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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 magneticresponse of ferrofluids. Traditional dynamic theories, however, are oftenrestricted to the near-equilibrium regime and/or only apply to nearly idealferrofluids that are monodisperse, dilute enough, and weakly interacting. Inthis paper I develop a self-consistent and nonperturbative dynamical mean fieldtheory for typical ferrofluids which are often polydisperse, concentrated, andstrongly interacting, possibly driven far from equilibrium. I obtain a generalnonperturbative expression for the dynamic magnetic susceptibility,quantitatively agreeing with the spectra obtained from Brownian Dynamicssimulations on both mono- and bidisperse samples. Furthermore, I derive ageneric magnetization relaxation equation (MRE) for both mono- and polydisperseferrofluids by employing the projection operator technique in nonequlibriumstatistical mechanics. This MRE is in simple closed form and independent ofwhich model is employed to approximate the equilibrium magnetization curve.Existing models can be recovered as low-order approximations of my generic andnonperturbative MRE. My theory can play a key role in studying the dynamics offerrofluids and other polar fluids. It may also have substantial and immediateconsequences to various ferrofluid applications.

Generic Theory of the Dynamic Magnetic Response of Ferrofluids