Numerical Simulation of Ionic Mass-Transfer Rates with Natural Convection in CuSO4 – H2SO4 Solution I. Numerical Study on the Developments of Secondary Flow and Electrolyte Stratification Phenomena

The ionic mass-transfer rates accompanying natural convective electrolyte flow in a CuSO 4 aqueous electrolyte solution acidified with an excess amount of H 2 SO 4 are numerically analyzed. The effects of a supporting electrolyte and an interaction behavior between both cathodic upward and anodic downward natural convections are examined. Both anodic and cathodic current density distributions along the vertical height are also calculated. A mathematical model is extended by incorporating an additional boundary condition at the limiting current. A measure of ionic migration effect e, a ratio of limiting current to limiting diffusion current, involving the transference number of a discharging metallic ion is introduced for this purpose. The present calculation predicts the oscillation behaviors in transient variations in both electrode surface concentration and maximal natural convective velocity, which are deeply related to the periodic fluctuating electrolyte flow patterns distorted by secondary flow. The addition of H 2 SO 4 maintains an e value around 1 and prevents the further development to the transition or turbulent natural convection.

[1]  S. Kida,et al.  Numerical Simulation of Transient Natural Convection along Vertical Plane Electrodes Caused by Electrolytic Current Modulation , 2008 .

[2]  S. Kida,et al.  Numerical simulation of transient natural convection induced by electrochemical reactions confined between vertical plane Cu electrodes , 2007 .

[3]  Y. Fukunaka,et al.  Anodic dissolution phenomena accompanying supersaturation of copper sulfate along a vertical plane copper anode , 2003 .

[4]  A. D. Davydov,et al.  Simulation of ion transfer under conditions of natural convection by the finite difference method , 2003 .

[5]  Y. Kondo,et al.  Copper dissolution phenomena along a vertical plane anode in CuSO4 solution , 2001 .

[6]  Y. Konishi,et al.  Ionic Mass‐Transfer Rates Associated with Natural Convection along a Plane Vertical Anode Measured by Two‐Wavelength Holographic Interferometry , 1998 .

[7]  M. Georgiadou.  Finite‐Difference Simulation of Multi‐Ion Electrochemical Systems Governed by Diffusion, Migration, and Convection Implementation in Parallel‐Plate Electrochemical Reactor and Backward‐Facing Step Geometries , 1997 .

[8]  F. Alavyoon,et al.  Free convection in an electrochemical system with nonlinear reaction kinetics , 1995, Journal of Fluid Mechanics.

[9]  A. Eklund,et al.  Theoretical and experimental studies of free convection and stratification of electrolyte in a copper refining cell , 1991 .

[10]  Y. Kondo,et al.  Structural Variation of Electrodeposited Copper Film with the Addition of an Excess Amount of H 2 SO 4 , 1990 .

[11]  Y. Kondo,et al.  Measurement of Concentration Profiles of Cu2+ Ion and H+ Ion near a Plane Vertical Cathode by Two‐Wavelength Holographic Interferometry , 1985 .

[12]  Y. Kondo,et al.  Concentration Profile of Cu2+ Ion near a Plane Vertical Cathode in Electrolytes Containing CuSO4 and an Excess of H2SO4 as a Supporting Electrolyte , 1983 .

[13]  Y. Kondo,et al.  Distribution of Local Current Densities during Copper Electrodeposition on a Plane Vertical Cathode , 1979 .

[14]  R. Alkire,et al.  Current Distribution in a Tubular Electrode under Laminar Flow: One Electrode Reaction , 1977 .

[15]  J. Newman,et al.  Mass Transfer to a Rotating Disk in Transition Flow , 1976 .

[16]  J. Selman,et al.  UNSTEADY-STATE EFFECTS IN LIMITING CURRENT MEASUREMENTS , 1975 .

[17]  C. Tobias,et al.  Derivation of one-dimensional refractive-index profiles from interferograms , 1975 .

[18]  C. Tobias,et al.  Light‐Deflection Errors in the Interferometry of Electrochemical Mass Transfer Boundary Layers , 1975 .

[19]  J. Newman,et al.  An Asymptotic Solution for the Warburg Impedance of a Rotating Disk Electrode , 1973 .

[20]  R. Alkire,et al.  The Current Distribution Within Tubular Electrodes under Laminar Flow , 1973 .

[21]  E. Sparrow,et al.  Local Natural Convection Mass Transfer Measurements , 1972 .

[22]  J. Newman,et al.  Limiting Current on a Rotating Disk with Radial Diffusion , 1971 .

[23]  J. Selman,et al.  Free‐Convection Mass Transfer with a Supporting Electrolyte , 1971 .

[24]  J. Newman,et al.  Current Distributions on Plane, Parallel Electrodes in Channel Flow , 1970 .

[25]  J. Newman,et al.  Current Distribution on a Rotating Disk Electrode , 1969 .

[26]  J. Newman,et al.  Current Distribution on a Plane Electrode below the Limiting Current , 1969 .

[27]  J. Newman.  Current Distribution on a Rotating Disk below the Limiting Current , 1966 .

[28]  S. Yoshizawa,et al.  Mass Transfer and Current Distribution under Free Convection Conditions , 1960 .

[29]  R. Müller,et al.  Studies of Natural Convection at Vertical Electrodes , 1958 .

[30]  C. Tobias,et al.  Correlation of Limiting Currents under Free Convection Conditions , 1953 .

[31]  C. Wagner,et al.  Theoretical Analysis of the Current Density Distribution in Electrolytic Cells , 1951 .

[32]  C. Wagner.  The Role of Natural Convection in Electrolytic Processes , 1949 .