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Predictions of the electrical energy cost for NaOH production are determined as a function of the independent operating variables and diaphragm characterizing properties. The predictions are based on data from a statistically designed experiment, a simple model of a diaphragm-type electrolyzer, a simple model of the cell voltage losses, and parameter estimation techniques. The data were obtained over a sufficiently large range of operating conditions so that the resulting design equation may be industrially useful. The simple model of the diaphragm is based on the mass transport of the hydroxyl ion, a linear potential gradient, and is presented in terms of measurable diaphragm properties.These properties are the thickness of the diaphragm (t) and a resistivityratio, P/Po, where p is the resistivity of the diaphragm filled with electrolyte and po is the resistivity of the electrolyte (this ratio may come to be known as the MacMullin number, NM). It is shown that, according to the model of the cell, the caustic yield or current efficiency of the diaphragm cell depends on the product of NM and t and not on each separately. The simple model of the cell voltage considers the diaphragm voltage drop, anode and cathode kinetics, and the bubble-filled brine-gap voltage drop. Parameter estimation techniques are used to determine the best values of the diffusion coefficient, average specific conductivity, exchange current densities, and transfer coefficients; these parameters and the simple models provide a design equation for the electrical energy cost of NaOH production using a diaphragm cell. The design equation is used to predict a

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A method is presented for determining the effects of time dependence, axial diffusion, and axial migration in a parallel-plate electrochemical reactor (PPER). The method consists of formulating the governing equations and applying a numerical integration technique to solve a set of time-dependent, nonlinear, coupled, multidimensional equations. This formulation reveals that the steady-state performance of the PPER depends on the cell potential and three dimensionless groups. Predictions of the concentration, potential, and local current distributions in a PPER are presented for the electrowinning of copper from an aqueous, hydrochloric acid solution. These predictions show that axial diffusion and axial migration are significant when the aspect ratio (i.e., the ratio of electrode separation to electrode length) is greater than 0.5. White et al. (1) presented a model of a parallel-plate