Determination of Dynamic Dispersion Coefficient for Solid Particles Flowing in a Fracture With Consideration of Gravity Effect
Bibliographic record
Abstract
Abstract A robust and pragmatic method has been developed and validated to analytically determine dynamic dispersion coefficients for particles flowing in a parallel-plate fracture, in which gravity settling has been considered due to its significant impact on particle flowing behavior. More specifically, a two-dimensional (2D) advection–diffusion equation together with the initial and boundary conditions has been formulated to describe the flow behavior of finite-sized particles on the basis of coupling the Poiseuille flow with vertical settling. Meanwhile, three types of instantaneous source conditions (i.e., point source, uniform line source, and volumetric line source) have been considered. Explicit expressions, which can directly and time-efficiently calculate dynamic dispersion coefficient, have been derived through the moment analysis and the Green’s function method. By performing the simulation based on the random walk particle tracking (RWPT) algorithm, the newly developed model has been verified to determine particle dispersion coefficients agreeing well with those obtained from the RWPT simulations. It is found that the point source is the most sensitive to gravity effect among different source conditions, while the volumetric line source is affected more than the uniform line source. For particle size larger than its critical value, an increased particle size leads to a decreased asymptotical dispersion coefficient for all the source conditions due to the significant gravity effect, while gravity positively affects the dispersion coefficient at early times for the point source condition. In addition, average flow velocity positively affects the dispersion coefficient for all the source conditions, while the associated gravity effect is influenced only at early times for the point source condition.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 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 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".