Theoretical reassessment of the first Stefan diffusion column experiment with a two-component liquid phase, consisting of a high-density volatile solvent and a low-density nonvolatile diluent

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.