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A Non-equilibrium Adsorption Model Based on Irreversible Thermodynamics

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Book cover Proceedings of the 8th International Congress on Environmental Geotechnics Volume 1 (ICEG 2018)

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Abstract

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.

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References

  1. Ahmed MJ (2016) Application of agricultural based activated carbons by microwave and conventional activations for basic dye adsorption: review. J Environ Chem Eng 4(1):89–99

    Article  Google Scholar 

  2. Anastopoulos I, Bhatnagar A (2016) Adsorption of rare earth metals: a review of recent literature. J Mol Liq 221:954–962

    Article  Google Scholar 

  3. Bachmat Y, Bear J (1987) On the concept and size of a representative elementary volume (Rev). Springer, Netherlands

    Book  Google Scholar 

  4. Bennethum LS, Cushman JH (1996) Multiscale, hybrid mixture theory for swelling systems—I: balance laws. Int J Eng Sci 34:125–145

    Article  MathSciNet  Google Scholar 

  5. Etci Ö, Bektaş N, Öncel MS et al (2009) Single and binary adsorption of lead and cadmium ions from aqueous solution using the clay mineral beidellite. Environ Earth Sci 61:231–240

    Article  Google Scholar 

  6. Foo KY, Hameed BH (2010) Insights into the modeling of adsorption isotherm systems. Chem Eng J 156:2–10

    Article  Google Scholar 

  7. Genuchten MTV, Wierenga PJ (1976) Mass transfer studies in sorbing porous media I. Analytical solutions. Sci Soc Am J 40:473–480

    Article  Google Scholar 

  8. Gray WG, Miller CT (2008) Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 3. Single-fluid-phase flow. Adv Water Resour 31:577

    Article  Google Scholar 

  9. Groenevelt PH, Bolt GH (1969) Non-equilibrium thermodynamics of the soil-water system: review paper. J Hydrol 7:358–388

    Article  Google Scholar 

  10. Hassanizadeh M, Gray WG (1979) General conservation equations for multi-phase systems: 1. Averaging procedure. Adv Water Resour 2:131–144

    Article  Google Scholar 

  11. Hendricks DW (1972) Sorption in flow through porous media. Dev Soil Sci 2:384–392

    Google Scholar 

  12. Ho YS, Mckay G (1999) Pseudo-second order model for sorption processes. Process Biochem 34:451–465

    Article  Google Scholar 

  13. Lapidus L, Amundson NR (1952) Mathematics of adsorption in beds. VI. The effect of longitudinal diffusion in ion exchange and chromatographic columns. J Chem Phys 56:984–988

    Article  Google Scholar 

  14. Lu N (2016) Generalized soil water retention equation for adsorption and capillarity. J Geotech Geoenviron 142:04016051

    Article  Google Scholar 

  15. Pagonabarraga I, Rubí JM (1992) Derivation of the Langmuir adsorption equation from non-equilibrium thermodynamics. Phys A 188:553–567

    Article  Google Scholar 

  16. Qiu H, Lv L, Pan BC et al (2009) Critical review in adsorption kinetic models. J Zhejiang Univ-Sci A 10:716–724

    Article  Google Scholar 

  17. Santamariaholek I, Grzywna ZJ, Rubi JM (2012) A non-equilibrium thermodynamics model for combined adsorption and diffusion processes in micro- and nanopores. J Non-equil Thermodyn 37:273–290

    MATH  Google Scholar 

  18. Winslow CEA, Walker HH, Sutermeister M (1932) The influence of aeration and of sodium chloride upon the growth curve of bacteria in various media. J Bacteriol 24:185

    Google Scholar 

  19. Ziegler H, Wehrli C (1987) The derivation of constitutive relations from the free energy and the dissipation function. Adv Appl Mech 25:183–238

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

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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Authors and Affiliations

  1. The Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing, 100124, China

    Zhihong Zhang, Wenlong Qin & Jiapei Zhang

  2. China Electronics Engineering Design Institute Co., Ltd., Beijing, 100142, China

    Zhaogang Xu

  3. Beijing Municipal Construction Co., Ltd., Beijing, 100048, People’s Republic of China

    Fei Guo

Authors
  1. Zhihong Zhang
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  2. Wenlong Qin
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  3. Jiapei Zhang
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  4. Zhaogang Xu
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  5. Fei Guo
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Corresponding author

Correspondence to Zhihong Zhang .

Editor information

Editors and Affiliations

  1. MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China

    Liangtong Zhan

  2. MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China

    Yunmin Chen

  3. Department of Civil Engineering, Monash University, Clayton, VIC, Australia

    Abdelmalek Bouazza

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Zhang, Z., Qin, W., Zhang, J., Xu, Z., Guo, F. (2019). A Non-equilibrium Adsorption Model Based on Irreversible Thermodynamics. In: Zhan, L., Chen, Y., Bouazza, A. (eds) Proceedings of the 8th International Congress on Environmental Geotechnics Volume 1. ICEG 2018. Environmental Science and Engineering(). Springer, Singapore. https://doi.org/10.1007/978-981-13-2221-1_56

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