  This paper seeks to carry out the rigorous homogenization of a particulate
flow consisting of a non-dilute suspension of a viscous Newtonian fluid with
magnetizable particles. The fluid is assumed to be described by the Stokes
flow, while the particles are either paramagnetic or diamagnetic, for which the
magnetization field is a linear function of the magnetic field. The
coefficients of the corresponding partial differential equations are locally
periodic. A one-way coupling between the fluid domain and the particles is also
assumed. The homogenized or effective response of such a suspension is derived,
and the mathematical justification of the obtained asymptotics is carried out.
The two-scale convergence method is adopted for the latter. As a consequence,
the presented result provides a justification for the formal asymptotic
analysis of L\'{e}vy and Sanchez-Palencia for particulate steady-state Stokes
flows.
