Phenomenological-based model of direct blue 2 adsorption on corncob in a fixed-bed

This work presents a phenomenologically based semi-physical model (PBSM) for the liquid-solid adsorption process, which has been experimentally validated. Two modes of operation of adsorption of direct blue 2 dye (DB2) on corn cobs in a fixed bed are discussed by applying the PBSM. The first mode of operation is the typical continuous liquid flow, whereas the second is a semicontinuous mode with the recirculation of liquid leaving the column. These modes of operation were used to illustrate different ways in which the system reaches equilibrium conditions. The equilibrium distribution curve (EDC) for low DB2 concentration was reached with the best fit using the Langmuir-Freundlich model (R2=0.998$$ {R}<^>2=0.998 $$). The local mass transfer coefficient for the solid phase was evaluated by the PBSM deduction, and subsequently, the diffusivity of the surface solid was experimentally evaluated through comparison in terms of the PBSM. Regardless of the mode of operation, surface diffusion is associated with only the nature of the adsorbent material rather than the concentration of the liquid phase. In addition, the PBSM exhibited liquid and solid concentration changes at different points in the column. Moreover, different operating curves of the process were constructed and validated, exhibiting similar results when comparing the predictions of the model and the experimental data. These findings support the strength of the constructed model, enabling its extension to other adsorbent-dye systems.