models.