Design of Primary and Secondary Cells

The current density distribution in a battery is a function of electrode height, electrode resistance, electrolyte resistance, and polarization. Mathematical solutions have been obtained for those cases where the polarization curves are either linear, logarithmic, or cubic. A numerical method is indicated for finding a general solution. In the case of linear polarization, the results are presented in graphs which show the current density distribution and other cell characteristics over a wide range of operating conditions. The determination of these cell characteristics can be of considerable importance in cell design. For practical applications, the complex mathematical calculations involved in the cases of logarithmic and cubic polarization can be eliminated by the use of transformations which convert them to the linear case.