Dynamical Effective Field Model for Interacting Ferrofluids: II. The proper relaxation time and effects of dynamic correlations

Abstract

The recently proposed dynamical effective field model (DEFM) is quantitatively accurate for describing dynamical magnetic response of ferrofluids. In paper I it is derived under the framework of dynamical density functional theory (DDFT) and generalized to the cases with inhomogeneous density distribution or polydispersity. Employing a phenomenological description of nonadiabatic effects beyond the regular DDFT, the original ensemble of bare Brownian particles is mapped to an ensemble of dressed particles. However, it remains to clarify how the characteristic rotational relaxation time of a dressed particle, denoted by τ r , is quantitatively related to that of a bare particle, denoted by τ 0 r . By building macro-micro connections via two different routes, I reveal that under some gentle assumptions well satisfied in typical monodisperse ferrofluids, τ r can be identified with the mean relaxation time characterizing long-time rotational self-diffusion. I further introduce two simple but useful integrated correlation factors, describing the effects of quasi-static (adiabatic)and dynamic (nonadiabatic) inter-particle correlations, respectively. The former is determined by the ratio of static magnetic susceptibility for a correlated ferrofluid to that for a uncorrelated one, while the latter is determined by τ r /τ 0 r . In terms of both correlation factors I reformulate the dynamic magnetic susceptibility in an illuminating and elegant form. Remarkably, it shows that the macro-micro connection is established via two successive steps: a dynamical coarse-graining with nonadiabatic effects accounted for by the dynamic factor, followed by equilibrium statistical mechanical averaging captured by the static factor. Surprisingly, τ r /τ 0 r is found insensitive to changes of particle volume fraction. I provide a physical picture to explain it. Furthermore, an empirical formula is proposed to characterize the dependence of τ r /τ 0 r on dipole-dipole interaction strength.The DEFM supplemented with this formula leads to parameter-free predictions in good agreement with results from Brownian dynamics simulations. The theoretical developments presented in this paper may have important consequences to studies of ferrofluid dynamics in particular and other systems modelled by DDFTs in general.