THERMAL RATCHET EFFECT IN FERROFLUIDS A.Engel

Introduction. The extraction of directed motion from random fluctuations is an old and controversial problem in statistical mechanics with a long and interesting history [1]. Although excluded by the second law of thermodynamics for equilibrium systems, rectification of fluctuations is possible in systems driven sufficiently far away from thermal equilibrium [2, 3]. The problem has gained renewed attention under the trademarks of “thermal ratchets” and “Brownian motors” due to its possible relevance for biological transport [4, 5] and the prospects of nano-technology [6, 7, 8]. Ferrofluids are ideal systems to investigate such fluctuation driven transport phenomena, both theoretically and experimentally [9]. The main reasons are the following. First, the magnetic energy of a ferromagnetic particle in a ferrofluid is for typical magnetic fields comparable to its thermal energy at room temperature. Hence, the rotational dynamics of the ferromagnetic grains is strongly influenced by thermal fluctuations [10]. Second, appropriate time-dependent potentials can be easily designed with the help of external magnetic fields. Third, due to the viscous coupling to the carrier liquid the rectification of microscopic orientational fluctuations of the ferromagnetic grains manifests itself in a macroscopic torque per fluid volume, which can be easily detected experimentally. In the present contribution we investigate how a suitably designed time dependent external magnetic field without net rotating component may rectify fluctuations of the ferrofluid particle orientation and set up a noise-induced rotation of the ferromagnetic grains. We will thus show how the angular momentum can be transferred from an oscillating magnetic field to a ferrofluid at rest. This is a rather indirect and subtle aspect of the interplay between the rotational Brownian motion of ferrofluid particles and their relaxational dynamics in an external magnetic field. In the present introductory discussion we will use two approximations which simplify the analysis without compromising the effect under consideration. The first is to neglect the Neel-relaxation of the magnetization, i.e., the rotation of the magnetization vector with respect to the ferromagnetic particle. This is justified for particle sizes that are not too small and amounts to assuming that the magnetic moments are firmly attached to the geometry of the particles. Any reorientation of the magnetic moment hence requires a rotation of the particle as a whole. The second approximation is to neglect interactions between the particles. We hence assume a sufficiently diluted ferrofluid and work in a single particle picture.