Higher corrections of the Ilkovich equation

Abstract

• Ilkovic polarography equation derived and augmented. • Asymptotic analysis leads systematically to higher-order terms. • Newman’s 1st-order correction verified; 2nd-order correction computed for the first time. • Asymptotic methods compared to accurate numerical computation. A short-time asymptotic analysis is performed to establish corrections of the Ilkovich equation, which describes the polarographic response of a dropping mercury electrode. The convective diffusion equation governing diffusion limited reactant flux for small drop times is solved by a regular perturbation based on powers of the sixth root of time. This produces a framework within which higher terms of the Ilkovich equation can be derived systematically. As well as reproducing Ilkovich’s original formula and verifying Newman’s correction of Koutecky’s first-order term, we calculate the second-order term for the first time. The calculation is compared to the Newman–Levich procedure and tested against numerical simulations with finite-element software.