Deformation and Coalescence of Ferrodroplets in Rosensweig Model using the Phase Field and Modified Level Set Approaches under Uniform Magnetic Fields
By using both a phase field approach and a modified level set approach, two multiphase numerical models are proposed and compared in this paper to investigate the ferrodroplet deformation and merging process in a non-magnetic viscous medium under the influence of uniform magnetic fields. The finite element method is utilized for the spatial discretization of both numerical models. The numerical results show excellent agreement with the analytical solutions in the simple axisymmetric setting. The effects of different magnetic bond numbers and magnetic susceptibility on the deformation of ferrodroplets are systematically investigated. The coalescence process, in which two small ferrodroplets merge into a single larger droplet under uniform magnetic fields, is also studied by using both the phase field approach and the modified level set approach. Moreover the attraction phenomenon between two ferrodroplets, which was previously discovered in numerical experiments, is observed in our numerical tests. By comparing with analytical solutions, our study demonstrates that the diffuse interface (phase field) approach performs better than the modified level set approach when there is large topological deformation of the ferrodroplet. Several other important aspects, including the evolution of the flow field, the magnetic energy distribution, the spurious flows near the interfaces, and conservation of mass in both approaches, are studied as well.
F. Bai et al., "Deformation and Coalescence of Ferrodroplets in Rosensweig Model using the Phase Field and Modified Level Set Approaches under Uniform Magnetic Fields," Communications in Nonlinear Science and Numerical Simulation, vol. 85, Elsevier B.V., Jun 2020.
The definitive version is available at https://doi.org/10.1016/j.cnsns.2020.105213
Mathematics and Statistics
Keywords and Phrases
Deformation and coalescence; Ferrodroplet; Finite element method; Modified level set approach; Phase field approach; Rosensweig model
International Standard Serial Number (ISSN)
Article - Journal
© 2020 Elsevier B.V., All rights reserved.
01 Jun 2020