For individual dye adsorption we can follow the Langmuir and Freundlich isotherm models.
In case of mixed dye adsorption (For example, methylene blue, rhodamine B and methyl orange dyes mixed together) suggest me some suitable models which could describe the adsorption of mixed dyes on the adsorbent.
For multi-dye adsorption, you can follow the modified multi-element Langmuir and Freundlich isotherm models or the modified multi-element Redlich-Peterson and Sips isotherm models. You can find these equations in our articles.
Article Evaluation of single and tri-element adsorption of Pb2+, Ni2...
Article Evaluation of adsorption processes of metal ions in multi-el...
The articles focus on the adsorption of metallic ions, however, these equations can also be applied to the study of dyes.
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