Modeling and analysis of the dynamic behavior of mechanisms that result in the development of inner radial humps in the concentration of a single adsorbate in the adsorbed phase of porous adsorbent particles observed in confocal scanning laser microscopy

A theoretical model for adsorption of a single charged adsorbate that accounts for the presence of an electrical double layer in the pores of adsorbent particles is constructed and solved. The dynamic behavior of the mechanisms of the model can result in the development of inner radial humps (concentration rings) in the concentration of a single charged analyte (adsorbate) in the adsorbed phase of porous adsorbent particles. The results of the present work demonstrate the implication of the concept regarding the effect of the presence of an electrical double layer in the pores of adsorbent particles and the induced interactions between the electrostatic potential distribution and the mechanisms of mass transport of the species by diffusion, electrophoretic migration, and adsorption. Furthermore, the mechanisms of the model could explain qualitatively the development of the concentration ring (hump) observed in confocal scanning laser microscopy experiments.