A steady two‐dimensional cylindrical mass transport model to determine binary gas diffusivities: A proof‐of‐concept theoretical development
Bibliographic record
Abstract
Abstract Binary 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".