标题： 吸附过程中的行波方程分析 显示英文标题

标题： Analysis of travelling wave equations in sorption processes

摘要： 本文提出了一种吸附柱的数学模型，用于研究沿柱体纵向轴线污染物浓度和吸附量的变化。 该模型由一组偏微分方程（PDEs）描述，通过行波方法进行分析，将系统转换为依赖于逆佩克莱特数的二阶常微分方程，通常该数很小。 通过奇异摄动方法，假设逆佩克莱特数可以忽略不计，将模型简化为一个一阶近似，这可以视为一个慢-快系统。 通过解析延拓，我们得出结论，至少对于逆佩克莱特数较小的情况，浓度从吸附剂基质的清洁状态变化到完全饱和。 我们进行了数值模拟，以说明不同佩克莱特数情况下的分析结果，并进行了敏感性分析，证明了系统的鲁棒性。 显示英文摘要

摘要： This works presents a mathematical model of an adsorption column to study the evolution of contaminant concentration and adsorbed quantity along the column's longitudinal axis. The model, described by a system of partial differential equations (PDEs), is analysed using a travelling wave approach, which transforms the system into a second-order ordinary differential equation dependent on the inverse P\'eclet number, typically small. The model is simplified by means of a singular perturbation to a leading-order approximation by assuming a negligible inverse P\'eclet number, which can be regarded as a slow-fast system. By analytical continuation, we conclude that, at least for small values of the inverse P\'eclet number, the concentration varies from the clean state of the adsorbent matrix to a full saturation. We present numerical simulations to illustrate the analytical results for different P\'eclet number values and conduct a sensitivity analysis that demonstrates the system's robustness.