Modelling and simulation of magnetic particle diffusion in a ferrofluid layer

O. Lavrova¹ , V. Polevikov¹ , L. Tobiska²

¹ Belarusian State University, 4 Nezavisimosti Ave., 220030 Minsk, Belarus }
² Otto-von-Guericke University, 2 Universitätsplatz, 39106 Magdeburg, Germany

Abstract
Three mathematical models on static equilibrium distribution of ferromagnetic particles in a ferrofluid, which has a free surface, are described for dilute, weakly concentrated and moderately concentrated ferrofluids, respectively. The models differ in description of the mass transfer of particles and fluid magnetization. Numerical computations are performed concerned with the problem of ferrofluid layer instability in an applied uniform magnetic field (the Rosensweig instability) to resolve axisymmetric equilibrium states relative to the particles' distribution, to the magnetic field structure and to the free surface shape of the fluid. It is observed that the onset of ferrofluid layer instability does not depend on the diffusion of particles (interacting or not). However, diffusion causes an elongation of peaks in a long-term range (several days) with the highest concentration in the peak region. Tables 1, Figs 6, Refs 16.