Magnetophoresis of weakly magnetic nanoparticle suspension around a wire

We present a combined experimental and numerical investigation into the magnetophoresis behavior of weakly magnetic nanoparticle suspensions in the vicinity of a wire under a non-uniform magnetic field and negligible inertia. The experiments were conducted within a closed rectangular cuvette, with a wire positioned between the poles of an electromagnet. Two types of nanoparticles-paramagnetic manganese oxide and diamagnetic bismuth oxide-were studied across a broad range of concentrations (10-100 mg/l), magnetic field strengths (0.25-1 T), and wire diameters (0.8-3.17 mm). Our experimental findings reveal that, upon the application of a magnetic field, paramagnetic nanoparticles experience a strong, attractive force toward the wire's periphery. This force generates vortices and secondary flows around the wire, depleting particles from the bulk of the cuvette and concentrating them near the wire surface. The magnetophoresis dynamics of paramagnetic nanoparticles are shown to scale with their initial concentration, wire diameter, and the strength of the external magnetic field. In contrast, diamagnetic nanoparticles exhibit markedly different behavior, with their magnetophoresis dynamics showing minimal dependence on initial concentration and magnetic field strength while being inversely proportional to the wire diameter. Multiphysics numerical simulations complement the experimental observations, revealing the formation of field-induced particle clusters in weakly paramagnetic nanoparticles, which enhance magnetophoresis. In addition, the critical magnetic field threshold for the onset of cluster formation is found to be lower than those predicted by theoretical models for clustering in uniform magnetic fields. Under specific conditions, including high magnetic field strengths and elevated nanoparticle concentrations, diamagnetic nanoparticles appear to undergo field-induced clustering, suggesting a previously unreported aspect of their magnetophoretic behavior.