Wave instability of a magnetic fluid surface at the boundary with water in an electric field

A layer of close-packed particles of a dispersed phase (magnetite) with a protective shell of oleic acid is formed on the interface of a weakly conducting magnetic colloid (magnetic fluid) and water in a perpendicular electric field. The formation of a layer leads to a decrease in the interfacial tension. When the magnetic particles come into contact with the electrode surface, the electrochemical interaction of oleic acid molecules surrounding the particle with water occurs. As a result of the reaction, released ions charge the surface layer. After some time, the particles in the layer get recharged and repelled from the interface. This leads to wave instability. This paper considers the mathematical modeling of instability in the form of a boundary value problem – a dispersion equation. The determining factor in the development of wave instability is the action of the electric field, the formation of the near-electrode layer and, as a consequence, a decrease in the interfacial tension.