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We performed a mathematical analysis of the theory of collective microplasma processes in solutions and the basic equation for the growth of a nanostructured nonmetallic inorganic coating during the formation of a coating - a film on the surface of a material immersed in an electrolyte solution during nanoscale localization of high-energy flows at the phase boundary. The microplasma process is considered as a process of collective microplasma discharges. It is shown that this model allows one to relate the main physicochemical parameters of electrochemical and microplasma processes in electrolyte solutions: concentration, temperature, pulse duration, polarization voltage with the characteristics of the coating formation process, growth rate, thickness, size, and grain weight of the coating. The total current of microplasma discharges is limited by the current passing through the boundary immiscible layer.

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Growth of nanostructured nonmetallic inorganic coatings obtained by nanoscale localization of high-energy flows at the boundary of the phase separation