  Ferrofluids containing nonmagnetic particles are called inverse ferrofluids.
On the basis of the Ewald-Kornfeld formulation and the Maxwell-Garnett theory,
we theoretically investigate the magnetophoretic force exerting on the
nonmagnetic particles in inverse ferrofluids due to the presence of a
nonuniform magnetic field, by taking into account the structural transition and
long-range interaction. We numerically demonstrate that the force can be
adjusted by choosing appropriate lattices, volume fractions, geometric shapes,
and conductivities of the nonmagnetic particles, as well as frequencies of
external magnetic fields.
