Interfacial geometry and its effect on the estimation of binary gas diffusivities in an isothermal Stefan column

Abstract

The Stefan column was developed in the 19th Century to estimate binary gas diffusivities, DAB’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, DAB,exp, were determined using the solution to a one-dimensional mass transport model for gas A. Tubes with flat interfaces had the smallest DAB,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 DAB,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 DAB,exp obtained using the isothermal Stefan column method. Therefore, curvature corrections should be considered whenever accurate DAB,exp’s are sought.