, Volume 25, Issue 8, pp 1525–1532 | Cite as

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

  • Zhihong ZhangEmail author
  • Jiapei Zhang
  • Zhaogang Xu


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.


Irreversible thermodynamics Adsorption kinetics Free energy Dissipation rate 



This work was supported by Key Program of Beijing Natural Science Foundation of China (Grant No. 8171001) and National Natural Science Foundation of China (Grant No. 51678012).The financial support is gratefully acknowledged.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.The Key Laboratory of Urban Security and Disaster EngineeringMinistry of Education, Beijing University of TechnologyBeijingChina
  2. 2.China Electronics Engineering Design Institute CO., LTDBeijingChina

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