Numerical study of ferrofluid covering of a current-carrying conductor taking into account diffusion of interacting particles

A ferrofluid drop located on a horizontal plane and covering a vertical current-carrying conductor under the action of a magnetic field generated by the conductor and gravity is considered. The numerical study is based on a mathematical model of equilibrium states, consisting of equations for the free-surface shape of the ferrofluid drop and equations for the concentration of interacting magnetic nanoparticles inside the ferrofluid. The computational algorithm is organized as an iterative coupling between the finite-difference approximation of the free-surface and the Newton's method for the concentration equations formulated on an a-posteriori adaptive mesh, representing the discrete free-surface. Numerical results predict that the interactions between magnetic nanoparticles have little effect on the equilibrium free-surface shapes in weak magnetic fields but lead to a stronger shape elongation in moderate magnetic fields when compared to simulations with diffusion of non-interacting particles. Simulations have shown a sharp transition from drop-like shapes to sheath-like coverage of the conductor for a ferrofluid drop of large volume at different contact angles. Figs 5, Refs 18.