Shear Dispersion in a Rough-Walled Fracture
Bibliographic record
Abstract
Summary An expression is analytically presented for the shear dispersion, or Taylor (1953) and Aris (1956) dispersion, of a solute transporting in a coupled system, which consists of a matrix and a rough-walled fracture. To derive a shear-dispersion coefficient in a fracture with rough and porous walls, the continuities of solute concentrations and their fluxes are imposed at the fracture walls. The dispersion coefficient for the coupled system is obtained as a function of the Péclet number and relative roughness, where the latter parameter is defined as the ratio of the maximum height of the roughness to the minimum half-aperture of the fracture. Several models for fracture-roughness geometry, including periodically and randomly shaped roughness models, are applied to study the effect of fracture-aperture variation on dispersion. The dispersion coefficient for all rough-walled fractures identifies three different regions in terms of the degree of relative roughness. The results show that for small values of the relative roughness (0<ε≤0.1), the dispersion coefficient is at maximum for bell-shaped geometry and at minimum for triangular-shaped and randomly shaped geometries. When the relative roughness is within 0.1<ε<10, the dispersion is observed to be at maximum for rectangular-walled and at minimum for triangular-walled fractures. The results also reveal that for high values of the relative roughness (ε≥10), the dispersion is higher for bell-shaped roughness, whereas the triangular-walled fracture results in the lowest dispersion. It is found that for all roughness geometries an increase in either the Péclet number or relative roughness leads to an increase in the dispersion.
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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) | 0.005 | 0.001 |
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; both teacher heads agree on what is shown here.
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".