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.