A material balance closure calculation is presented to test the consistency of a previously published model of a parallel plate electrochemical reactor. New expressions are used in this procedure to calculate the average concentration of species normali and the average current density for reaction normalj from the predicted concentration and potential distributions. Also, the previously presented model equations are simplified by assuming that the axial concentration gradient for species normali can be approximated by a step change from the known feed concentration to the unknown outlet concentration. This one‐step model provides a qualitative evaluation of cell performance and adds insight into understanding of the previous model, while providing substantial savings in computer time. The models are compared using a hypothetical case of the electrowinning of copper from a chloride solution. For a small aspect ratio false(S/Lfalse) , the models show that a set of independent variables consists of the cell potential false(Enormalcellfalse) , the surface area of an electrode per unit of cell volume false(1/Sfalse) , and the residence time false(L/υnormalavgfalse) when the feed concentrations false(cnormali,normalfeedfalse) are fixed.

A method is presented for predicting shunt currents in stacks of undivided and divided bipolar plate cells. The method is an efficient way of solving the coupled sets of algebraic equations that arise from using circuit analog models to represent the current paths in stacks of undivided or divided bipolar plate cells. These algebraic equations can be either linear or nonlinear depending upon the current‐potential relationships used in the model (i.e., nonlinear circuit elements can be included). The method is used to show the importance of including nonsymmetrical resistances and nonlinear circuit elements in the models. Also, the method is used to predict the shunt currents for a nine cell stack of pilot plant scale bipolar plate, membrane chlor‐alkali cells. It is shown that these predictions agree qualitatively with measured values. Finally, the method is used to predict the shunt currents for stacks of 60 and 120 of these cells.

A mathematical model is presented for a system comprised of a parallel plate electrochemical reactor (PPER) and a continuous, stirred‐tank reactor (CSTR) under both total and partial recycle. The model is used to predict the time dependent behavior of the electrowinning of copper from an aqueous, hydrochloric acid solution. The model includes many important aspects of a PPER/CSTR system which have been neglected previously. These aspects are the kinetics of electrode reactions, the electroneutrality condition, three mass transfer processes for ionic species in the electrolyte (diffusion, ionic migration, and convection) and the electrode gap in the PPER, and the inclusion of a true CSTR in the recycle stream.

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