Displacement flows in horizontal, narrow, eccentric annuli with a moving inner cylinder
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Bibliographic record
Abstract
We analyze the effects of rotation and axial motion of the inner cylinder of an eccentric annular duct during the displacement flow between two Newtonian fluids of differing density and viscosity. The annulus is assumed narrow and is oriented near the horizontal. The main application is the primary cementing of horizontal oil and gas wells, in which casing rotation and reciprocation is becoming common. In this application it is usual for the displacing fluid to have a larger viscosity than the displaced fluid. We show that steady traveling wave displacements may occur, as for the situation with stationary walls. For small buoyancy numbers and when the annulus is near to concentric, the interface is nearly flat and a perturbation solution can be found analytically. This solution shows that rotation reduces the extension of the interface in the axial direction and also results in an azimuthal phase shift of the steady shape away from a symmetrical profile. Numerical solution is used for larger buoyancy numbers. We see that the phase shift results in the positioning of heavy fluid over light fluid along segments of the interface. When the axial extension of the interface is sufficiently large, this leads to a local buoyancy-driven fingering instability, for which a simple predictive theory is advanced. Over longer times, the local fingering is replaced by steady propagation of a diffuse interfacial region that spreads slowly due to dispersion. Slow axial motion of the annulus walls on its own is apparently less interesting. There is no breaking of the symmetry of the interface and hence no instability. However, axial wall motion does generate secondary flows which may combine with those from cylinder rotation resulting in enhanced dispersive effects.
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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 | 0.000 | 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 it