ISSN 1023-1935, Russian Journal of Electrochemistry, 2012, Vol. 48, No. 6, pp. 565–569. © Pleiades Publishing, Ltd., 2012. Original Russian Text © V.M. Volgin, A.D. Davydov, 2012, published in Elektrokhimiya, 2012, Vol. 48, No. 6, pp. 627–632. 565 The electrochemical technologies: the electro- chemical synthesis of inorganic and organic sub- stances, the electrochemical machining of metals and semiconductors (the cathodic and anodic shaping, various types of etching, etc.), the electrochemical processing of liquids (various types of cleaning), the development of various devices based on the electro- chemical principles (for an analysis of composition of various media; for conversion of chemical energy into electrical one; for conversion of information, for example, in order to record shifts, acceleration, gravi- tational field strength, and other parameters of mechanical wave fields and fluxes) were progressing rapidly in the second half of the twentieth century. This called for the development of theory and experi- mental methods for investigating mass-transfer pro- cesses in the electrochemical systems (ECS). At present, about 1500 papers on this problem per year are published (according to the ScienceDirect, more than 4500 papers were published in 2009–2011, search by the words: mass transfer electrochemical). Here, several books and reviews devoted to the prob- lems of mass transfer in the ECS are cited [1–15]. To provide high efficiency of many electrochemical tech- nologies and electrochemical devices, it is necessary to know the dependences of output parameters on many factors characterizing mechanism and kinetics of elec- trochemical reactions, transfer processes in the bulk electrolyte solution, in the diffusion and diffuse layers, etc. Along with the experimental methods, the meth- ods of mathematical simulation are widely used to investigate the mass transfer in the ECS. They enable one to study the effect of parameters of ECS on its out- put characteristics in more detail. The main lines of theoretical study of mass transfer in the ECS are the development of more precise mathematical models (one-dimensional problems give way to two- and three-dimensional problems; the dependence of parameters on the concentration and temperature are taken into consideration; homogeneous chemical reactions and conjugate transfer processes are taken into account; the transfer processes are considered on the macro-, micro-, and nano-levels, etc.), the devel- opment of analytical and numerical methods includ- ing the methods of computational hydrodynamics. By the middle of the 20th century, the theoretical models for describing transfer processes in the ECS were developed: the models of convective diffusion, multi-component diffusion of Stefan–Maxwell, and the Nernst–Planck model, which are commonly accepted now. The Nernst–Planck model takes into account the migration transfer of ions. In this case, the determination of distribution of electrical potential involved in the Nernst–Planck equations requires an additional equation: the Poisson’s equation relating the electrical field strength to the charge density or the electroneutrality condition, which can be obtained by equalizing the right-hand side of Poisson’s equation to zero. The Poisson’s equation is a second-order differ- ential equation with a small coefficient at the highest derivative; its solution involves some difficulties, because it is necessary to prescribe two boundary con- ditions and take into account the “boundary” layer. The use of the electroneutrality condition, which is an algebraic equation, instead of the Poisson’s equation, Mass-Transfer Problems in the Electrochemical Systems V. M. Volgin a, z and A. D. Davydov b, z a Tula State University, pr. Lenina 92, Tula, 300600 Russia b Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Leninskii pr. 31, Moscow, 119071 Russia Received June 3, 2011 Abstract—The problems concerning quantitative analysis of mass-transfer processes in the electrochemical systems (ECS) are briefly reviewed. The interrelation between the mass-transfer problems in the electro- chemical and heat systems is considered. Various approaches to the numerical determination of distributions of concentrations of ions of all types and electrochemical potential in the ECS are considered. The methods of allowance for the migration transfer and choosing the boundary conditions for the transfer equations and other problems are considered. Some actual lines of development of the theory of mass-transfer in the ECS are pointed out. Keywords: electrochemical systems, mass transfer, mathematical models, migration DOI: 10.1134/S1023193512060146 z The invited editors of special issue devoted to the problems of mass transfer in the electrochemical systems: e-mail: vol- gin@tsu.tula.ru and davydov@elchem.ac.ru