J. Rojo et A. Bronson, NUMERICAL-ANALYSIS OF CERTAIN SOLUTIONS OF LAPLACES-EQUATION TO CALCULATE THE OHMIC POTENTIAL DROP AFTER SCRIBING, Electrochimica acta, 38(17), 1993, pp. 2525-2532
The accuracy of certain solutions to Laplace's equation for various el
ectrode geometries is examined and compared to the accuracy of new sol
utions based on a Taylor's series expansion. Whereas previous solution
s are accurate only for cases where the counter-electrode is remotely
placed from the working electrode, the new solutions are highly accura
te for all values of relevant geometric parameters. In particular, for
an electrode with a non-uniform current or uniform current distributi
on, the ohmic drop computed with an equation assuming an infinite spac
ing can deviate substantially from the correct potential drop for a co
unter-electrode near a working electrode. For the specific case of a r
ectangular electrode, the solution computed here provides a better fit
to experimental data than available solutions in the literature. A di
rect benefit to the user of these results is the freedom from having t
o make the decision as to what constitutes a large enough separation (
or spacing) between the working- and counter-electrodes. In addition,
error bounds on the use of the new solutions are provided for the bene
fit of the user.