  Ferrofluids belong to an important class of highly functional soft matter,
benefiting from their magnetically controllable physical properties. Therefore,
it is of central importance to quantitatively predict the dynamic magnetic
response of ferrofluids. Traditional dynamic theories, however, are often
restricted to the near-equilibrium regime and/or only apply to nearly ideal
ferrofluids that are monodisperse, dilute enough, and weakly interacting. In
this paper I develop a self-consistent and nonperturbative dynamical mean field
theory for typical ferrofluids which are often polydisperse, concentrated, and
strongly interacting, possibly driven far from equilibrium. I obtain a general
nonperturbative expression for the dynamic magnetic susceptibility,
quantitatively agreeing with the spectra obtained from Brownian Dynamics
simulations on both mono- and bidisperse samples. Furthermore, I derive a
generic magnetization relaxation equation (MRE) for both mono- and polydisperse
ferrofluids by employing the projection operator technique in nonequlibrium
statistical mechanics. This MRE is in simple closed form and independent of
which model is employed to approximate the equilibrium magnetization curve.
Existing models can be recovered as low-order approximations of my generic and
nonperturbative MRE. My theory can play a key role in studying the dynamics of
ferrofluids and other polar fluids. It may also have substantial and immediate
consequences to various ferrofluid applications.
