Movement of electrolyte at metal etching and deposition under a non-uniform steady magnetic field

O. Yu. Gorobets^{1, 2} , Yu. I. Gorobets^{1, 2} , V. P. Rospotniuk¹

¹ National Technical University of Ukraine KPI, 37 Peremogy Avenue, Kyiv 03056, Ukraine
² Institute of Magnetism, NAS of Ukraine and MESYS of Ukraine, 36-b Vernadsky Avenue, Kyiv 03142, Ukraine

Abstract
The paper presents a promising model of MHD effects caused by the presence of cluster products in the processes of deposition, etching and corrosion of metals near the surface of a ferromagnetic electrode in an electrolyte solution. The above mentioned processes occur at the electrode surface in non-uniform magnetic fields, with no electric current through the electrolyte. This approach is based on a system of MHD equations for a poorly conducting fluid and on the convective diffusion equation of effectively paramagnetic or diamagnetic cluster components of electrolyte under the influence of the gradient magnetic force. The equation of convective diffusion of cluster products of electro-chemical reactions in electrolyte is supplemented with boundary conditions, which are based on the balance of the diffusion surface flow of clusters, their flow under the influence of the gradient magnetic force and their surface source power. As an illustration, the proposed approach is used to model electrolyte stirring near a ferromagnetic ball-shaped electrode in case of adiabatic changes in the concentration of clusters in the system. In particular, the calculated velocity distribution of the solution and the form of a cylindrically symmetrical surface in the vicinity of a magnetized steel ball, which separates the regions of the electrolyte with the opposite directions of rotation, are discussed. Figs 3, Refs 35.