Brownian Dynamics Study on Ferrofluids using Iterative Constraints to Satisfy Maxwell's Equations

Ferrofluids are steadily rising in applications across many fields, preferred for their ability to be remotely positioned and controlled via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally reproduced using Brownian dynamics, Stokesian dynamics, and Monte Carlo schemes. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely Maxwell’s Equations. Prior ferrofluid modeling assumes that magnetization is a direct consequence of the magnetic field, a postulate that may be justifiable in dilute homogeneous solutions but invalid for dense suspensions or nonuniform magnetic fields. Moreover, hardly any research has been developed to explore magnetophoresis, a migration phenomenon that ferroparticles experience in the presence of magnetic field gradients, especially at the particulate level. Therefore, an iterative constraint mechanism was developed to satisfy Maxwell’s Equations when uniform or nonuniform magnetic fields are implemented across a dense colloidal suspension in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters amidst a mesoscale particle collection. The procedure ensures that essential laws of magnetostatics are rigorously fulfilled. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time-step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint algorithm. Non-Newtonian fluid properties, aggregation activity, and separation results were compared to relevant Brownian dynamics simulations and experimental data in order to validate the constraint method. Testing under uniform magnetic fields with activated constraints exhibited reduced trends in the spin viscosity when compared to trials that disregarded the constraint process. Mitigation in the magnetoviscous effect was detected across varying intensities of particle-particle interactions, Brownian motion, and viscous shearing. Although the dispersion activity developed similarly in both cases, the chaining ultimately progressed to a lesser extent in the constraint model than in the unconstrained. Consequently, separation due to magnetic field gradients occurred at a decreased rate under the constraint scheme, since cooperative magnetophoresis is less effective due to weakened magnetoviscosity. Thus, aggregation and magnetic separation modeling of ferrofluid colloidal suspensions without sufficient adherence to Maxwell’s equations is inaccurate. In conclusion, the resultant constraint model, employed with the Brownian dynamics technique, generates chain-like cluster formations, magnetic separation, and realistic ferrofluid behavior under uniformly or nonuniformly applied magnetic fields while observing fundamental magnetostatic laws.