Supporting electrolyte asymptotics and the electrochemical pickling of steel

Asymptotic methods are used to analyse a recent numerical model for the electrochemical pickling of steel. Although the process is characterized by an excess of supporting electrolyte, the asymptotic structure of the solution turns out not to be the same as that given classically for such situations. In the original theory, the asymptotic expansions for the ionic concentrations and electric potential are regular and uniformly valid; here, singular perturbation theory is required to take account of the bulk electrolyte and concentration boundary layers adjacent to reacting surfaces. The reworked theory gives a leading-order problem that is solved numerically; the results are in excellent agreement with those of the earlier computations. Also, invoking the slenderness of the geometry yields, in a combined quintuple asymptotic limit, an analytical estimate for the current density that captures well the qualitative trends and that enables a rapid assessment of the effect of operating conditions on the process.