Modern Aspects of Electrochemistry No. 44 Modelling and Numerical Si
MODERN ASPECTS OF ELECTROCHEMISTRY No. 44 Edited by Mordechay Schlesinger University of Windsor, Windsor, Ontario, Canada Topics in Number 44 include: The basic mathematical models which arise in some electrochemical processes in regards to galvanic corro
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Current Distribution in Electrochemical Cells: Analytical and Numerical Modeling Uziel Landau Department of Chemical Engineering, Case Western Reserve University, Cleveland, OH 44106, USA, [email protected]
I.
INTRODUCTION AND OVERVIEW
The topic of current distribution modeling is central to the analysis of electrochemical systems and has been addressed in textbooks,1 reviews (e.g., Refs. [2–4]) and numerous journal publications. Newman’s textbook1 provides a meticulous and comprehensive treatment of the subject. Prentice and Tobias2 present a review of the early (up to about 1980) publications in the area. Dukovic’s more recent review3 is very comprehensive, providing critical analysis of both the electrochemical and the numerical aspects of the topic. A recent review by Schlesinger4 focuses primarily on the numerical techniques. The present monograph introduces the fundamental processes and equations underlying the modeling of the current distribution, and critically analyzes common assumptions and approximations. Focus is placed on discussing scaling parameters for the characterization of the current distribution. Commonly used algorithms for numerical determination of the current distribution are compared and a few numerical implementations are discussed. Lastly, the modeling of M. Schlesinger (ed.), Modelling and Numerical Simulations II, Modern Aspects of Electrochemistry 44, DOI 10.1007/978-0-387-49586-6 10, c Springer Science+Business Media LLC 2009 451
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the current distribution in some special configurations and applications is introduced, emphasizing recent publications.
II. SIGNIFICANCE OF MODELING THE CURRENT DISTRIBUTION The current distribution is among the most significant parameters characterizing the operation of the electrochemical cell. The current density on the electrodes is directly proportional to the reaction rate and its distribution critically affects the electrochemical process. In electroplating, the deposit thickness distribution, and properties such as the deposit surface texture and its morphology are directly linked to the current distribution. When multiple simultaneous electrode reactions are present, such as in alloy deposition or in hydrogen coevolution, the alloy composition in the former case and the current efficiency in the latter are controlled by the overpotential distribution, which, as discussed below, is directly related to the current distribution. Electrolytic processes which do not involve deposition are also strongly affected by the current distribution. Examples include optimized utilization of catalytic electrodes and the need to prevent the current density from surging on electrode sections, on separators, and on membranes. The power required for operating an electrochemical cell, and particularly the ohmic loss are also dependent on the current distribution. Lastly, the correct interpretation of experimental data hinges on understanding the range of current densities to which the tested electrode has been subjected. The current distribu
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