Magnetophoretic Drift of a Single Nanoparticle: From Langevin Theory to Atomistic Validation

ABSTRACT An exact analytical expression is derived for the magnetic field gradient of a rectangular permanent magnet, and the mean magnetophoretic velocity is obtained from the overdamped Langevin equation under the constant gradient approximation. To challenge the underlying assumptions of point particle Stokes drag, neglect of thermal fluctuations in the mean drift, and constant gradient closure, a molecular dynamics framework is developed to simulate a faceted magnetite nanoparticle in explicit water with a spatially varying magnetic force applied directly to each iron atom. The simulations calibrate two effective parameters: an enhanced drag coefficient () due to faceting, and an effective magnetisation ( kA/m) that lies 12% below the bulk saturation value because of surface spin canting. The constant gradient approximation holds for displacements below 0.1 mm, beyond which a first‐order correction accounting for gradient decay yields a unified predictive model. Linear scaling with field strength permits direct extrapolation to experimental conditions. A parity plot across 50 state points gives , confirming the predictive power of the approach. The model provides design rules for magnetophoretic separators and is adaptable to arbitrary magnet geometries.