On the theory of reactions in continuous mixtures

TLDR

A continuous mixture, described by concentration distributions, can sustain infinitely many reactions and is applicable to polymerization, cracking, and complex biological processes. The paper aims to establish the stoichiometry, thermodynamics, and kinetics of reactions in continuous mixtures and to outline methods for solving the resulting integro‑differential equations. The authors propose techniques for solving the integro‑differential equations and address parameter fitting to experimental data.

Abstract

A mixture with a very large number of components approaches the condition of a continuous mixture in which the components are not distinguished by a discrete index but by a continuous variable. Such a mixture can be described by distributions of concentration and is capable of sustaining an infinite number of reactions. Polymerization and cracking reactions can be treated in this way and there may be applications to the very complex processes of biology. The aim of this paper is to lay the foundations for the stoicheiometry, thermodynamics and kinetics of such reactions and to outline several techniques for solving the resulting integro-differential equations. Attention is also paid to the problem of fitting the parameters of such a model to experimental data.