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Adsorption Kinetics: Classical, Fractal, or Fractional?

Evangelos Bakalis1, Francesco Zerbetto1

  • 1Dipartimento di Chimica "G. Ciamician", Università di Bologna, V. P. Gobetti 85, 40129 Bologna, Italy.

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Summary
This summary is machine-generated.

This study introduces fractional calculus to model adsorption kinetics, offering a new framework beyond classical and fractal models. This approach captures memory effects, providing a more nuanced understanding of adsorption processes.

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Area of Science:

  • Chemical Engineering
  • Physical Chemistry
  • Materials Science

Background:

  • Adsorption kinetics are often described by pseudo-order models based on concentration-dependent rates.
  • Classical and fractal models have limitations in describing adsorption kinetics under non-ideal conditions.

Purpose of the Study:

  • To introduce fractional calculus for modeling adsorption kinetics.
  • To present solutions for pseudo-first-order fractional kinetics and recursive relations for higher orders.
  • To discuss the application of these fractional models in adsorption processes.

Main Methods:

  • Phenomenological pseudo-order models were reviewed.
  • Fractional calculus was applied to adsorption kinetics, introducing fractional-order derivatives.
  • Analytical and numerical methods were used to derive and present model solutions.

Main Results:

  • Fractional modeling captures memory effects absent in fractal models.
  • Detailed expressions for pseudo-first-order fractional kinetics were derived.
  • Recursive relations for higher-order fractional kinetics amenable to numerical treatment were provided.

Conclusions:

  • Fractional calculus offers a powerful framework for describing adsorption kinetics, especially when memory effects are present.
  • The proposed fractional models provide a more comprehensive understanding of adsorption processes compared to classical and fractal approaches.
  • This work opens new avenues for research in adsorption science and engineering.