Denso Corporation assisted in meeting the publication costs of this article. REFERENCES 1. K. Shigematsu, K. Kondo, K. Hayakawa, and M. Irie, This Journal, 142, 1149 (1995). 2. D. J. Henderson, M. H. Brodsky, and P Chaoudhari, Appl. Phys. Lett. 25, 641 (1974). 3. M. J. Brett, J. Vac. Sci. Technol., A6 (1988). 4. J. F Knight and P A. Monson, Molec. Phys., 6, 921 (1987). 5. M. K. Carpenter and M. W. Verbrugge, This Journal, 137, 123 (1990). 6. K. Kondo, J. Ishikawa, 0. Takenaka, T. Matsubara, and M. Irie, ibid., 138, 12 (1991). 7. G. Bourghesani and F Pulidori, Electrochim. Acta, 2, 107 (1984). 8. P Hepel, This Journal, 134, 2685(1987. 9. G. M. Barrow, Physical Chemistry, McGraw-Hill Book Company, Inc., New York (1996). 10. J. J. P. Stewart, J. Comp. Chem., 10, 209 (1989). 11. J. J. P Stewart, Quantum Chem. Program Exchange Bull., 9, 10 (1989) MOPAC Ver. 6. 12. J. A. Nelder and R. Mead, Comp. J., 71, 308 (1965). 13. M. Matsuoka, S. Ito, and T. Hayashi, J. Met. Finish. Soc. Jpn., 33, 385 (1982). 14. Y. Okinaka and H. K. Straschil, This Journal, 133, 2608 (1986). 15. H. Nagata, I. Koiwa, T. Osaka, and T. Yoshii, J. Met. Finish. Soc. Jpn., 36, 230 (1985).16. K. Kondo, K. Kojima, N. Ishida, and M. Irie, Bull.Chem. Soc. Jpn., 66, 2380(1993. 17. K. F Blurton, Plat. Surf. Fin., 73, 52 (1986). Governing Equations for Transport in Porous ElectrodesPauline De Vidtst and Ralph E. White* Department of Chemical Engineering, University of South Carolina, Columbia, South Carolina 29208, USA ABSTRACT General governing equations for a porous electrode containing three phases (liquid, solid, and gas) are developed using the volume-averaging technique. These equations include the mass transfer in each phase, ohmic drop in the liquid and solid phases, and the equations resulting from applying the principle of conservation of charge. The electrolyte is considered to be a concentrated binary solution. InfroductionThe purpose of this paper is to present the derivation of transport equations for porous electrodes using the volume-averaging technique.' The application of this technique results in the representation of a porous medium with multiple phases (gas, liquid, and solid) as a continuum. This eliminates the need for the description and representation of the microscopic configuration of the medium, which in many practical cases is not known. This technique has been used extensively for deriving governing equations for mass and heat transfer in porous media. ' In electrochemical applications, Prins-Jansen et al.° used volume averaging to develop a model of a molten carbonate fuel cell. Newman and Tiedemann9 presented general equations for porous electrodes based on a form of averaging which is similar to the technique used here. The derivation of their equatipns was presented by Dunning'°a nd again by Trainham," who gave a more detailed derivation. These authors9" used an area-averaging technique to define some variables (for example, the molarflux vector), which results in expressions that a...

A mathematical model for the discharge of a metal-hydride electrode was developed. The model was used to study the effect of various parameters on predicted discharge curves. The simulations obtained using the mode] show the expected decrease of charge utilization as the rate of discharge is increased. Increasing the particle size of the alloy and decreasing the diffusion coefficient of the hydrogen atoms in the hydride showed a similar effect on the discharge curves. The model simulations also show the critical role that the kinetic and transport parameters play in determining the overall shape of the predicted discharge curves for a metal-hydride electrode. The kinetic parameters used in the model predictions are those for TiMnI.~H~ (x < 0.31).

A mathematical model is presented for the discharge of a NiOOH/H2 cell. This model includes diffusion and migration in the electrolyte phase as well as proton diffusion and ohmic drop across the Solid active material in the porous nickel electrode. A theoretical analysis of the cell performance is presented for different design parameters using this model. It is predicted that proton diffusion in the solid active material is the main factor in limiting the cell voltage and the utilization of the active material. It is also predicted that use of a thick nickel electrode is an effective method for increasing electrode capacity per unit area. This model can be used to predict the two-discharge-plateau behavior of a nickel electrode.

In this paper we present a mathematical model of a sealed nickel-cadmium cell that includes proton diffusion and ohmic drop through the active material in the nickel electrode. The model is used to calculate sensitivity coefficients for various parameters in the model. These calculations show that the discharge voltage of the cell is affected mostly by the kinetics of the nickel reaction. Toward the end of discharge, proton diffusion also becomes important, because the proton diffusion process affects the active material utilization significantly. During charge, the cell voltage is mainly affected by the kinetics of the nickel reaction until the oxygen evolution reaction begins, after which time the kinetics of the oxygen evolution has the largest effect. The oxygen evolution reaction is also the most influencing factor on the actual charge uptake of the cell by the end of a charge operation (charge efficiency). Compared to the rates of reaction and proton diffusion, the ohmic drop in the active material of the nickel electrode and the mass transport and ohmic drop in the electrolyte have negligible effect on the behavior of the cell studied here.

A previously presented mathematical model for a nickel-hydrogen cell has been extended to include thermal effects. A general energy balance, integral mass balances for the gases, and temperature-dependent parameters have been added to the model. Results for simulated isothermal and adiabatic conditions are shown. A comparison of simulation results to experimental data shows qualitative agreement.

A mathematical model for a nickel/hydrogen cell is developed to investigate the dynamic performance of the cell's charge and discharge processes. Concentrated solution theory and the volume averaging technique are used to characterize the transport phenomena of the electrolyte and other species in the porous electrode and separaton Other physical fundamentals, such as Ohm's law, are employed to describe the electrical and other physical processes in the cell. The model is designed to predict the distribution of electrolyte, hydrogen, and oxygen concentrations within the cell, hydrogen and oxygen pressure, potential, current density, electrochemical reaction rates, and state of charge. The model can be used to evaluate the influences of all the physical, design, and operation parameters on the behavior of a nickel-hydrogen cell. The model simulations show excellent agreement with experimental data for charge and discharge operations. The model simulations show the formation of a secondary discharge plateau by the end of discharge. This plateau is caused by oxygen reduction at the nickel electrode. It is the first model that predicts this feature, which is a characteristic of the nickel electrode. The model simulations also show the existence of an optimum charge rate that maximizes the charge efficiency, which can be used for the implementation of optimal operating conditions. InfroductionIn this article we present a mathematical model for a nickel/hydrogen cell (NiOOH/H,) for charge and discharge operations. The nickel/hydrogen battery has several attractive features that make it the prime candidate for energy storage in many aerospace applications. Salient features of this battery are a long cycle lifetime that exceeds any other maintenance-free secondary battery system, high specific energy (energy/weight), high power density, and tolerance to overcharge.1

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