Understanding of resonance phenomena on a catalyst under forced concentration and temperature oscillations

Resonance is an interesting phenomenon that may be observed for reactions on catalytic surfaces during periodic forcing of operating variables. Forcing of the variables for non-linear systems may result in substantially changed time averaged behaviour. These resonance phenomena have been observed experimentally by coincidence rather than by systematic analysis. It is not clear for what type of reaction kinetics such behaviour may be expected and predictions are therefore impossible. Clearly, this forms a serious obstacle for any practical application. In this work we set out to analyse the nature of resonance behaviour in heterogeneously catalysed reactions. A Langmuir Hinshelwood microkinetic model is analysed. It is demonstrated that for weakly non-linear forcing variables — as inlet concentrations — forcing leads to resonance phenomena in terms of the reaction rate only in case high total surface occupancies exist in the steady state. In contrast, forcing of strongly non-linear variables — like temperature — may give rise to resonance phenomena for both low and high surface occupancies. Necessary conditions for resonance to occur are derived. The analysis of resonance phenomena is greatly simplified by the availability of explicit analytical expressions as can be derived from Carleman linearization. We will demonstrate the merits of Carleman linearization as compared to numerical integration.