Abstract

The Stefan column was developed in the 19th Century to estimate binary gas diffusivities, D_AB’s, and this goal has been achieved by many research groups. In the classical device, volatile liquid A is placed at the bottom and overlaid with stagnant gas B. A slow gas B sweep is provided at the top to remove the diffused gas A. However, column “end effects” have been largely ignored or neglected during data analysis. The present study addressed the effect of interfacial curvature on diffusivity determination. Curvature affects the interfacial transport area and the diffusion path length of gas A. Cylindrical aluminum punches with flat or curved tips were used to imprint solid naphthalene surfaces. The naphthalene-containing tubes were subjected to standard Stefan column sublimation-diffusion experiments at ∼60 °C and atmospheric pressure. With the mass loss from each tube obtained gravimetrically and the punch/tube dimensions, the experimental diffusivities, D_AB,exp, were determined using the solution to a one-dimensional mass transport model for gas A. Tubes with flat interfaces had the smallest D_AB,exp errors relative to the literature, while the curved surfaces (spherical and elliptical) had the largest when assumed to be flat in the calculations. When curvature was accounted for mathematically, the D_AB,exp errors changed sign and magnitude depending on the actual punch shape and system dimensions. This is the first study to show that neglect of interfacial curvature can lead to significant errors in D_AB,exp obtained using the isothermal Stefan column method. Therefore, curvature corrections should be considered whenever accurate D_AB,exp’s are sought.

摘要

Stefan 柱是在 19 世纪开发的，用于估计二元气体扩散系数 D _AB的，并且这个目标已经被许多研究小组实现。在经典装置中，挥发性液体 A 放置在底部并与静止气体 B 重叠。顶部提供缓慢的气体 B 吹扫以去除扩散的气体 A。然而，塔“末端效应”在很大程度上被忽略或忽略在数据分析过程中。本研究解决了界面曲率对扩散率测定的影响。曲率影响界面传输面积和气体 A 的扩散路径长度。带有扁平或弯曲尖端的圆柱形铝制冲头用于压印固体萘表面。在~60°C和大气压下对含萘的管进行标准Stefan柱升华扩散实验。通过重量分析获得每个管的质量损失和冲头/管尺寸，_AB,exp是使用气体 A 的一维传质模型的解来确定的。具有平坦界面的管具有相对于文献的最小 D _AB,exp误差，而曲面（球形和椭圆形）具有最大当在计算中假定为平坦时。当用数学方法计算曲率时，D _AB,exp误差会根据实际冲头形状和系统尺寸改变符号和大小。这是第一个表明忽略界面曲率会导致使用等温 Stefan 柱方法获得的D _AB,exp出现重大误差的研究。因此，只要准确 D _{AB,exp 就}应考虑曲率校正正在寻找。