Diffusion Influenced Adsorption Kinetics

Area of Science:

• Physical Chemistry
• Chemical Engineering
• Surface Science

Background:

• Adsorption kinetics are crucial in chemical processes.
• Surface concentration is influenced by solute diffusion and Langmuir-Hinshelwood adsorption.
• This leads to a nonlinear integro-differential equation governing surface coverage.

Purpose of the Study:

• To solve the nonlinear integro-differential equation for surface coverage.
• To develop analytical expressions for the bounds of numerical results.
• To investigate the effects of dispersive diffusion and molecular rearrangement.

Main Methods:

• Utilized the Grünwald-Letnikov formula for fractional kinetics.
• Solved the nonlinear integro-differential equation numerically.
• Derived analytical upper and lower bounds for surface coverage.

Main Results:

• Obtained analytical bounds that closely approximate numerical results in diffusion- and reaction-controlled limits.
• Validated analytical expressions for the diffusion-controlled limit.
• Extended findings to include dispersive diffusion and molecular rearrangement effects.

Conclusions:

• The Grünwald-Letnikov method effectively solves complex adsorption kinetics.
• Analytical bounds provide valuable approximations for surface coverage.
• Dispersive diffusion and molecular rearrangement significantly impact adsorption processes.