Application of nonuniform magnetic fields in a Brownian dynamics model of ferrofluids with an iterative constraint scheme to fulfill Maxwell’s equations

Abstract

Ferrofluids are steadily rising in applications across many fields, preferred for their ability to be remotely positioned and controlled via external magnetic fields. In magnetic separation operations, nonuniform magnetic fields elicit a phenomenon known as magnetophoresis so that the ferroparticles will undergo migration toward areas of higher magnetism. To comprehend this behavior, the authors developed a Brownian dynamics simulation of particles in ferromagnetic clusters under the influences of a simple shear flow and an applied magnetic field gradient. An iterative constraint mechanism was implemented to satisfy Maxwell’s equations throughout the dense colloidal suspension, ensuring that essential laws of magnetostatics are rigorously fulfilled at all times over small, finite sub-volumes of the system. Because of the presence of nonuniform magnetic fields, magnetophoresis and magnetic separation behavior were analyzed to assess the effectiveness of the model. Results showed that, when compared to “unconstrained” models, separation caused by magnetic field gradients occurred at a decreased rate under the constraint scheme due to relatively weaker non-Newtonian aggregation property trends. Through application of a dimensionless number analysis to observe varied levels of particle-particle interactions, thermal fluctuations, and viscous shearing, it was confirmed that the aggregation and magnetic separation modeling of ferrofluid colloidal suspensions without acceptable adherence to Maxwell’s equations produces an unreliable representation of current ferrofluids.