Effect of a sweeping air stream and gas–phase aspect ratio of an isothermal Stefan diffusion column on the experimental estimation of binary gas diffusivities

Abstract

The Stefan column consists of liquid A evaporating into an inert/stagnant gas B with a sweeping B stream at the top. It was designed to estimate binary gas diffusivities, D_AB’s, but “end effects” such as gas mixing at the top and interfacial curvature have been either ignored or uncorrelated to the operational settings. This study’s hypothesis is that gas mixing at the top and the gas–phase aspect ratio affect D_AB estimation in the acetone (A)-ambient air (B) system at 50 °C. The sweeping stream Reynolds number (Re) and the gas–phase aspect ratio (AR = initial gas phase height to column internal diameter) were the variables tested. Isothermal evaporation-diffusion experiments were conducted in which the temporal interfacial descent was tracked. The settings were 492 ≤ Re ≤ 5378 and AR between 5 and 15. A 1D transport model allowed determination of the experimental diffusivity, D_AB,exp, by nonlinear regression. For Re < 600, the D_AB,exp errors relative to D_AB,CE (predicted by the Chapman–Enskog kinetic theory for low-density gases) were small and unrelated to AR, while for Re > 600 the errors increased considerably with Re and were inversely proportional to AR. This study is the first to relate the column’s operational settings to the D_AB estimation errors. The column should be operated at low sweeping gas Re and large AR for accurate D_AB,exp’s. The low Re region deserves further study, while the present transport model may have to be replaced by computational fluid dynamics simulations to account for the multidimensional gas flow patterns.

Keywords:

• Acetone–air evaporation–diffusion process
• Diffusivity estimation by nonlinear regression
• End effects in a Stefan diffusion column
• Experimental binary gas diffusivities
• Gas–phase aspect ratio of an isothermal diffusion column
• 1D transport modeling
• Sweeping gas stream Reynolds number

Acknowledgments

The authors are grateful to Professor E. Meléndez and laboratory technician E. Quiñones for making available the experimental facilities in the Department of Chemistry, University of Puerto Rico, Mayagüez, throughout this study. Also, the Interlibrary Loans Section of the General Library is acknowledged for their tireless support in tracking most of the archival references. In addition, a special recognition is extended to the University of Wisconsin Professors R. B. Bird, W. E. Stewart, and E. N. Lightfoot for being a source of academic inspiration to our research efforts, and for giving science their venerable Transport Phenomena text. Finally, the manuscript’s anonymous reviewers are thanked for their insightful comments and suggestions. Author M. E. Graniela received undergraduate research credit for carrying out and analyzing the acetone-air evaporation-diffusion experiments.

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