Dimensionless approach-to-steady-state criteria required for estimating binary gas diffusivities in the Stefan column

The Stefan column is useful for determining binary gas diffusivities DABs experimentally. Two operating modalities are the stationary interface with liquid replenishment and the descending interface without replenishment. This study focuses on the stationary modality which attains a steady-state. No dimensionless criteria are available for estimating the time-of-approach-to-steady-state of the mole fraction profiles of gas A required for DAB evaluation. This report develops a transient one-dimensional (1D) mole balance for gas A with specific initial and spatial boundary conditions. Case I fixes the inlet mole fraction of gas A and Case II sets the molar flux. A numerical integrator solved for the normalized mole fraction as a function of position and time. Results from Case I were on the order of minutes for the approach-to-steady-state in experiments reported previously. This time will be affected by the DAB and characteristic length of interest. The model also predicted that some Case II scenarios could quadruple the time-of-approach-to-steady-state in Case I. These results can be readily applied to descending interface experiments to estimate the DABs. Researchers now have for the first time dimensionless criteria, which can be extrapolated to similar systems, for the approach-to-steady-state of the mole fraction profiles of gas A useful to estimate experimental DABs.

Abstract licence: CC BY-NC

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