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Wavelet method to film-pore diffusion model for methylene blue adsorption onto plant leaf powders

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Abstract

In this paper, we have developed an accurate and efficient Haar wavelet method 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. The use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, and computationally attractive. The power of the manageable method is confirmed. It is shown that film-pore diffusion model satisfactorily describes the kinetics of methylene blue adsorption onto three low-cost adsorbents, Gauva, teak and gulmohar plant leaf powders, used in this study.

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Abbreviations

As :

Total surface area of all the particles, m2dm−3

Bt:

Biot number (Bt =  k fdp/Deff), −

Ct :

Bulk concentration at time t, mg dm−3

Cs :

Surface concentration, mg dm−3

Co :

Initial bulk concentration, mg dm−3

dp :

Diameter of particle, m

Deff :

Internal effective diffusivity, m2 s−1

KL :

Langmuir adsorption constant, dm3mg−1

r:

Radial position in the particle, m

R:

Radius of the particle, m

qe :

Solid phase dye concentration at equilibrium, mg g−1

qi :

Solid phase dye concentration at grid i at time t, mg g−1

t:

Time, s or min

V:

Volume of solution, dm3

ε :

Particle porosity, –

ρ p :

Particle density, kg m−3

kf :

External film transfer coefficient, m s−1

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Authors and Affiliations

  1. Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur, 613 401, Tamilnadu, India

    G. Hariharan & R. Srikanth

  2. School of Chemical and Biotechnology, SASTRA University, Thanjavur, 613 401, Tamilnadu, India

    V. Ponnusami

Authors
  1. G. Hariharan
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  2. V. Ponnusami
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  3. R. Srikanth
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Correspondence to G. Hariharan.

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Hariharan, G., Ponnusami, V. & Srikanth, R. Wavelet method to film-pore diffusion model for methylene blue adsorption onto plant leaf powders. J Math Chem 50, 2775–2785 (2012). https://doi.org/10.1007/s10910-012-0063-1

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  • DOI: https://doi.org/10.1007/s10910-012-0063-1

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