The Kinetic Parameters Evaluation for the Adsorption Processes at “Liquid–Solid” Interface

Abstract

The kinetic parameters of the adsorption process at “liquid–solid” interface have been evaluated through the sets of time-based experiments of the Cr(III) adsorption under varying temperature, initial metal concentration, and carbon loading for two sets of the commercially available activated carbons and their post-oxidized forms with different texture and surface functionality.

Several kinetic models, such as the pseudo-first-order, pseudo-second-order, chemisorptions kinetics, external and intra-particle mass transfer diffusion models were applied to follow the adsorption process. Kinetic parameters such as the rate constants, equilibrium adsorption capacities, and related correlation coefficients for each kinetic model were calculated and discussed. The energy of activation E _a was determined using the Arrhenius equation for the systems with different carbon loading.

Additionally, the Systems Dynamics modeling approach (derivatives in order to time) was applied to investigate the dynamic behavior of the adsorption process for the “liquid–solid interface” systems aimed at process control. Based on the analysis provided, the studied systems were considered as Distributed Parameter Systems and the heterogeneous models were proposed via partial differential equations for both batch and dynamic modes adsorption taking into account external and intra-particle mass transfer diffusions.

It was concluded that at “liquid–solid” interface for the heavy metal ions adsorption on activated carbons (a) both the adsorption diffusion and chemisorptions reaction models should be considered for the kinetic parameters evaluation and (b) that intra-particle mass transfer diffusion of the metals ions form liquid phase into microporous carbon structure is the rate limiting step for the overall adsorption process.