## Seminarium Zakładu Mechaniki i Fizyki Płynów## Magnetic relaxation in ferrofluids## prof. Rudi Schmitz, RWTH Aachen, Niemcy |

A ferrofluid is described as a monodisperse suspension of hard spheres immersed in an incompressible liquid. The spheres have a permanent magnetic dipole moment and interact via the excluded volume repulsion, the orientation-dependent magnetic dipole interaction, and the hydrodynamic interaction which is mediated by the host fluid. The time-evolution of the system is governed by Brownian dynamics and quantitatively described by a generalized Smoluchowski equation for the probability distribution of the positions and orientations of all the ferroparticles. The response theory for the time-dependent magnetization is elaborated on the basis of this generalized Smoluchowski equation. By applying Zwanzig's projection operator technique the problem is turned into a field theory which can be analyzed by means of a renormalized perturbation theory of the Martin-Siggia-Rose type. The theory requires input for the static direct correlation functions which are evaluated on the basis of the mean-spherical approximation. This takes into account both the hard-sphere repulsion and the magnetic-dipole interactions. The hydrodynamic interactions enter in a non-local diffusion kernel which is explicitly evaluated by applying a Cluster expansion up to 2-body terms. This is sufficient for dilute and moderately dense systems. The short-time (large frequency) dynamics is governed by the propagator of the field theory which is evaluated explicitly. The effects of the three types of interaction are discussed and compared.