Buoyant displacement flows in slightly non-uniform channels
Bibliographic record
Abstract
We consider displacement flows in slightly diverging or converging plane channels. The two fluids are miscible and buoyancy is significant. We assume that the channel is oriented close to horizontal. Employing a classical lubrication approximation, we simplify the governing equations to furnish a semi-analytical solution for the flux functions. Then, we demonstrate how the non-uniformity of the displacement flow geometry can affect the propagation of the interface between the heavy and light fluids in time, for various parameters studied, e.g. the viscosity ratio, a buoyancy number and rheological features. By setting the molecular diffusion effects to zero, certain solution behaviours at longer times can be practically predicted through the associated hyperbolic problem, using which it becomes possible to directly compute the interfacial features of interest, e.g. leading and trailing front heights and speeds. For a Newtonian displacement flow in a converging or uniform channel, as the buoyancy number increases from zero, we are able to classify three flow regimes based on the behaviour of the trailing front near the top of the channel: a no-back-flow regime, a stationary interface flow regime, and a sustained back-flow regime. For the case of a diverging channel flow, the sustained back-flow regime is replaced by an eventually stationary interface flow regime. In addition, as the displacement flow progresses, the leading front speed typically increases (decreases) in a converging (diverging) channel, while the opposite is usually true for the front height. For the no-back-flow regime (i.e. with small buoyancy), the solution of the displacement flow at long times in all the geometries considered converges to a similarity form, while no similarity form is found for the other flow regimes. As the displacement flow develops, frontal diffusive effects are reduced (enhanced) in a converging (diverging) channel and multiple fronts are progressively less (more) present in a converging (diverging) channel. Regarding non-Newtonian effects, a shear-thinning fluid displacing a Newtonian fluid exhibits an increasingly fast front that has a short height in a converging channel. When a yield stress is present in the displaced fluid, it is possible to find residual wall layers of displaced fluid that are completely static. These layers disappear at a certain critical downstream distance in a converging channel while they appear at a critical distance in a diverging channel. Finally, the combination of strong buoyant and yield-stress effects can modify the destiny of a second front that follows the leading front.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".