Extended linear driving-force approximation for intraparticle diffusion rate including short times

An extended linear driving-force (LDF) approximation for the intraparticle diffusion rate is derived based on a cubic intraparticle concentration profile. It is shown that a cubic concentration profile with a time-dependent coefficient (A₃) for the cubic term can lead to the exact solution for the intraparticle diffusion rate. The extended LDF approximation is valid for both long and short times upon step changes. It has been demonstrated to be useful for both single-step changes and cyclic adsorption-desorption processes. It is applicable to cyclic processes involving mixed dimensionless times (θ), i.e. long θ for the fast-diffusing component and short θ for the slow-diffusing component. From the extended LDF approximation, intraparticle concentration profiles during a cyclic process can be calculated and an insight can be gained on the dynamic changes during the process. Experimental data for adsorption and cyclic adsorption-desorption of CO₂, N₂ and CH₄ in molecular sieve carbon are gathered and used to demonstrate the application of the extended LDF approximation.