Numerical study of diffusion of interacting particles in a magnetic fluid layer

Abstract

The paper is devoted to construction of mathematical model and computational algorithm for determining equilibrium shapes of a free surface of a magnetic fluid subject to diffusion of ferromagnetic particles in the fluid. The mathematical model consists of the Maxwell equations to determine the structure of magnetic field, the mass transfer equation for the particles, and the Young-Laplace equations for the fluid-air interface as well. Models of the uniform distribution of the particles, the nonuniform distribution without considering the particle interaction, and the nonuniform distribution subject to the particle interaction are considered. Numerical comparison of the models is carried out on the ferrohydrostatic problem of stability of a magnetic-fluid layer under a uniform magnetic field