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Monte Carlo model of nonlinear chromatography: correspondence between the microscopic stochastic model and the macroscopic Thomas kinetic model

机译：非线性色谱的蒙特卡洛模型：微观随机模型与宏观托马斯动力学模型之间的对应关系

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摘要

The Monte Carlo model of chromatography is a description of the chromatographic process from a molecular (microscopic) point of view and it is intrinsically based on the stochastic theory of chromatography originally proposed by Giddings and Eyring. The program was previously validated at infinite dilution (i.e., in linear conditions) by some of the authors of the present paper. In this work, it has been further validated under nonlinear conditions. The correspondence between the Monte Carlo model and the well-known Thomas kinetic model (macroscopic model), for which closed-form solutions are available, is demonstrated by comparing Monte Carlo simulations, performed at different loading factors, with the numerical solutions of the Thomas model calculated under the same conditions. In all the cases investigated, the agreement between Monte Carlo simulations and Thomas model results is very satisfactory. Additionally, the exact correspondence between the Thomas kinetic model and Giddings model, when near-infinite dilution conditions are approached, has been demonstrated by calculating the limit of the Thomas model when the loading factor goes to zero. The model was also validated under limit conditions, corresponding to cases of very slow adsorption-desorption kinetics or very short columns. Different hypotheses about the statistical distributions of the random variables "residence time spent by the molecule in mobile and stationary phase" are investigated with the aim to explain their effect on the peak shape and on the efficiency of the separation. [References: 76]
机译：色谱的蒙特卡洛模型是从分子（微观）角度描述色谱过程的方法，其本质上是基于Giddings和Eyring最初提出的色谱随机理论。本程序的某些作者先前已经在无限稀释下（即在线性条件下）验证了该程序。在这项工作中，它已经在非线性条件下得到了进一步验证。通过比较在不同载荷系数下进行的蒙特卡罗模拟与托马斯的数值解，可以证明蒙特卡洛模型与著名的托马斯动力学模型（宏观模型）之间的对应关系，该模型可以使用封闭形式的解。在相同条件下计算的模型。在所有调查的案例中，蒙特卡洛模拟与托马斯模型结果之间的一致性都非常令人满意。此外，当接近接近无限稀释条件时，通过计算载荷因子为零时的托马斯模型极限，可以证明托马斯动力学模型和吉丁斯模型之间的精确对应关系。该模型还在极限条件下进行了验证，这对应于非常缓慢的吸附-解吸动力学或非常短的色谱柱情况。研究了有关随机变量“分子在流动相和固定相中停留的时间”的统计分布的不同假设，目的是解释它们对峰形和分离效率的影响。 [参考：76]

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