Electrochimica Acta 49 (2004) 365–372 Calculation of limiting current density of metal electrodeposition on vertical plane electrode under conditions of natural convection V.M. Volgin a,∗,1 , A.D. Davydov b,1 a Chair Physical-Chemical Processes and Technology, Tula State University, Pr. Lenina 92, Tula 300600, Russia b Frumkin Institute of Electrochemistry, Russian Academy of Sciences, Leninskii Pr. 31, Moscow 119071, Russia Received 4 July 2003; received in revised form 13 August 2003; accepted 16 August 2003 Abstract An approximate analytical solution of problem of ion transfer near a vertical plane electrode surface is obtained for the metal electrodeposition proceeding at the limiting current from electrolyte containing ions of three types under the conditions of natural convection. In contrast to previous studies, no transport numbers are used here, and the migration transfer of electroactive electrolyte component is taken into account. The equations obtained take into consideration the effect of supporting electrolyte concentration and its migration on the limiting current. The limiting current densities (mass-transfer coefficients), which are calculated by equations proposed here and by the finite-difference method, are compared. © 2003 Elsevier Ltd. All rights reserved. Keywords: Electrodeposition; Limiting current; Natural convection 1. Introduction During the metal electrodeposition, the variations in the concentrations of electrolyte species and, consequently, in the solution density are observed near the cathode surface. As a result, convective electrolyte flow, i.e. natural con- vection, arises near the vertical electrode surface under the action of buoyancy force [1,2]. In the case of forced convection, the equations of electrolyte (incompressible viscous liquid) flow can be solved independently of the equations of material balance of species. By contrast, in the case of natural convection, these equations should be solved simultaneously. In the case of natural convection, the ion transfer, which is caused by the diffusion, migration, and convection, and the hydrodynamic processes are interre- lated. This seriously complicates the problem of ion trans- fer. At present, no exact analytical solutions of the problem are available; however, several approximate analytical [3–7] and numerical [8] solutions were reported. In general, the ∗ Corresponding author. Tel.: +7-0872-352452; fax: +7-0872-331305. E-mail address: volgin@uic.tula.ru (V.M. Volgin). 1 ISE member. numerical solutions are more precise; however, approximate analytical solutions are more efficient and enable one to determine the effect of system’s parameters on the limiting current density in the explicit form. Therefore, approximate analytical solutions are of great practical and theoretical importance. Approximate analytical solutions only for the limiting cases—a binary electrolyte and a large excess of supporting electrolyte—are available from the literature. In the case of binary electrolyte, the migration term can be eliminated and the problem can be reduced to the mass- transfer problem for nonelectrolytes and the problem of heat convection. These problems were much studied and several approximate solutions of these problems were reported [9]. In the case of a large excess of supporting electrolyte, the migration transfer of electroactive species can be ignored, but the migration transfer of supporting electrolyte should be taken into account as it affects the distribution of electrolyte density over the near-electrode layer leading to the variations in the profile of hydrodynamic velocities. The latter, in its turn, has an effect on the distribution of electroactive species concentration and, consequently, on the limiting current den- sity. This restricts the application of solutions obtained for heat transfer and mass transfer in the nonelectrolytes [10]. 0013-4686/$ – see front matter © 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2003.08.019