Adsorption Kinetics: Classical, Fractal, or Fractional?

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.