Binary gas diffusivity estimates from transient, one-dimensional sublimation–diffusion experiments in a spherical enclosure

ABSTRACT

Binary gas diffusivities D_AB’s are extremely useful in the analysis/design of mass transfer systems and to develop correlations. This study used an unsteady experimental method to determine D_AB’s in gas pairs starting with a sublimating solid (A) such as naphthalene or camphor and air (B). The cumulative fractional mass transferred from the surface of a solid A sphere placed concentrically within an isothermal spherical enclosure was followed gravimetrically with time. The experimental D_AB,exp for the gas pair was determined by nonlinear regression using the solution to a transient, one-dimensional (radial) diffusion model. The model’s Case 1 option assumed impermeability (no flux of gas A) at the enclosure’s outer surface, while Case 2 assumed zero concentration of gas A at the same location. For naphthalene–air, D_AB,exp overestimated the literature values, the errors ranging from −110 to −185% for Case 1 and −21 to −65% for Case 2. For camphor–air, the error in D_AB,exp was −36% for Case 1 and −16% for Case 2. D_AB,exp for camphor in atmospheric air is herein reported for the first time. Potential improvements to the experiments include automation of the sphere melt-casting process and tighter control of the enclosure’s environmental conditions. Likewise, the theoretical model could be extended to three dimensions with multicomponent diffusion to assess the effect of air humidity on the transport of gas A. This is the first attempt to determine D_AB,exp for naphthalene–air and camphor–air from an unsteady sublimation–diffusion experiment and to model the results using rigorous mass transport theory.

KEYWORDS:

• Experimental binary gas diffusivities
• diffusivity estimation by nonlinear regression
• naphthalene and camphor sublimation in air
• transient, one-dimensional (radial) diffusion
• spherical gas enclosure
• theoretical transport modeling

View correction statement:

Correction

Erratum

Acknowledgments

The authors are extremely grateful to Professors E. Meléndez and R. J. Romañach, as well as to laboratory technician E. Quiñones, for making available the experimental facilities in the Department of Chemistry, University of Puerto Rico, Mayagüez, throughout this study. In addition, the tireless staff of the Interlibrary Loans Section of the General Library is thanked for tracking down most of the archival references. Finally, 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 two generations of chemical engineers, and for giving science their venerable Transport Phenomena text.

M. J. Ubernosky, A. R. Ramírez, and A. L. Braña provided many insightful suggestions for the technical execution of the experiments.

J. Castañer received undergraduate research credit for carrying out and analyzing the sublimation–diffusion experiments with naphthalene and camphor.