Branched-pore model applied to the adsorption of basic dyes on carbon

The branched-pore adsorption model, expressed by an external mass transfer coefficient k_f, a solid diffusivity D_s, a lumped micropore diffusion rate parameter k_b, and the fraction of macropores f, describes kinetic data from initial contact of adsorbent-adsorbate to the long-term ( > 24 hours) adsorption stages with reasonable accuracy.In this work the model is applied for three basic dye systems, namely Basic Red 22, Basic Yellow 21 and Basic Blue 69, all on carbon. A single value of each parameter describes each dye system. The k_f values are 0.18 × 10⁻²±28%, 0.3 × 10⁻²±17% and 0.2 × 10⁻² ± 20% cm s⁻¹, the D_s values are 0.33 × 10⁻⁹ 21%, 0.72 × 10⁻⁹ ± 9% and 0.72 × 10⁻⁹ ± 9% cm² s⁻¹, the k_b values are 0.65 × 10⁻⁶ ± 7.7%, 1.8 × 10⁻⁶ 0.2 × 10⁻⁶ 1% s⁻¹, while the f values are 0.55 ± 9%, 0.60 ± 10 % and 0.18 ± 11%, each for Basic Red 22, Basic Yellow 21 and Basic Blue 69 respectively.The model is based on the internal structure of the carbon particle being divided into a macropore and a micropore region. The latter has an upper-bound capacity of 241, 245 and 656 mg g⁻¹ for Basic Red 22, Basic Yellow 21 and Basic Blue 69 respectively. A sensitivity analysis for each parameter has been carried out.