### Abstract

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∞d ^{1/2}. 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.

Original language | English |
---|---|

Pages (from-to) | 56-65 |

Number of pages | 10 |

Journal | Chemical Engineering Science |

Volume | 83 |

DOIs | |

Publication status | Published - Dec 3 2012 |

### Fingerprint

### Keywords

- Electrochemistry
- Mathematical modeling
- Model reduction
- Nonlinear dynamics
- Nullclines
- Oscillations

### ASJC Scopus subject areas

- Chemical Engineering(all)
- Chemistry(all)
- Applied Mathematics
- Industrial and Manufacturing Engineering

### Cite this

*Chemical Engineering Science*,

*83*, 56-65. https://doi.org/10.1016/j.ces.2011.10.073

**Quantitative dynamical relationships for the effect of rotation rate on frequency and waveform of electrochemical oscillations.** / Urvölgyi, Mónika; Gáspár, V.; Nagy, Timea; Kiss, István Z.

Research output: Contribution to journal › Article

*Chemical Engineering Science*, vol. 83, pp. 56-65. https://doi.org/10.1016/j.ces.2011.10.073

}

TY - JOUR

T1 - Quantitative dynamical relationships for the effect of rotation rate on frequency and waveform of electrochemical oscillations

AU - Urvölgyi, Mónika

AU - Gáspár, V.

AU - Nagy, Timea

AU - Kiss, István Z.

PY - 2012/12/3

Y1 - 2012/12/3

N2 - 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∞d 1/2. 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.

AB - 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∞d 1/2. 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.

KW - Electrochemistry

KW - Mathematical modeling

KW - Model reduction

KW - Nonlinear dynamics

KW - Nullclines

KW - Oscillations

UR - http://www.scopus.com/inward/record.url?scp=84866149619&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866149619&partnerID=8YFLogxK

U2 - 10.1016/j.ces.2011.10.073

DO - 10.1016/j.ces.2011.10.073

M3 - Article

AN - SCOPUS:84866149619

VL - 83

SP - 56

EP - 65

JO - Chemical Engineering Science

JF - Chemical Engineering Science

SN - 0009-2509

ER -