Stationary residual layers in buoyant Newtonian displacement flows
Bibliographic record
Abstract
We study buoyant displacement flows with two miscible fluids of equal viscosity in ducts that are inclined at angles close to horizontal (β≈90°). As the imposed velocity (V̂0) is increased from zero, we change from an exchange flow dominated regime to a regime in which the front velocity (V̂f) increases linearly with V̂0. During this transition, we observed an interesting phenomenon in which the layer of displaced fluid remained at the top of the pipe (diameter D̂) during the entire duration of the experiment, apparently stationary for times t̂≳103D̂/V̂0 (the stationary residual layer). Our investigation revealed that this flow marks the transition between flows with a back flow, counter to the imposed flow, and those that displace instantaneously. The same phenomena are observed in pipes (experiments) and in plane channels (two-dimensional numerical computations). A lubrication/thin-film model of the flows also shows the transition from back flow to instantaneous displacement. At long times, this model has a stationary residual layer solution of the type observed, which is found at a unique ratio χ of the axial viscous velocity to the imposed velocity. The prediction of the stationary residual layer from the lubrication model is compared with the transition in observed behavior in our pipe flow experiments and our 2D numerical displacements in the channel. Reasonable agreement is found for the pipe and excellent agreement for the channel. Physically, in either geometry at transition, the upper layer of the fluid is in a countercurrent motion with zero net volumetric flux; the velocity at the interface is positive, but the velocity of the interface is zero. This results from a delicate balance between buoyancy forces against the mean flow and viscous forces in the direction of the mean flow.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| 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".