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Mathematical Problems in Engineering
Volume 2015, Article ID 512404, 10 pages
http://dx.doi.org/10.1155/2015/512404
Research Article

Dynamical Analysis of a Continuous Stirred-Tank Reactor with the Formation of Biofilms for Wastewater Treatment

1Departamento de Matemáticas y Estadística, Universidad Nacional de Colombia, Sede Manizales, Manizales, Colombia
2Departamento de Matemáticas y Estadística, Universidad del Tolima, Ibagué, Colombia

Received 2 February 2015; Revised 7 April 2015; Accepted 7 April 2015

Academic Editor: Seungik Baek

Copyright © 2015 Karen López Buriticá et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Ghaniyari-Benis, R. Borja, S. A. Monemian, and V. Goodarzi, “Anaerobic treatment of synthetic medium-strength wastewater using a multistage biofilm reactor,” Bioresource Technology, vol. 100, no. 5, pp. 1740–1745, 2009. View at Publisher · View at Google Scholar · View at Scopus
  2. L. M. Chen and L. H. Chai, “A theoretical analysis on self-organized formation of microbial biofilms,” Physica A: Statistical Mechanics and its Applications, vol. 370, no. 2, pp. 793–807, 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. V. Lazarova and J. Manem, “Biofilm characterization and activity analysis in water and wastewater treatment,” Water Research, vol. 29, no. 10, pp. 2227–2245, 1995. View at Publisher · View at Google Scholar
  4. C. Nicolella, M. C. M. van Loosdrecht, and J. J. Heijnen, “Wastewater treatment with particulate biofilm reactors,” Journal of Biotechnology, vol. 80, no. 1, pp. 1–33, 2000. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Rodgers, X.-M. Zhan, and J. Prendergast, “Wastewater treatment using a vertically moving biofilm system followed by a sand filter,” Process Biochemistry, vol. 40, no. 9, pp. 3132–3136, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. T. Leiknes and H. Ødegaard, “The development of a biofilm membrane bioreactor,” Desalination, vol. 202, no. 1–3, pp. 135–143, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. U. Jeppsson, Modelling Aspects of Wastewater Treatment Processes. Reprocentralen, Lund University, 1996.
  8. B. Capdeville and K. M. Nguyen, “Kinetics and modelling of aerobic and anaerobic film growth,” Water Science and Technology, vol. 22, no. 1-2, pp. 149–170, 1990. View at Google Scholar · View at Scopus
  9. J. W. T. Wimpenny and R. Colasanti, “A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models,” FEMS Microbiology Ecology, vol. 22, no. 1, pp. 1–16, 1997. View at Publisher · View at Google Scholar · View at Scopus
  10. C. Picioreanu, M. C. M. Van Loosdrecht, and J. J. Heijnen, “Discrete-differential modelling of biofilm structure,” Water Science and Technology, vol. 39, no. 7, pp. 115–122, 1999. View at Publisher · View at Google Scholar · View at Scopus
  11. G. Pizarro, D. Griffeath, and D. R. Noguera, “Quantitative cellular automaton model for biofilms,” Journal of Environmental Engineering, vol. 127, no. 9, pp. 782–789, 2001. View at Publisher · View at Google Scholar · View at Scopus
  12. L.-M. Chen and L.-H. Chai, “Mathematical model and mechanisms for biofilm wastewater treatment systems,” World Journal of Microbiology & Biotechnology, vol. 21, no. 8-9, pp. 1455–1460, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. C. Nicolella, S. Chiarle, R. Di Felice, and M. Rovatti, “Mechanisms of biofilm detachment in fluidized bed reactors,” Water Science and Technology, vol. 36, no. 1, pp. 229–235, 1997. View at Publisher · View at Google Scholar · View at Scopus
  14. C. Dreszer, A. D. Wexler, S. Drusová et al., “In-situ biofilm characterization in membrane systems using Optical Coherence Tomography: formation, structure, detachment and impact of flux change,” Water Research, vol. 67, pp. 243–254, 2014. View at Publisher · View at Google Scholar
  15. M. Walter, A. Safari, A. Ivankovic, and E. Casey, “Detachment characteristics of a mixed culture biofilm using particle size analysis,” Chemical Engineering Journal, vol. 228, pp. 1140–1147, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. A. Mašić and H. J. Eberl, “Persistence in a single species CSTR model with suspended flocs and wall attached biofilms,” Bulletin of Mathematical Biology, vol. 74, no. 4, pp. 1001–1026, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. A. Hernández, Microbiologia Industrial, Las Fermentaciones, 2003.
  18. J. A. Aracil, F. G. Salas, and F. A. Gordillo, Notas del Curso ‘Análisis de Sistemas No Lineales’, Universidad de Sevilla, Seville, Spain, 2007.
  19. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer, New York, NY, USA, 2nd edition, 2000. View at MathSciNet
  20. Análisis de la Estabilidad Interna de los Sistemas No Lineales, UNR—Ingeniería, Cátedra D.S.F.
  21. H. K. Khalil, Nonlinear Systems, Prentice Hall, 3rd edition, 2000.
  22. G. B. Baca, Estudio de la DiNoamica No-lineal de un Servomecanismo Neumático de Posicionamiento, Universidad Nacional de Colombia Sede Manizales, 2011.
  23. L. Perko, Differential Equations and Dynamical Systems, Springer, 3rd edition, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  24. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, Redwood City, Calif, USA, 2nd edition, 1989. View at MathSciNet
  25. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, 2nd edition, 2000.
  26. T. S. Parker and L. O. Chua, Practical Numerical Algorithms for Chaotic Systems, Springer, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  27. V. M. Trejos, J. Fontalvo, and M. A. Gómez, “Descripción matemática y análisis de estabilidad de procesos fermentativos,” Dyna, vol. 76, pp. 111–121, 2009. View at Google Scholar
  28. L. A. Melo, Dinámica de un biorreactor con modelo de crecimiento de bacterias lineal por tramos [M.S. thesis], Universidad Nacional de Colombia Sede Manizales, Caldas, Colombia, 2011.
  29. O. P. Ward, Biotecnología de la fermentación, Acribia S.A., 1989.