Abstract
The lattice Boltzmann approach is used to solve continuum equations describing colloids of ferromagnetic particles (ferrofluids) in a regime, where the particle spins are in equilibrium with magnetic torques. This limit of rapid spin adjustment yields a symmetric total stress tensor that is essential for a kinetic formulation based on the Boltzmann equation. The magnetisation equation is solved using a vector-valued distribution function analogous to the earlier treatment (J. Comput. Phys. 179, 95) of the induction equation in magnetohydrodynamics, but the details are rather more complex because the magnetisation equation is not in conservation form except in a weakly magnetised limit.
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Dellar, P.J. Lattice Kinetic Formulation for Ferrofluids. J Stat Phys 121, 105–118 (2005). https://doi.org/10.1007/s10955-005-8056-0
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DOI: https://doi.org/10.1007/s10955-005-8056-0