Environmental Science and Pollution Research

, Volume 25, Issue 10, pp 9797–9805 | Cite as

Estimation of oxygen effective diffusion coefficient in a non-steady-state biofilm based on response time

  • Jian-Hui Wang
  • Hai-Yan Li
  • You-Peng ChenEmail author
  • Shao-Yang Liu
  • Peng Yan
  • Yu Shen
  • Jin-Song GuoEmail author
  • Fang Fang
Research Article


In wastewater treatment, oxygen effective diffusion coefficient (D eff ) is a key parameter in the study of oxygen diffusion-reaction process and mechanism in biofilms. Almost all the reported methods for estimating the D eff rely on other biokinetic parameters, such as substrate consumption rate and reaction rate constant. Then, the estimation was complex. In this study, a method independent of other biokinetic parameters was proposed for estimating the dissolved oxygen (DO) D eff in biofilms. It was based on the dynamic DO microdistribution in a non-steady-state inactive biofilm, which was measured by the oxygen transfer modeling device (OTMD) combining with an oxygen microelectrode system. A pure DO diffusion model was employed, and the expression of the DO D eff was obtained by applying the analytical solution of the model to a selected critical DO concentration. DO D eff in the biofilm from the bioreactor was calculated as (1.054 ± 0.041) × 10−9 m2/s, and it was in the same order of magnitude with the reported results. Therefore, the method proposed in this study was effective and feasible. Without measurement of any other biokinetic parameters, this method was convenient and will benefit the study of oxygen transport-reaction process in biofilms and other biofouling deposits.

Graphical abstract


Oxygen microelectrode Wastewater treatment Dynamic oxygen profiles Diffusion distance Response time Dynamic oxygen microdistribution 



The oxygen concentration in biofilms


The saturated oxygen concentration in the experimental solution

C(t, z)

The DO concentration at position z and time t (ML–3)


Dissolved oxygen


The effective diffusion coefficient (L2T–1)


The error-function complement

Jx, Jy, and Jz

The components of the mass flux J (ML–2T–1) along the coordinates


The oxygen uptake rate (ML3T–1)

r(t, z)

The oxygen uptake rate at z site and t time (ML–3)


Time (T)


Rotating biological contactor


The distance from the surface of biofilms (L)


Funding information

The authors gratefully acknowledge the financial support of the Chongqing Science and Technology Commission (cstc2014yykfC20001, cstc2015shms-ztzx20001) and the National Key Project of China (2015ZX07103-007).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Jian-Hui Wang
    • 1
  • Hai-Yan Li
    • 1
  • You-Peng Chen
    • 1
    • 2
    Email author
  • Shao-Yang Liu
    • 3
  • Peng Yan
    • 1
  • Yu Shen
    • 4
  • Jin-Song Guo
    • 1
    • 2
    Email author
  • Fang Fang
    • 1
  1. 1.Key Laboratory of the Three Gorges Reservoir Region’s Eco-Environments of MOEChongqing UniversityChongqingChina
  2. 2.Key Laboratory of Reservoir Aquatic Environment of CAS, Chongqing Institute of Green and Intelligent TechnologyChinese Academy of SciencesChongqingChina
  3. 3.Department of Chemistry and PhysicsTroy UniversityTroyUSA
  4. 4.National Base of International Science and Technology Cooperation for Intelligent Manufacturing ServiceChongqing Technology and Business UniversityChongqingChina

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