A Non-equilibrium Adsorption Model Based on Irreversible Thermodynamics

  • Zhihong ZhangEmail author
  • Wenlong Qin
  • Jiapei Zhang
  • Zhaogang Xu
  • Fei Guo
Conference paper
Part of the Environmental Science and Engineering book series (ESE)


A non-equilibrium model for adsorption process of single ionic species onto solid adsorbent has been proposed within the framework of irreversible thermodynamics. Based on Ziegler’s principle of maximal rate of dissipation and combining mass balance equation of ionic species, a theoretical formulation of general description for non-equilibrium adsorption was obtained. Fatherly, the dispersion-type energy functions included two Helmholtz free energy and one dissipation rate density were constructed by complementary error function, which introduced into the general form of non-equilibrium model to achieve the specific form. The predicted results of the presented model were compared with the tested kinetics of adsorption processes of Pb2+ and Cd2+ onto Beidellite, which provided a better agreement with the experimental data.


Thermodynamics Non-equilibrium adsorption Free energy Dissipation rate 



This work were supported by Key Program of Beijing Natural Science Foundation of China (No. 8171001) and National Basic Research Program of China (973 Program) (No. 2014CB744702). The financial supports are gratefully acknowledged.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Zhihong Zhang
    • 1
    Email author
  • Wenlong Qin
    • 1
  • Jiapei Zhang
    • 1
  • Zhaogang Xu
    • 2
  • Fei Guo
    • 3
  1. 1.The Key Laboratory of Urban Security and Disaster Engineering, Ministry of EducationBeijing University of TechnologyBeijingChina
  2. 2.China Electronics Engineering Design Institute Co., Ltd.BeijingChina
  3. 3.Beijing Municipal Construction Co., Ltd.BeijingPeople’s Republic of China

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