Transient Thin-Film Flow on a Moving Boundary of Arbitrary Topography
Bibliographic record
Abstract
The transient two-dimensional flow of a thin Newtonian fluid film over a moving substrate of arbitrary shape is examined in this theoretical study. The interplay among inertia, initial conditions, substrate speed, and shape is examined for a fluid emerging from a channel, wherein Couette–Poiseuille conditions are assumed to prevail. The flow is dictated by the thin-film equations of the “boundary layer” type, which are solved by expanding the flow field in terms of orthonormal modes depthwise and using the Galerkin projection method. Both transient and steady-state flows are investigated. Substrate movement is found to have a significant effect on the flow behavior. Initial conditions, decreasing with distance downstream, give rise to the formation of a wave that propagates with time and results in a shocklike structure (formation of a gradient catastrophe) in the flow. In this study, the substrate movement is found to delay shock formation. It is also found that there exists a critical substrate velocity at which the shock is permanently obliterated. Two substrate geometries are considered. For a continuous sinusoidal substrate, the disturbances induced by its movement prohibit the steady-state conditions from being achieved. However, for the case of a flat substrate with a bump, a steady state exists.
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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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| 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".