Physical Consistency of Generalized Linear Driving Force Models for Adsorption in a Particle

The so-called (first-order) linear driving force (LDF) model for gas adsorption kinetics is frequently and successfully used for analysis and design of adsorptive processes because it is simple, analytical, and physically consistent. Yet, for certain operating conditions, such as cyclic adsorption and desorption, significant differences between the LDF model and the rigorous Fickian diffusion (FD) model can be found. In principle, increasing the order of the approximate LDF model can yield predictions closer to the FD model. As in the classical first-order LDF model, generalized LDF must be consistent with the physics of the FD model. This paper provides a minimal set of properties that generalized LDF models should meet in order to be physically consistent. This is done by showing that the FD model describes positive real dynamics, which are closely related to the thermodynamics of the adsorption-diffusion process. In this form, a generalized LDF model should inherit this property in order to guarantee that the main thermodynamic characteristics of the adsorption-diffusion dynamics will be retained to some extent.