Unified Multilayer Diffusion Model and Application to Diffusion Experiment in Porous Media by Method of Chambers
Bibliographic record
Abstract
Diffusion coefficient is an important parameter for examining contaminant transport in the environment. Chamber methods (with or without external mixing devices) are the most popular methods for measuring effective diffusion coefficients in porous media (Deff) through air or water. The objectives of this paper were to apply simplified and unified analytical methods for both perfectly mixed and nonmixed (one- or two-) chamber systems and to examine how mixing affects the estimation of Deff. An analytical solution for a multilayer transient diffusion model was applied to the chamber methods without external mixing. By increasing the diffusion coefficient in reservoirs (D1 and D3) more than 10 times from the value for air or water (D0), the model was sufficient to approximate the well-mixed condition and, consequently, can be used to model transient diffusion in chamber systems with external mixing devices. We demonstrated that at long time Deff was related to the first eigenvalue (beta1) of a transcendental equation, which provided a quick method for determining Deff accurately from experimental data. The error caused by using the well-mixed approximation can be significant for a single-chamber system when there are no external mixing devices. This error increased rapidly with decreases in the experimental duration. A good fit for the concentration versus time curve could not be obtained forthe well-mixed solution, especially when sampling ports were near the boundary (x=0) and interface (x = l1). The proposed solutions are useful when the reservoir or chamber methods are used for measuring Deff and have wide applications in predicting contaminates transport in porous media and groundwater.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".