A D-type adsorption kinetic model for single system based on irreversible thermodynamics

The adsorption process is a highly efficient and widely applied fundamental technique in the field of Geo-environmental engineering. Most existing adsorption models are empirical or semi-empirical and lack a consistent and unified scientific theoretical basis. In this work, a new adsorption kinetic model with dispersion-type (D-type) has been proposed within the framework of irreversible thermodynamics for investigating the adsorption behavior of a single ionic species onto a solid adsorbent. Based on Ziegler’s maximal rate of dissipation, an expression for mass exchange rate was determined after a detailed theoretical deviation by defining the thermodynamic force and thermodynamic flow; and by formulating two dispersion-type free energy functions and a dispersion-type dissipation rate density function. The mass exchange rate expression was introduced into the mass balance equation as further validation of the D-type adsorption kinetic model for a single system. Comparing the adsorption process predicted by the presented model with the tested adsorption processes of Pb²⁺ and Cd²⁺ onto beidellite and Pb²⁺ on bentonite, the results reveal good agreement with experimental data. The D-type adsorption kinetic model could provide a correct description of the kinetics of adsorption process for single ionic species onto solid adsorbent.