Static wall layers in the displacement of two visco-plastic fluids in a plane channel
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Bibliographic record
Abstract
In a plane-channel displacement flow of two visco-plastic fluids, it is possible for there to be a static residual layer of the displaced fluid left stuck to the walls of the channel. This phenomenon provides an idealized model for the formation of a wet micro-annulus , due to poor mud removal, during the primary cementing of an oil well. Using a lubrication approximation, it is shown that sufficient conditions for the non-existence of a static wall layer can be computed simply in terms of two dimensionless parameters: the Bingham number for the displacing fluid ( B 1 ) and the ratio of the yield stresses of the two fluids (ϕ Y ). When these conditions are not met, it is possible to compute the maximum possible static wall layer thickness h max , which depends on B 1 , ϕ Y and on a third dimensionless parameter ϕ B , a buoyancy to yield stress ratio. On computing displacements using the lubrication approximation, the interface is observed to asymptotically approach the maximum static layer thickness as t → ∞. Results from fully two-dimensional displacement computations are also presented. These indicate that the displacement front propagates at a steady speed along the channel, leaving behind a static layer which is significantly thinner than h max . Surprisingly, the computed static layer thickness is observed to decrease with a parametric increase in the dimensionless yield stress of the displaced fluid. To explain these results we analyse the streamline configuration close to a steadily advancing displacement front. We demonstrate heuristically that the local visco-plastic dissipation functional will be approximately minimized by a critical layer thickness at which the displaced fluid begins to recirculate ahead of the displacement front. Comparison of the critical recirculation limit with the static layer thickness computed from the fully transient model gives a very close agreement, suggesting that a form of energy minimization is responsible in this case for selecting the static layer thickness.
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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 | 0.001 | 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 it