Theoretical and Experimental Estimation of Binary Gas Diffusivities in a Nonisothermal Stefan Diffusion Column

Binary gas diffusivities D_AB are essential to analyze chemical engineering transport processes. One of Josef Stefan's memorable moving-front problems involved a column with liquid A at the bottom and a gas mixture of A and B on top. This system has been used by several groups to determine D_AB's under assumed isothermal conditions. A device for such purposes is Armfield's CERa apparatus; however, its operation is not isothermal. This study's hypothesis is that the nonisothermality of the gas relative to the liquid affects the D_AB estimates. A mass and energy transport model was developed to describe events in the gas once the evaporation-diffusion of A begins. The model included D_AB as a key parameter and different phase temperatures (liquid hotter than gas). A numerical algorithm solved for the instantaneous mole fraction of A, temperature, and interfacial position. The model predicted the transient and spatial transport phenomena of four gas pairs (A = common solvent; B = bone-dry air). The simulations gave lower D_AB's in nonisothermal versus isothermal columns, the errors being proportional to the temperature difference between the phases. Six binary gas experiments were carried out in a nonisothermal CERa at two room temperatures. The experimental D_AB's underestimated the isothermal diffusivities with errors of 23–52%, while the parallel simulations followed this trend but with smaller errors (4.1–6.3%). D_AB underestimation due to column nonisothermality is novel in the gas diffusivity literature. Improvements to the theoretical and experimental techniques presented should result in better D_AB estimates.