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Highlights • Closed-form magnetic moment and magnetic force analysis. • The influence of magnetic dipole interaction force on the self-assembly of MNPs. • 3D self-assembly process of MNPs. Abstract The self-assembly of magnetic core-shell nanoparticles in the presence of a magnetic template, which consists of an array of soft-magnetic elements embedded in non-magnetic substrate, is analyzed by using discrete element method. An external bias magnetic field is used to magnetize the soft-magnetic elements to saturate state. The high-gradient field produced by elements combined with biased uniform magnetic field provides a flexible way to control the behavior of particles. An equivalent source method is adopted to obtain the closed-form magnetic field analysis, which not only improves the calculation efficiency but also enables accurate prediction of the Kelvin force. In the presence of magnetic field, the behavior of the magnetic nanoparticles is dependent on the magnetic and hydrodynamic forces. Therefore, the assembled structures of magnetic nanoparticles are firstly investigated without considering the magnetic dipole interaction force, in which an unordered nanostructure is formed. As a contrast, the self-assembly of particles is also simulated by taking all forces into account. In this case, the magnetic nanoparticles assemble into an ordered 3D structure, which presents a hexagonal close packed structure. A comparison between the results of the mentioned two cases denotes that the magnetic dipole interaction force plays an important role in controlling the self-assembly of magnetic nanoparticles. [ABSTRACT FROM AUTHOR]

Highlights • The dye-tracing and concentration-measuring experiments provide a means of observing the behavior of particle and fluid. • A closed-form magnetic field analysis is performed to obtain an accurate prediction of magnetic force. • Three-dimensional distribution of particle concentration is investigated by using Fluent, Ansys. • A comparison between the uncoupled model and coupled model is provided. • A comparison between experimental and numerical results is provided. Abstract Dye-tracing and concentration-measuring experiments are carried out to investigate the magnetophoresis of magnetic nanoparticles (MNP) in the presence of an external cylindrical permanent magnet. The magnetophoresis of MNP, inducing an obvious forced-convective flowing of the carrier fluid, which can be observed by visualizing flowing of carrier fluid, results in a temporal and spatial variation of particle concentration. Moreover, in order to get insight into the physical mechanisms of magnetophoresis of MNP, a coupled particle-fluid analysis, in which the non-linear drift-diffusion differential equation is incorporated into the Navier-Stokes equation, is adopted to discuss the influence of particle-fluid interaction on the variation of particle concentration and the kinetics of carrier fluid. It is worth noting that the equivalent current source (ECS) method is adopted to obtain a closed-form field analysis, which provides exactly prediction of the Kelvin force and enables magnetophoretic analysis more efficient. In dye-tracing experiments, an obvious vortex can be observed as the methylene blue moves with the convection of carrier fluid. Furthermore, this phenomenon is also predicted by using the coupled particle-fluid model. A comparison between the experimental and numerical results shows that the hydrodynamic interactions between MNP and carrier fluid plays an important role in inducing forced-convective flowing of carrier fluid and enhancing the magnetophoresis of MNP. Furthermore, these results also denote that the coupled particle-fluid model provides a more efficient and accurate method in investigating the magnetophoresis of MNP. [ABSTRACT FROM AUTHOR]