Quantitative dynamical relationships for the effect of rotation rate on frequency and waveform of electrochemical oscillations

We investigate the effect of changing mass transfer conditions through variation of rotation rate of a rotating disk electrode on features of oscillatory dynamics of negative differential resistance electrochemical systems. The theoretical analysis and numerical simulation of a prototype two-variable electrochemical model show that for oscillations close to a Hopf bifurcation the frequency (ω) increases with increase in rotation rate (d) following an approximate square root formula ω∝d1/2. For relaxation oscillations, the oscillations maxima, minima, and transition points between the high- and low-current states do not depend on rotation rate; the oscillation waveform invariance is explained using nullcline analysis by showing that the rotation does not affect the nullcline of the fast variable (electrode potential) along which the oscillations occur. The numerical and theoretical predictions are confirmed in experiments with copper electrodissolution in phosphoric acid electrolyte using a rotating electrode setup. The results thus indicate that simplifying concepts related to invariant manifolds and parameter dependence of bifurcation points (principle of critical simplification) are efficient approaches to obtaining quantitative dynamical relationships for decoding complexity in electrochemical reaction systems.

► Periodic current oscillations are studied on a rotating disk electrode.
► Frequency depends on square root of the rotation rate for smooth oscillators.
► Amplitude does not depend on the rotation rate for relaxation oscillators.
► Experiments with copper electrodissolution in phosphoric acid confirm theory.