Lattice kinetic formulation for ferrofluids

 P. J. Dellar  (2005) Lattice kinetic formulation for ferrofluids   J. Statist. Phys. 121 105-118  doi:10.1007/s10955-005-8056-0

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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 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.

  Author    = {Dellar, Paul},
  Title     = {Lattice Kinetic Formulation for Ferrofluids},
  Journal   = {J. Statist. Phys.},
  Year      = {2005},
  Volume    = {121},
  Pages     = {105--118},
  DOI       = {doi:10.1007/s10955-005-8056-0},
  URL       = {}