Skip to main content

Wavelet Method to Film–Pore Diffusion Model for Methylene Blue Adsorption onto Plant Leaf Powders

  • Chapter
  • First Online:
Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

  • 1807 Accesses

Abstract

In this chapter, we have developed an accurate and efficient Haar wavelet method (HWM) to solve film–pore diffusion model. Film–pore diffusion model is widely used to determine study the kinetics of adsorption systems. To the best of our knowledge, until now rigorous wavelet solution has been not reported for solving film–pore diffusion model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 19.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 29.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 29.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. V. Ponnusami, K.S. Rajan, S.N. Srivastava, Application of film-pore diffusion model, for methylene blue adsorption onto plant leaf powders. Chem. Eng. J. 163(3), 236–242 (2010)

    Article  Google Scholar 

  2. V. Ponnusami, V. Gunasekar, S.N. Srivastava, Kinetics of methylene blue removal from aqueous solution using gulmohar (Delonix regia) plant leaf powder: Multivariate regression analysis. J. Hazard. Mater. 169, 119–127 (2009)

    Article  Google Scholar 

  3. V. Ponnusami, V. Krithika, R. Madhuram, S.N. Srivastava, Biosorption of reactive dye using acid treated rice husk: Factorial design analysis. J. Hazard. Mater. 142, 397–403 (2007)

    Article  Google Scholar 

  4. C.W. Cheung, C.K. Chan, J.F. Porter, G. McKay, Film-pore diffusion control for the batch sorption of cadmium ions from effluent onto bone char. J. Colloid Interface Sci. 234(2), 328–336 (2001)

    Article  Google Scholar 

  5. B.H. Hameed, Removal of cationic dye from aqueous solution using jackfruit peel as non-conventional low-cost adsorbent. J. Hazard. Mater. 162(1), 344–350 (2009)

    Article  Google Scholar 

  6. B.H. Hameed, R.R. Krishni, S.A. Sata, A novel agricultural waste adsorbent for the removal of cationic dye from aqueous solutions. J. Hazard. Mater. 162(1), 305–311 (2009)

    Article  Google Scholar 

  7. N. Gupta, A.K. Kushwaha, M.C. Chattopadhyaya, Adsorption studies of cationic dyes onto Ashoka (Saraca asoca) leaf powder. J. Taiwan Inst. Chem. Eng. 43(4), 604–613 (2012)

    Article  Google Scholar 

  8. B.H. Hameed, D.K. Mahmoud, A.L. Ahmad, Sorption of basic dye from aqueous solution by pomelo (Citrus grandis) peel in a batch system. Colloids Surf. A Physicochem. Eng. Aspects 316(1–3), 78–84 (2008)

    Article  Google Scholar 

  9. A. Çelekli, G. Ilgün, H. Bozkurt, Sorption equilibrium, kinetic, thermodynamic, and desorption studies of reactive red 120 on Chara contraria. Chem. Eng. J. 191, 228–235 (2012)

    Article  Google Scholar 

  10. S. Kumar, V. Gunasekar, V. Ponnusami, Removal of methylene blue from aqueous effluent using fixed bed of groundnut shell powder. J. Chem. (in press). https://doi.org/10.1155/2013/259819

    Google Scholar 

  11. B.H. Hameed, M.I. El-Khaiary, Sorption kinetics and isotherm studies of a cationic dye using agricultural waste: broad bean peels. J. Hazard. Mater. 154(1–3), 639–648 (2008)

    Article  Google Scholar 

  12. C.F. Chen, C.H. Hsiao, Haar wavelet method for solving lumped and distributed-parameter systems. IEEE Proc. Pt. D 144(1), 87–94 (1997) 123 J Math Chem (2012) 50:2775–2785 2785

    Article  MathSciNet  Google Scholar 

  13. C.H. Hsiao, State analysis of linear time delayed systems via Haar wavelets. Math. Comput. Simul. 44(5), 457–470 (1997)

    Article  MathSciNet  Google Scholar 

  14. Z. Shi, T. Liu, B. Gao, Haar wavelet method for solving wave equation. in International Conference on Computer Application and System Modeling (ICCASM 2010), IEEE Proceeding. (2010)

    Google Scholar 

  15. F.I. Haq, I. Aziz, S.U. Islam, A Haar wavelets based numerical method for eight-order boundary problems. Int. J. Math. Comput. Sci. 6(1), 25–31 (2010)

    Google Scholar 

  16. J.L. Wu, A wavelet operational method for solving fractional partial differential equations numerically. Appl. Math. Comput. 214(1), 31–40 (2009)

    MathSciNet  MATH  Google Scholar 

  17. Z. Shi, Y.-Y. Cao, Q.-J. Chen, Solving 2D and 3D Poisson equations and biharmonic equations by the Haar wavelet method. Appl. Math. Model. 36(11), 5143–5161 (2012)

    Article  MathSciNet  Google Scholar 

  18. W. Geng, Y. Chen, Y. Li, D. Wang, Wavelet method for nonlinear partial differential equations of fractional order. Comput. Inf. Sci. 4(5), 28–35 (2011)

    Google Scholar 

  19. U. Lepik, Numerical solution of evolution equations by the Haar wavelet method. Appl. Math. Comput. 185, 695–704 (2007)

    MathSciNet  MATH  Google Scholar 

  20. U. Lepik, Numerical solution of differential equations using Haar wavelets. Math. Comput. Simul. 68, 127–143 (2005)

    Article  MathSciNet  Google Scholar 

  21. U. Lepik, Application of the Haar wavelet transform to solving integral and differential equations. Proc. Estonian Acad. Sci. Phys. Math. 56(1), 28–46 (2007)

    MathSciNet  MATH  Google Scholar 

  22. G. Hariharan, K. Kannan, Haar wavelet method for solving some nonlinear parabolic equations. J. Math. Chem. 48(4), 1044–1061 (2010)

    Article  MathSciNet  Google Scholar 

  23. G. Hariharan, K. Kannan, A comparative study of a Haar Wavelet method and a restrictive Taylor’s series method for solving convection-diffusion equations. Int. J. Comput. Methods Eng. Sci. Mech. 11(4), 173–184 (2010)

    Article  MathSciNet  Google Scholar 

  24. G. Hariharan, Haar wavelet method for solving Sine-Gordon and Klein-Gordon equations. Int. J. Nonlinear Sci. 9(2), 1–10 (2010)

    Google Scholar 

  25. G. Hariharan, K. Kannan, Haar wavelet method for solving fitz Hugh-Nagumo equation. Int. J. Math. Stat. Sci. 2, 2 (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. Hariharan .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Hariharan, G. (2019). Wavelet Method to Film–Pore Diffusion Model for Methylene Blue Adsorption onto Plant Leaf Powders. In: Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-32-9960-3_4

Download citation

Publish with us

Policies and ethics