Drag coefficients and rotational behavior of spheres descending through liquids along an inclined wall at high Reynolds numbers
Bibliographic record
Abstract
Spherical particles immersed in liquids were observed in their descent along a glass wall inclined at various angles α, over a range of particle-based Reynolds numbers (Rep) extending to high values (15 < Rep < 50 000), rarely reported in such flows. Plastic, ceramic, and metal spheres were used, characterized as to surface roughness and their friction coefficients against the glass. Liquids were selected to achieve a viscosity variation by a factor of 300, as well as having widely differing chemical natures. A drag coefficient (Cp) used to correlate sphere velocity data was found to define a near-universal curve Cp (Rep) over the entire Rep-range, provided that spheres rolled down the wall without slipping, and here there was no need to accommodate roughness effects of solid-to-solid friction explicitly. This correlation was especially good for Rep > 103. For lower Rep, deviations appeared in systematic fashion, falling below the universal curve when slip was present. Several unexpected features were observed: (a) a threshold angle, α0, needed before sphere motion could begin; (b) spheres lifting off from the wall at high Rep, but always at the same maximum angle αm = 74°; and (c) prior to lift-off, a buzzing sound (not reported previously) for which explanations are offered.
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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".