Numerical Simulation of Rayleigh–Bènard Instability in Solutions Containing Ions of Three Types

The conditions for appearance of a Rayleigh–Benard instability (RBI) induced by a constant current between two horizontal electrodes in solution containing electroactive ions and indifferent electrolyte (system with three kinds of ions) are analyzed. It is taken into account that all the components take part in the formation of buoyant forces. The problem is solved for a stationary case (as an expansion to a series by a small parameter), and then equations for low perturbations are solved by the Galerkin method. The calculation is performed with a program that accounts for any number of members in a Galerkin expansion. A diagram is obtained, which determines conditions for the RBI emergence in terms of ratios of partial Raleigh numbers. The ratio of diffusion coefficients for supporting cations and anions significantly affects position of the boundary dividing ranges of convective stability and RBI in a diagram of nonequilibrium phase transitions.     

Oscillatory Convective Instability in a Ternary Electrolyte: Effect of the Electrode Reaction Rate

The effect the electrode reaction rate has on the oscillatory instability, which is induced by buoyancy forces in a solution containing univalent cations of two types and a common anion, is considered. It is shown that, at a decrease in the rate, the spectrum of acceptable fluctuations of concentrations of electroactive ions narrows down, thus raising the system's stability. Diagrams of nonequilibrium phase transitions are constructed for various ratios between diffusion coefficients for anions and cations.     

Convective instability of a zinc sulfate solution in a cell with horizontal plane-parallel electrodes

The Rayleigh-Bénard convective instability in a cell with horizontal zinc electrodes is considered. The space between the electrodes is filled with a ZnSO₄ solution. The linear plot of the difference between the zinc deposition currents (I) in the cases where the anode is the upper or lower electrode vs. the square root of the zinc deposition current in the absence of convection is found experimentally. It is shown that the critical Rayleigh number can be determined by an extrapolation of this plot.Translated from Elektrokhimiya, Vol. 41, No. 2, 2005, pp. 247–249.Original Russian Text Copyright © 2005 by Tomashova, Teplitskaya, Grigin, Davydov.     

Limiting Current of Copper Electrodeposition from a Copper Sulfate Solution under Conditions of Natural Convection: The Space Charge Effect

Copper electrodeposition from a copper sulfate solution under conditions of natural convection is analyzed theoretically and examined experimentally. The space charge, which forms in the near-cathode layer, is shown to affect the limiting current density and to change its concentration dependence.     

Natural convective diffusion between two nonconcentric spheres

A study is made of the natural convective diffusion in a nonconcentric spherical layer formed by a ball of radius R₁ in a sphere of radius R₂. The centers of the ball and sphere are separated by a distance d R₁. The spherical layer is filled with a binary electrolyte, and the outer surface of the ball and the inner surface of the sphere serve as the anode and cathode, respectively, of an oxidation—reduction reaction. It is assumed that the reaction proceeds in accordance with diffusion kinetics, i.e., the current in the circuit limits the rate at which the reacting substances reach the electrodes [1]. If a current passes in the system, a concentration gradient develops in the reacting substances, and in a gravitational field a convective motion of the fluid is generated, which changes the rate at which the reacting substances arrive at the electrodes. For a binary eletrolyte in the leading approximation in the small parameter r_D(R₂ – r₁)^–1, where r_D is the Debye radius, the migration current can be eliminated, and one need consider only the diffusion and convective fluxes of the ions [2]. If the centers of the ball and the sphere coincide, the integrated diffusion flux at small Grashof numbers is not changed, and there is merely a local redistribution.[3–5]. At small Grashof numbers, a strong dependence of the integrated diffusion flux on the eccentricity of the spherical layer must be expected. In the present paper, the hydrodynamic velocity field of the fluid, and also the change in the integrated diffusion flux due to the convective transport of the ions are found in the linear approximation in the small parameter = d/R₁.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 151–154, January–February, 1984.     

Convective boundary layers in electrolyte solutions

During current passage through an electrolyte solution, ions entrain their hydration shells, which gives rise to the accompanying diffusion flow of water molecules and internal convection analogous to that observed in superfluid He³+He⁴ solutions. Hydrodynamic conditions are determined under which the total water flux on a solid surface is zero. The convective boundary layer on a vertical plate is theoretically described using the von Karman method. The diffusion-mechanical effect in thin capillaries is evaluated.     

Numerical Solution of the Problem of the Limiting Current for the Copper Electrodeposition from a Solution of Cupric Sulfate and Sulfuric Acid in Conditions of Natural Convection

Equations for a boundary layer, written in self-similar variables, are integrated numerically to obtain distributions of concentration of ions Cu²⁺, H⁺, and SO₄ ^2–; a hydrodynamic velocity; partial currents of electrolyte components; and the limiting current of copper deposition and determine the Rayleigh number for the system under consideration. The results are compared with an approximate analytical solution obtained earlier.     

Numerical Study of Electroconvective Instability of Binary Electrolyte in a Cell with Plane Parallel Electrodes

Electroconvective instability of a binary electrolyte in a cell with plane parallel electrodes is studied using a numerical method. When a direct current is passed through the cell, a space charge and an electrical force acting upon the solution form under certain conditions. If the electric force density reaches a critical value, convective instability emerges in the cell, leading to the formation of nonequilibrium dissipative structures similar to Rayleigh–Benard cells in a nonuniformly heated liquid. The critical parameter _crit, at which instability emerges in the system, is determined. Dependences of _crit on the ratio between the diffusion coefficients for electrolyte cations and anions and on the current passed through solution are determined.     

Influence of Two-step Mechanism of Dissociation of H2SO4 on the Limiting Cathodic Current of Copper Deposition from Sulfate Solutions in Conditions of Natural Convection

The limiting cathodic current of copper deposition at a flat vertical electrode from solutions containing a mixture of copper sulfate and sulfuric acid (in excess) in conditions of natural convection is calculated. The possibility of the two-step dissociation of sulfuric acid is accounted for. The obtained formulas yield the limiting cathodic current at any ratio of bisulfate and sulfate anions in solution.