The aggregation process of a two-component dilute system (3 vol %), made of alumina submicrometer particles and silica nanoparticles, is studied by Brownian dynamics simulations. Alumina and silica particles have very different sizes (diameters of 400 and 25 nm, respectively). The particle-particle interaction potential is of the DLVO form. The parameters of the potential are extracted from the experiments. The simulations show that the experimentally observed aggregation phenomena between alumina particles are due to the silica-alumina attraction that induces an effective driving force for alumina-alumina aggregation. The experimental data for silica adsorption on alumina are very well reproduced.