Models for microrheology of complex magnetic fluids

Abstract

A review of some aspects of orientational magnetodynamics of viscoelastic magnetic fluids and ferrogels is given. As an archetypal theoretical model we use an assembly of non-interacting dipolar Brownian nanoparticles embedded in and coupled to a matrix that possesses either a dynamic (Maxwellian) or a weak equilibrium (Hookean) elasticity or both. With regard to their magnetic properties, the particles are assumed to be rigid dipoles. In the mechanical aspect the particles are taken to be two-dimensional, i.e., are modeled by disks, either inertial or inertia-less. Two types of dissipative interaction between a particle and its environment—a simple Stokes viscous friction and a friction with a simple exponential memory (like in a Maxwellian fluid)—are analyzed. Using the linear response approach we find the equilibrium correlation functions and the dynamic magnetic susceptibilities of the media. For the case of inertia-less particles the kinetic equation of rotary diffusion is derived and certain peculiarities in its properties are discussed.