Dynamics of weakly magnetic nanoparticle suspensions near a magnetized sphere

We report experimental and multiphysics simulation studies of magnetophoretic transport and capture of nanoparticles around a magnetized sphere under high-gradient magnetic fields. Experiments were performed using a broad range of paramagnetic and diamagnetic nanoparticles at an imposed magnetic field up to B₀ = 1 T and concentrations of c₀ = 10-100 mg L^-1. Paramagnetic nanoparticles exhibited substantially enhanced capture compared to diamagnetic nanoparticles, with capture efficiency increasing nonlinearly with magnetic field strength, initial nanoparticle concentration, and magnetic susceptibility. In addition, increasing the sphere diameter also improved the capture efficiency of paramagnetic nanoparticles despite reducing local magnetic field gradients. Our analysis showed that the observed rate of nanoparticle capture by the non-uniform magnetic-field exceeded predictions from a simple scaling analysis and isolated-particle magnetophoresis. More detailed analysis using multiphysics numerical simulations suggests magnetic field-induced nanoparticle clustering, which in turn significantly enhances the transport of nanoparticles. In addition, field-induced convective flows were found to substantially promote nanoparticle transport. These results highlight that magnetophoretic capture of weakly paramagnetic materials in high-gradient magnetic systems is governed by a nonlinear coupling of magnetic and flow-driven transport mechanisms. These results provide insights into the design of magnetic separation systems for recovery and recycling of weakly magnetic nanoparticles and colloidal suspensions.