On the use of equilibrium models to describe dynamic adsorption regimes
We present a column adsorption model that couples a Pseudo-First-Order (PFO) kinetic formulation with the Sips isotherm framework. Using a traveling wave approximation, we derive analytical solutions for specific operating conditions. Qualitatively, these solutions deviate significantly from their pure Sips counterparts: instead of a smooth, continuous increase in concentration at the column outlet, the PFO-Sips model predicts an abrupt, sudden breakthrough. We validate these analytical solutions against diverse experimental datasets from the literature. The results reveal that the PFO-based model consistently underperforms compared to the original Sips formulation. Furthermore, this validation exposes fundamental inconsistencies within the PFO framework. We demonstrate that despite its widespread use in the literature for almost a century, the PFO model is inherently flawed and structurally unfit for describing column adsorption dynamics.