Generalization and Evaluation of the Analytical Solution of Intraparticle Diffusion Models in Finite Batch Adsorption

In this paper, a detailed description of particle adsorption/diffusion model in batch systems is presented. The phenomenological equations are based on a mechanism combining mass transfer by convection from bulk phase to particle surface, intraparticle mass diffusion and equilibrium adsorption processes. The change of bulk and particle concentration is modeled through differential mass balance equations, leading to a system of one ordinary differential equation and one partial differential equation. When adsorption equilibrium follows a linear relationship, this system of equations can be solved by the Laplace transform method. The purpose of this paper is the development of a generalized analytical solution, that is rewritten specifically for each of the traditional particle shapes: slab, cylinder, and sphere. Finally, this analytical solution is evaluated through several simulations in different batch conditions and compared to simulated experimental data, showing the capability of this analytical solution to predict batch adsorption processes when adsorbate concentration is low. This result clearly indicates the feasibility of applying the analytical solution presented in this paper, which is based on phenomenological concepts, to describe the adsorption kinetics of processes, when the linear isotherm can be considered adequate to represent the adsorption equilibrium.