The deposition of nanometer-scale particles is of significant interest in various industrial processes. Although these particles offer several advantages, their deposition can have detrimental effects, such as reducing the heat transfer efficiency in nanofluid-based battery cooling systems. In this study, we investigated particle deposition around different square substrate configurations and experimentally obtained a complex porous structure in a two-dimensional setup. The particles were modeled as concentration fields using the lattice Boltzmann method, with a given external flow following a parabolic profile. Our results revealed that the deposition of particles around a substrate increases with higher fluid velocity, larger particle concentration, and higher deposition probability. Additionally, placing a number of substrates in the channel resulted in an increase in deposition on upstream substrates compared to those on downstream ones. As particle deposition around upstream substrates increases, it eventually obstructs the flow to downstream regions, thereby affecting overall system performance. The insights gained from this simplified model of particle deposition will play a crucial role in advancing our understanding of deposition processes in complex systems.