Slow, steady discharge regime for concentrated lead-acid cells with planar, cylindrical, and spherical electrodes
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A recent theoretical study of slow, steady discharge for a lead-acid cell carrying current I, with planar electrodes, predicts a nonzero bulk charge distribution with an associated voltage profile within the electrolyte that is quadratic in space. A second theoretical study finds that the Ohmic voltage resistance R=V/I across the electrolyte differs from the Joule heating resistance RJ=P/I2. The very different diffusion constants of the charge-carrying ions H+ and HSO4- is responsible for the quadratic voltage profile. The presence of changing chemical energies is responsible for the different resistances. In the present work we study this same chemical system for the cylindrical and spherical geometries, with Pb at inner radius a and PbO2 at outer radius b. For the cylindrical case, the voltage varies with radius as the sum of a logarithm and a quadratic. For the spherical case, the voltage varies with the radius as a sum of an inverse r and a quadratic. For both cases, the quadratic is the signature of a uniform nonzero bulk charge distribution. For both cases, RRJ. For large enough b/a, in both the spherical and cylindrical cases, we find that R<0; current flows from lower to higher electrical potential. This does not violate energy conservation when chemical as well as electrical energies are included. 1998 American Institute of Physics.
