Numerical study of the influence of diffusion of magnetic particles on equilibrium shapes of a free magnetic fluid surface

A mathematical model and a computational method for studying the influence of the particle diffusion on equilibrium shapes of a magnetic liquid is developed. It is then applied on the ferrohydrostatic problem of doubly connected equilibrium shapes of a magnetic fluid located on a horizontal plate around a vertical cylindrical conductor with a direct current. Numerical simulations show the limits of the uniform concentration approximation.