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Magnetic iron oxide nanoparticles are attracting increased attention due to their interesting properties that can be applied in a large number of applications such as catalysis and biomedicine. This paper focuses on the synthesis, characteristics, and biomedical applications of iron oxide nanoparticles. The two most common iron oxides, including magnetite and maghemite, are discussed in this study. For most of their applications, the magnetic behavior of iron oxide nanoparticles in a fluid is very important – especially, the high-gradient magnetic separation of the particles from a non-magnetic liquid medium such as blood in the human body. A two-dimensional model, which represents a slice through the center of a spherical particle in a fluid, is proposed in this study, and only the magnetic force and the drag force are taken into consideration. The magnetization of the particles is calculated by using the Langevin function, and the fluid drag force is calculated by using the Navier–Stokes equation. The trajectory function for this model is calculated and the trajectories are drawn for specific cases.

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