Thin film flow on the inside surface of a horizontally rotating cylinder: Steady state solutions and their stability
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Bibliographic record
Abstract
We present an approximate evolution equation for the film thickness on the inner surface of a horizontally rotating cylinder and solve it numerically by a collocation method. The influences of gravity, inertia, viscous and surface tension forces, and liquid volume fraction are included in the model. We investigate steady two-dimensional solutions and their linear stability to both axially uniform and two-dimensional perturbations and map stable and unstable regions depending on the relevant dimensionless numbers. It is shown that while an increase of the liquid volume fraction or surface tension always has a destabilizing effect on the solution, inertia may stabilize or destabilize the flow depending on the values of other parameters. At the same time, the inertial influence on the solution itself is relatively small. To obtain more insights into the flow after the loss of stability, we examine the growth rate of disturbances and demonstrate that it varies significantly through the considered parameter range. In addition, we obtain the most unstable wave numbers. This provides a means to distinguish between capillary and inertial instabilities. Finally, we present some steady three-dimensional solutions to illustrate possible film shapes that can be obtained after the loss of stability.
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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)
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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