NONLINEAR TRANSIENT REACTION-DIFFUSION PROBLEM FROM ELECTROANALYTICAL CHEMISTRY

A nonlinear reaction-diffusion partial differential equation occurring in models of transient controlled-potential experiments in electroanalytical chemistry is investigated analytically and numerically, with a view to determining a relationship between the concentration of a chemical species and its flux at a reacting electrode. It is shown that a previously known relation that holds for the steady-state case can be used as the first term in a singular perturbation expansion for the time-dependent case. However, in trying to determine the second term, so as to extend the range of validity of the solution, it is found that a phenomenon akin to switchbacking occurs, with the asymptotic details being strongly dependent on the reaction order; this appears to be a consequence of the spatial algebraic decay of the leading-order solution far from the electrode. Comparison of asymptotic results with numerical solutions obtained using finite element methods indicates a relation involving the homogeoneous reaction order for which the two-term asymptotic approximation would work best for all time. Links to problems that involve algebraically decaying boundary layers are briefly discussed.

Automated summary

An analytical and numerical investigation was conducted on a nonlinear reaction-diffusion partial differential equation in models of transient controlled-potential experiments in electroanalytical chemistry, aiming to determine the relationship between the concentration of a chemical species and its flux at a reacting electrode. It was found that a known relation for the steady-state case could be used in a singular perturbation expansion for the time-dependent case, but encountering a phenomenon akin to switchbacking when trying to determine the second term to extend the validity of the solution.