AI 中文总结
研究柱吸附动力学，将PFO动力学公式与Sips等温线框架结合构建模型，用行波近似推导解析解，经实验数据集验证，发现基于PFO的模型表现不佳，揭示PFO框架存在基本不一致性，表明其不适用于描述柱吸附动力学。
AI 中文摘要
我们提出了一个柱吸附模型，该模型将伪一级（PFO）动力学公式与Sips等温线框架相结合。利用行波近似，我们推导出了特定操作条件下的解析解。定性地说，这些解与纯Sips模型的解有显著偏差：PFO-Sips模型预测的是突然的突破，而不是柱出口处浓度的平滑、连续增加。我们针对文献中的各种实验数据集验证了这些解析解。结果表明，基于PFO的模型与原始Sips公式相比始终表现不佳。此外，这种验证揭示了PFO框架内的基本不一致性。我们证明，尽管PFO模型在文献中广泛使用了近一个世纪，但它本质上存在缺陷，在结构上不适用于描述柱吸附动力学。
英文摘要
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.
Comments36 pages, 14 figures
