A simplified phase-field lattice Boltzmann method with a self-corrected magnetic field for the evolution of spike structures in ferrofluids

This research presents a numerical analysis of the normal field instability for an initially flat layer of ferrofluid under the influence of magnetic field. A coupling between the simplified lattice Boltzmann method and the self-correcting procedure is developed to capture the velocity field and magnetic field. The proposed method has the ability to simulate complex hedgehog and comb-like spike structures without using an additional magnetization equation. A single dipole permanent magnet is defined instead of multiple point dipoles which makes this method much simpler and more efficient compared to the numerical approaches available in the literature. A comparison between the simulation results and experimental findings is provided to verify the validity of our method. A criterion for the prediction of spikes is presented for uniform magnetic fields. This study also investigates the effects of different types of magnetic fields, their strengths, and the effect of surrounding non-magnetic fluid on the spike structures. Moreover, the description of magnetic field lines, distribution of magnetic flux density, and energy estimation are also provided in this work which gives a useful insight into the hydrodynamic as well as the magnetostatic behavior of ferrofluids.