Dynamic Dispersion Coefficient of Solutes Flowing in a Circular Tube and a Tube-Bundle Model
Bibliographic record
Abstract
Mathematical formulations have been proposed and verified to determine dynamic dispersion coefficients for solutes flowing in a circular tube with fully developed laminar flow under different source conditions. Both the moment analysis method and the Green's function are used to derive mathematical formulations, while the three-dimensional (3D) random walk particle tracking (RWPT) algorithm in a Cartesian coordinate system has been modified to describe solute flow behavior. The newly proposed formulations have been verified to determine dynamic dispersion coefficients of solutes by achieving excellent agreements with both the RWPT results and analytical solutions. The differences among transverse average concentration using the Taylor model with and without dynamic dispersion coefficient and center-of-mass velocity are significant at early times but indistinguishable when dimensionless time (tD) approaches 0.5. Furthermore, compared to solutes flowing in a 3D circular tube, dispersion coefficients of solutes flowing in a two-dimensional (2D) parallel-plate fracture are always larger for a uniform planar source; however, this is not always true for a point source. Solute dispersion in porous media represented by the tube-bundle model is greatly affected by pore-size distribution and increases as standard deviation of pore-size distribution (σ) increases across the full-time scale.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".