Abstract

The Stefan column was designed in the 19th century to allow the experimental estimation of binary gas diffusion coefficients starting with a pure volatile liquid A placed at the bottom overlaid with a stagnant/inert gas B. A sweeping B stream was provided at the top to remove the diffused gas A. In 1959, Richardson first studied a two-component liquid mixture in the Stefan column. One of his systems, a high-density volatile liquid A (carbon tetrachloride) dissolved in a low-density nonvolatile liquid O (dibutyl phthalate), is of interest to our ongoing research efforts. He collected interfacial descent-time data in his single isothermal Stefan column experiment, and analyzed them with a diffusion transport model, which contained unnecessary assumptions and simplifications, to obtain the binary liquid diffusivity of A in O, D_AO. The present study removes the major restrictions of the previous model, reanalyzing the reported data with an improved numerical diffusion model that includes realistic features of the one-dimensional transport problem and statistical information on the estimated D_AO. The average ± standard deviation of D_AO were 8.82E-10 ± 1.85E-15 m²/s (12 data points), with an error of −13.3% relative to the Richardson value. The new model also provides detailed insight on the diffusive transport dynamics of liquid A by predicting interfacial descent rates, instantaneous concentration profiles in the liquid phase, and the time-dependent fraction of the mass of A lost from the original solution. The model is valuable to chemical engineering researchers studying diffusion–evaporation phenomena and multicomponent distillation processes.

摘要

Stefan 色谱柱设计于 19 世纪，用于对二元气体扩散系数进行实验估计，从底部的纯挥发性液体 A 开始，并覆盖有停滞/惰性气体 B。顶部提供吹扫 B 流以去除扩散气体 A. 1959 年，Richardson 首次在 Stefan 塔中研究了一种双组分液体混合物。他的系统之一是溶解在低密度非挥发性液体 O（邻苯二甲酸二丁酯）中的高密度挥发性液体 A（四氯化碳），这对我们正在进行的研究工作很感兴趣。他在他的单等温 Stefan 柱实验中收集了界面下降时间数据，并使用包含不必要假设和简化的扩散传输模型对其进行分析，以获得 A 在 O 中的二元液体扩散率，道_奥。本研究消除了先前模型的主要限制，使用改进的数值扩散模型重新分析报告的数据，该模型包括一维传输问题的现实特征和估计的D _AO的统计信息。D _AO的平均值±标准偏差为 8.82E-10 ± 1.85E-15 m ²/s（12 个数据点），相对于 Richardson 值的误差为 -13.3%。新模型还通过预测界面下降速率、液相中的瞬时浓度分布以及从原始溶液中损失的 A 质量的时间相关分数，提供了对液体 A 的扩散传输动力学的详细见解。该模型对研究扩散蒸发现象和多组分蒸馏过程的化学工程研究人员很有价值。