Document Type

Article

Source of Publication

Applied Mathematical Modelling

Publication Date

6-1-2024

Abstract

We develop a mathematical model for adsorption based on averaging the flow around, and diffusion inside, adsorbent particles in a column. The model involves three coupled partial differential equations for the contaminant concentration both in the carrier fluid and within the particle as well as the adsorption rate. The adsorption rate is modelled using the Sips equation, which is suitable for describing both physical and chemical adsorption mechanisms. Non-dimensionalisation is used to determine the controlling parameter groups as well as to determine negligible terms and so reduce the system complexity. The inclusion of intra-particle diffusion introduces new dimensionless parameters to those found in standard works, including a form of internal Damköhler number and a new characteristic time scale. We provide a numerical method for the full model and show how in certain situations a travelling wave approach can be utilized to find analytical solutions. The model is validated against published experimental data for the removal of Mercury(II) and CO2. The results show excellent agreement with measurements of column outlet contaminant concentration and provide insights into the underlying chemical reactions.

ISSN

0307-904X

Publisher

Elsevier BV

Volume

130

First Page

827

Last Page

851

Disciplines

Chemical Engineering

Keywords

Adsorption, Advection-diffusion, Asymptotics, Contaminant removal, Mathematical analysis

Scopus ID

85189748209

Creative Commons License

Creative Commons Attribution-NonCommercial 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

Indexed in Scopus

yes

Open Access

yes

Open Access Type

Hybrid: This publication is openly available in a subscription-based journal/series

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