A steady two-dimensional cylindrical mass transport model to determine binary gas diffusivities: A proof-of-concept theoretical development

Binary gas diffusivities, D_ABs, are key parameters in the analysis of many chemical engineering processes. Significant efforts to estimate diffusivities experimentally were made by Josef Stefan in the 19th century, who designed a column with liquid A at the bottom overlaid by a gas phase through which gas A diffused. His studies led to the determination of D_ABs for many gas pairs (B is commonly air), and to the development of alternate mass transport systems. The present proof-of-concept theory describes a steady two-dimensional (2D) diffusion model consisting of a vertical cylinder thinly coated on its inner surfaces with either a sublimating or evaporating species A. The gas-phase mass conservation partial differential equation is rendered dimensionless and solved by separation of variables. The theoretical molar flow rate of species A at the top of the cylinder, calculated analytically, can be equated to the experimental rate of mass loss from the coated walls, ultimately leading to D_AB. The solution of the steady 2D diffusion model is explored in terms of the cylinder aspect ratio (height/radius), showing that the latter quantity can be tailored to obtain preselected sublimation rates of A. The interplay of the radial and axial diffusion mechanisms is also demonstrated as a function of geometry. Finally, the model's use in analyzing a projected sublimation/evaporation–diffusion experiment is discussed. This is the first time that a steady 2D diffusive transport model has been proposed to estimate D_ABs from experimental data.