The behavior of distributed systems with complex reactions and diffusion in the regime of transport limitation

Abstract

The be havior of distributed systems with complex chemical reactions and diffusive transport is investigated in the regime of transport limitation. It is shown that, asymptotically with increasing size, the reaction rates and concentration gradients are negligible except in a surface layer of constant thickness. Due to a lack of symmetry in the constraints, the equilibrium state in distributed systems is not related to the extremization of a thermodynamic potential function. It is closely related, however, to the entropy production and flow. Upper bounds for the surface fluxes and effectiveness factors are derived for general complex reactions. These have theoretical interest but are not accurate enough for predictive purposes. A less general but more accurate estimating technique is also developed. Examples of two simultaneous second-order exothermic irreversible reactions and of two simultaneous isothermal, isomerization reactions with nonlinear kinetics are treated in detail.

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