Adsorption fixed beds modeling revisited: Generalized solutions for S-shaped isotherms

Activated ZnCl2 biochar and humic acid as additives in monoammonium phosphate fertilizer: Physicochemical characterization and agronomic effectiveness

Activated zinc biochar (ZnBC) and humic acid (HA) were used as coating agents in a soluble monoammonium phosphate (MAP) to modify phosphorus (P) use efficiency by altering adsorption/desorption kinetics between the granule region and the soil. The coated treatments MAPZnBC and MAPHA were compared with MAP through P diffusivity, kinetics, and agronomic evaluation. Eucalyptus sawdust was used as biomass for biochar synthesis, and a pre-pyrolysis treatment with zinc chloride (ZnCl₂) was applied. The P diffusivity was evaluated in the fertosphere zone. Adsorption and desorption potential of the ZnBC compared with control biochar (BC) was evaluated separately. Desorption kinetics of P from soil was assessed after incubation with MAPZnBC and MAPHA. The shoot dry matter yield (SDM), P uptake, and P use efficiency (PUE) were evaluated with a pot experiment in a clay Oxisol sown with maize and soybeans as successive plant trials, under glasshouse conditions. Surface area values of 940 and 305 m² g^-1 combined with adsorption capacities of 106 and 53 mg P g^-1 for ZnBC and BC, respectively, confirm the increased capacity of activated biochar to adsorb P. Both MAPZnBC and MAPHA decreased P diffusivity compared to MAP after 20 days of incubation. Moreover, MAPZnBC and MAPHA presented 20% and 34% more water-soluble phosphorus recovery. MAPZnBC expressed an increase in SDM while MAPHA highlighted P uptake and PUE compared with MAP. Both kinetic studies and agronomic evaluations showed that ZnBC and HA are suitable as coatings for phosphate fertilizers in terms of increasing P efficiency in the fertosphere on high P-fixing soils.

A Fractal-Based Correlation for Time-Dependent Surface Diffusivity in Porous Adsorbents

Fluid–solid adsorption processes are mostly governed by the adsorbate transport in the solid phase and surface diffusion is often the limiting step of the overall process in microporous materials such as zeolites. This work starts from a concise review of concepts and models for surface transport and variable surface diffusivity. It emerges that the phenomenon of hindered surface diffusion for monolayer adsorption, which is common in zeolites, and models able to fit a non-monotonic trend of surface diffusivity against adsorbate solid phase concentration, have received limited attention. This work contributes to the literature of hindered diffusion by formulating a time-dependent equation for surface diffusivity based on fractal dynamics concepts. The proposed equation takes into account the contributions of both fractal-like diffusion (a time-decreasing term) and hopping diffusion (a time-increasing term). The equation is discussed and numerically analyzed to testify its ability to reproduce the possible different patterns of surface diffusivity vs. time.

Variable diffusivity homogeneous surface diffusion model and analysis of merits and fallacies of simplified adsorption kinetics equations

Adsorption and ion exchange phenomena are encountered in several separation processes, which in turn, are of vital importance across various industries. Although the literature on adsorption kinetics modeling is rich, the majority of the models employed are empirical, based on chemical reaction kinetics or oversimplified versions of diffusion models. In this paper, the fifteen most popular simplified adsorption kinetics equations are presented and discussed. A new versatile variable-diffusivity two-phase homogeneous diffusion model is presented and used to evaluate the analytical adsorption models. Aspects of ion exchange kinetics are also addressed.