  Quite recently I have proposed a nonperturbative dynamical effective field
model (DEFM) to quantitatively describe the dynamics of interacting
ferrofluids. Its predictions compare very well with the results from
simulations. In this paper I put the DEFM on firm theoretical ground by
deriving it within the framework of dynamical density functional theory (DDFT),
in which the relevant part of correlation-induced free energy is approximated
by a function of the instantaneous magnetization. The DEFM is generalized to
inhomogeneous finite-size samples for which the macroscopic and mesoscopic
scale separation is nontrivial due to the presence of long-range dipole-dipole
interactions. The demagnetizing field naturally emerges from microscopic
considerations and is consistently accounted for. The resulting particle
dynamics on the mesoscopic scale only involves macroscopically local quantities
such as local magnetization and Maxwell field. Nevertheless, the local
demagnetizing field essentially couples to magnetization at distant macroscopic
locations. Thus, a two-scale parallel algorithm, involving information transfer
between different macroscopic locations, can be applied to fully resolve
particle rotational dynamics in an inhomogeneous sample. I also derive the DEFM
for polydisperse ferrofluids, in which the dynamics of particles belonging to
different species can be strongly coupled to each other. I discuss the
underlying assumptions in obtaining a thermodynamically consistent polydisperse
magnetization relaxation equation, which is of the same generic form as that
for monodisperse ferrofluids. The theoretical advances presented in this paper
are important for both qualitative understanding and quantitative modeling of
ferrofluid dynamics.
