Starting Poiseuille Flow in a Circular Tube With Two Immiscible Fluids
Bibliographic record
Abstract
Starting flow due to a suddenly applied pressure gradient in a circular tube containing two immiscible fluids is solved using eigenfunction expansions. The orthogonality of the eigenfunctions is developed for the first time for circular composite regions. The problem, which is pertinent to flow lubricated by a less viscous near-wall fluid, depends on the ratio of the radius of the core region to that of the tube, and the ratios of dynamic and kinematic viscosities of the two fluids. In general, a higher lubricating effect will lead to a longer time for the starting transient to die out. The time development of velocity profile and slip length are examined for the starting flows of whole blood enveloped by plasma and water enveloped by air in a circular duct. Owing to a sharp contrast in viscosity, the starting transient duration for water/air flow can be ten times longer than that of blood/plasma flow. Also, the slip length exhibits a singularity in the course of the start-up. For blood with a thin plasma skimming layer, the singularity occurs very early, and hence for the most part of the start-up, the slip length is nearly a constant. For water lubricated by air of finite thickness, the singularity may occur at a time that is comparable to the transient duration of the start-up, and hence, an unsteady slip length has to be considered in this case.
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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 | 0.001 |
| 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".