Thin film flow on the inside surface of a horizontally rotating cylinder: Steady state solutions and their stability
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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".