Reaction-Diffusion Systems: Self-Balancing Diffusion and the Use of the Extent of Reaction as a Descriptor of Reaction Kinetics

Self-balancing diffusion is a theoretical concept that restricts the introduction of extents of reactions. This concept is analyzed in detail for general mass- and molar-based balances of reaction-diffusion mixtures, in relation to non-self-balancing cases, and with respect to its practical consequences. Self-balancing is a mathematical restriction on the divergences of diffusion fluxes. Fulfilling this condition enables the proper introduction of the extents of (independent) reactions that reduce the number of independent variables in thermodynamic descriptions. A note on a recent generalization of the concept of reaction and diffusion extents is also included. Even in the case of self-balancing diffusion, such extents do not directly replace reaction rates. Concentration changes caused by reactions (not by diffusion) are properly described by rates of independent reactions, which are instantaneous descriptors. If an overall descriptor is needed, the traditional extents of reactions can be used, bearing in mind that they include diffusion-caused changes. On the other hand, rates of independent reactions integrated with respect to time provide another overall, but reaction-only-related descriptor.