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Mathematical modelling and simulation of adsorption processes at spherical microparticles
François G Chevallier1, Biljana Sljukić, Gregory G Wildgoose
1Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford, OX1 3QZ, United Kingdom.
Summary
A new model for microparticle adsorption reveals transient diffusion is governed by adsorption rate and saturation parameters. This work provides analytical tools to study mass transport and extract adsorption constants.
Area of Science:
- Physical Chemistry
- Chemical Engineering
- Materials Science
Background:
- Adsorption processes at microparticles are crucial in various chemical and environmental applications.
- Understanding mass transport dynamics, including diffusion and convection, is key to optimizing these processes.
- Existing models often simplify complex transient conditions.
Purpose of the Study:
- To develop and solve a numerical model for adsorption onto spherical microparticles under transient diffusion.
- To derive analytical models for steady-state mass transport conditions.
- To apply these models to experimental data for copper ion uptake and determine adsorption rate constants.
Main Methods:
- Numerical simulation of a transient diffusion adsorption model.
- Derivation of analytical models for steady-state diffusion and diffusion/convection.
- Utilizing empirical relationships for mass transfer coefficient (kc) calculation.
- Analysis of experimental Cu(II) uptake data.
Main Results:
- The transient adsorption model is controlled by two dimensionless parameters: adsorption rate constant (ka') and saturation parameter (beta).
- Analytical models were successfully derived for both diffusion-only and coupled diffusion/convection scenarios.
- A minimum adsorption rate constant of approximately 10(-4) cm s(-1) was determined for Cu(II) uptake by modified glassy carbon.
Conclusions:
- The developed models provide robust mathematical tools for analyzing adsorption kinetics.
- Transient and steady-state conditions offer different insights into the adsorption process.
- The study successfully quantified adsorption parameters for a specific material system, contributing to material design and process optimization.