Mass transfer in ducts with transpiring walls. (April 2019) - Ciofalo, M.; Di Liberto, M.; Gurreri, L.; La Cerva, M.; Scelsi, L.; Micale, G.
Graphical abstract: Highlights: Mass transfer in ducts with transpiring walls was analysed. New dimensionless numbers appropriate to transpiration problems were introduced. The simplifying assumption of self-similar concentration profiles was made. Under this assumption, a simple theory was developed to predict the Sherwood number. Predictions were validated against CFD results based on no simplifying assumption. Abstract: The problem of mass transfer in ducts with transpiring walls is analysed: the concepts of "solvent" and "solute" fluxes are introduced, all possible sign combinations for these fluxes are considered, and relevant examples from membrane processes such as electrodialysis, reverse osmosis and filtration are identified. Besides the dimensionless numbers commonly defined in studying flow and mass transfer problems, new dimensionless quantities appropriate to transpiration problems are introduced, and their limiting values, associated with "drying", "desalting" and "saturation" conditions, are identified. A simple model predicting the Sherwood number Sh under all possible flux sign combinations is derived from the single simplifying assumption that concentration profiles remain self-similar (so that the Sherwood number based on diffusion only remains unchanged) also under transpiration conditions. The simple model provides not only local values of Sh, but also its axial profiles. Predictions are validated against fully predictive CFD results, not based on the above simplifying assumption, and a good agreement is demonstrated provided the transpiration rate complies with certain limitations, depending on the Schmidt number.