Consistent hydrodynamics of ferrofluids

Abstract

We develop a consistent hydrodynamic theory for ferrofluids that can be concentrated, strongly interacting, and polydisperse. We analyze the dynamics of ferrocolloids under imposed flow and magnetic field, from micro-, meso-, and macroscopic points of view. We settle the long-standing debate on the correct reactive contribution to magnetization dynamics near or far from equilibrium. We obtain a fundamental mesoscopic rotational fluctuation-dissipation relation, linking vortex viscosity and rotational self-diffusivity and with far-reaching consequences on ferrofluid hydrodynamics. It distinguishes from the traditional Stokes–Einstein–Debye relation that only applies to dilute and noninteracting systems. Furthermore, it is used to infer the size of structure units whose rotational diffusion is responsible for the primary Debye peak of water. The characteristic hydrodynamic radius is estimated to be ∼0.18 nm, considerably larger than the geometrical radius of water molecules. This is in contrast to the result obtained by naively employing the Stokes–Einstein–Debye relation. We revisit the magnetoviscous effect in ferrofluids and obtain novel expressions for the rotational viscosity, shedding new light on the effects of inter-particle correlations and particle packing. In particular, previous models usually confuse solvent vorticity with suspension vorticity and do not yield the actual rotational viscosity measured in experiments. We compare our theoretical predictions with recent simulations and find quantitatively good agreements. Our work is to be a cornerstone for understanding ferrofluid dynamics and of considerable importance to various applications. It can be also valuable for studying the hydrodynamics of other structured fluids.