On the use of transfer and dispersion coefficient concepts in low-dimensional diffusion–convection-reaction models

The two most important concepts in transport phenomena in the past century are that of transfer and dispersion coefficient. While both concepts reduce the local degrees of freedom and provide a coarse-grained low-dimensional description of the transport process at the macroscale, their physical interpretations and mathematical descriptions differ. The transfer coefficient concept uses two concentration or temperature modes and upscales the microscale molecular effects as an exchange between the local and global scales, leading to hyperbolic models and Cauchy (initial value) problems. The dispersion coefficient concept uses a single mode and incorporates the microscale effects as an effective diffusion or dispersion term in the macroscale transport equation and leads to parabolic models and requires additional boundary conditions or physical constraints. We examine here the application of these concepts for reacting systems and provide some guidelines for their proper use in the low-dimensional description of reacting as well as non-reacting systems.