Relaxation characteristics of the parallel adsorption mechanism

Let us now examine the behaviour of the solutions for the dynamic system (20) in time and analyze the system trajectories in the phase pattern. This analysis permits us to characterize peculiarities of the unsteady-state behaviour (in particular to establish whether the steady state is stable or unstable), to determine its type (focus, node, saddle, etc.) and to find attraction regions for stable steady states, singular lines, etc. 

For numerical studies [223] of system (20) corresponding to the three-step mechanism (8) its parameters were taken to be kx = k2 = l, k3 = 10, k = 0.01, and k 2 — 0.1. Values of PAz and PB were varied over a wide range. A sequence of phase portraits for reaction (8) with one or three steady 

Similar alterations in the phase portrait also take place with increasing PA,. The only difference is that at low PA, the unique steady state is charac- 

In several experiments, in particular the study by Temkin and co-workers [224] of the kinetics in ethylene oxidation, slow relaxations, i.e. the extremely slow achievement of a steady-state reaction rate, were found. As a rule, the existence of such slow relaxations is ascribed to some side reasons rather than to the purely kinetic ( proper ) factors. The terms proper and side were first introduced by Temkin [225], As usual, we classify as slow side processes variations in the chemical or phase composition of the surface under the effect of reaction media, catalyst deactivation, substance diffusion into its bulk, etc. These processes are usually considered to require significantly longer times to achieve a steady state compared with those characterizing the performance of chemical reactions. The above numerical experiment, however, shows that, when the system parameters attain their bifurcation values, the time to achieve a steady state, tr, sharply increases. 

This increase cannot be ascribed to the side reasons that have not been included into the reaction model. Similar increases of rr, namely long induction periods for the ignition and quenching of the reaction, were observed by Barelko et al. [5,42 44,46,69] in the oxidation of simple molecules 

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