Numerical study on the magnetic field-induced dynamics of microparticles in a microchannel by three-dimensional lattice Boltzmann simulation

Microfluidic systems integrated with magnetic manipulation of microparticles, serving as a functional component, have been extensively used in various applications, including biomedical diagnostics and targeted drug delivery. Microparticle dynamics in confined microchannels is governed by hydrodynamic viscous effects, magnetic dipole interactions and enhanced interactions with microchannel boundaries, while an in-depth understanding of the underlying mechanisms is still evolving. This work presents a systematic investigation on the dynamic response of microparticles suspended in a quasi-stationary liquid within a microchannel under an external magnetic field using a three-dimensional lattice Boltzmann model (LBM). The hydrodynamic viscous effects and the two-way fluid–structure interaction are fully resolved in this model. A dimensionless analysis of the microparticle dynamic equation is performed first, leading to the identification of two key characteristic parameters central to this work: the magnetic number upper N Subscript italic mag N mag N₌₀₆, which characterises the synergy of the hydrodynamic viscous effect and the magnetic dipole interaction, and the particle–wall separation distance upper R divided by l R / l R/l, which accounts for the microchannel wall interaction. Further, a series of LBM simulations with different upper N Subscript italic mag N mag N₌₀₆ and upper R divided by l R / l R/l are carried out. The results suggest that the spatial trajectories of microparticles remain unaffected in response to variation in upper N Subscript italic mag N mag N₌₀₆, while their aggregation times demonstrate a linear dependence on the reciprocal of upper N Subscript italic mag N mag N₌₀₆ when released from the same initial position. Moreover, vortices generated by the motion of microparticles within microchannels tend to migrate toward the microparticles themselves as they approach the microchannel walls. As a result, microparticles experience an enhanced hydrodynamic viscous effect, which prolongs their aggregation time and leads to slight deviations in their spatial trajectories. A predictive model for the aggregation time is established, accounting for the effects of the external magnetic field, the microchannel wall interaction, as well as the initial positions of microparticles. Th