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

Abstract

AbstractBinary gas diffusivities, DABs, 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 DABs 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 DAB. 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 DABs from experimental data.