We systematically investigate the magnetophoresis of weakly paramagnetic manganese oxide nanoparticles under nonuniform magnetic fields using a combination of experiments and multiphysics numerical simulations. Experiments were conducted in a closed cuvette exposed to a nonuniform magnetic field generated by an electromagnet, covering a wide range of particle concentrations (25–200 mg/L) and magnetic field gradients (0–110 ${\mathrm{T}}^2/\mathrm{m}$). The experimental results reveal that paramagnetic manganese oxide nanoparticles exhibit significant magnetophoretic behavior, leading to particle depletion within the cuvette. The depletion rate is independent of the initial particle concentration but strongly depends on the magnetic field gradient. At low magnetic field gradients, magnetophoresis progresses slowly, while at higher gradients, the particle depletion rate increases significantly before stabilizing. Transient concentration gradients emerge within the cuvette during magnetophoresis, which we hypothesize are driven by magnetic Grashof numbers (${\mathrm{Gr}}_m$) near unity. When ${\mathrm{Gr}}_m>1$, the formation of concentration gradients induces bulk fluid flows that accelerate particle capture at regions of maximum magnetic field strength. In systems where magnetophoresis opposes sedimentation, particle-depleted regions form when the ratio of magnetic to gravitational Péclet numbers exceeds 1. The numerical simulations suggest formation field-induced aggregation for manganese oxide nanoparticles with radii of 130 nm or larger. These insights highlight the potential of magnetic separation for sustainable metal recovery, offering a scalable and environmental friendly solution for recycling critical materials from spent electronics.

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• Magnetohydrodynamics
• Multiphase flows
• Particle phenomena
• Particle-laden flows
• Navier-Stokes equation
• Stokes equations