Uniformly Coupled Kinetics

We have thus far considered systems in which the disappearance of a reactant depends only on the concentration of that reactant. To consider the interactions between reactants, Astarita and Ocone proposed a class of 

w is also expanded as w k) wjc as 0 ( + y 0). For Langmuir-Hinshelwood reactions, competitive adsorption should become increasingly unimportant as time increases, thus degenerating Ra(C) to that for first-order reactions regardless of reactor type. Indeed, Ra(C) C for a PFR at large t with = 1 + 1/y For a CSTR, Ra(C) degenerates to the three cases for first-order kinetics discussed earlier. For bimolecular power-law kinetics in the PFR, = n y + - Y ly In particular, if the feed 

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Tertiary distributions apply when Laplace s equation is replaced by a series of n equations of the form (5.59) coupled with electroneutrality (5.62) where n represents the number of ionic species in the system. Thus, tertiary distributions relax the assumption that concentrations are uniform. Ohmic, kinetic, and mass-transfer resistances all play a role. 

A different approach to the estimation of the overall effectiveness factor in porous catalysts was recently presented by Ho et al. (1994). These authors analyze the case of parallel bimolecular reactions, a case that is in general not one of uniform kinetics. Rather than trying to solve the coupled set of differential equations, Ho et al. chose to search directly for upper and lower bounds to the overall effectiveness factor, which are found by reducing the problem to that of finding the effectiveness factor for a single second-order reaction. The bounds can be es-... 

Chemical oscillators are described on the basis of nonlinear dynamics, in that the underlying kinetic equations under steady-state conditions are nonlinear. If one assumes that the spatial distribution of the reaction species is uniform, then these variables will only depend on time, and mathematical description in the mean field approximation for the concentration variables c,- is achieved by a set of coupled (nonlinear) ordinary differential equations (ODEs). This will be the approach applied in this chapter. 

For kinetic schemes that like the Oregonator model and pure activator-inhibitor schemes in general have /21 > 0, a stationary instability can occur only if c and F have opposite signs, i.e., if the coupling is inhibitory. The uniform steady state of an array of photochemically coupled Oregonator undergoes a stationary instability at... 

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