Combined reaction and diffusion across the interface in reactive nonuniform liquid systems

Abstract

A recently introduced theoretical framework is generalized to multicomponent reactive nonuniform systems. The modified and generalized Cahn-Hilliard equation is combined with a chemical kinetics model. Kinetic rate equations, which are formulated with activities rather than concentrations, are combined with non-Fickian diffusion driven by gradients in chemical potential. Based on the incompressible density gradient theory, which provides an expression for the Gibbs energy of a nonuniform system, a generalized method is developed to model the combined reaction and diffusion associated with reactive liquid-liquid systems. A set of partial differential equations describing the temporal evolution of the mole fractions of all the involved components in the bulk phases and the spatial and temporal evolution of the mole fractions in the interface has been derived. The obtained equations were used to investigate the dynamics of the interfacial properties of a ternary mixture with a simple chemical reaction. Special attention is given to reacting mixtures with reaction rates that are much smaller than diffusion rates. In particular, it was found that the mixture will remain in phase equilibrium upon reaction and that the interfacial chemical reaction will not affect the dynamics of the overall system, the latter being only affected by the bulk phase kinetics.