Detailed numerical solution of pore volume and surface diffusion model in adsorption systems

In this work, the numerical solution of pore volume and surface diffusion model (PVSDM) was developed and presented in detail. The finite difference approximations method was employed to solve the partial differential equations of the diffusional model. The experimental adsorption of Malachite Green dye (MG) on bentonite clay was selected as case study. The equilibrium data were obtained from batch systems and, the Redlich-Peterson isotherm was suitable to represent the results. Due to non-linearity of the isotherm, the non-linear least squares technique was used to estimate the diffusional parameters. The Biot number has shown that the adsorption was simultaneously controlled by external mass transfer and intraparticle diffusion. Thus, both internal resistances (pore volume and surface) must be considered. The MG concentrations as a function of time decreases and the amount of MG mass adsorbed on bentonite clay as a function of the radial position increases until reaching equilibrium. The experimental concentration decay curve of MG was properly represented by PVDSM model. Further, the amount of MG mass adsorbed at higher radial positions was larger than at lower radial positions, within the PVSDM boundaries (particle boundaries), indicating that the method of finite difference approximations was appropriate for the numerical solution of PVSDM model. (C) 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.