Instability in Thin Liquid Film Flow Over an Uneven, Periodic Incline in the Presence of Surfactant
Bibliographic record
Abstract
<p>We consider gravity-driven fluid flow down a wavy inclined surface in the presence of surfactant. The periodicity of the bottom topography allows us to leverage Floquet theory to determine the correct form for the solution to the linearized governing partial differential equations. The result is that perturbations from steady state are wavelike, and a dispersion relation is identified which relates the wavenumber of an initial perturbation, κ, to its complex frequency, ω. The real part of ω ultimately determines the stability of the flow. We observe that the addition of surfactant generally has a stabilizing effect on the flow, but has a destabilizing effect for small wavenumbers. These results are compared and validated against nonlinear results, which are obtained by numerically solving the governing equations directly. The linear and nonlinear analyses show good agreement, except at small wavenumbers, where the linear results could not be replicated.</p>
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How this classification was reachedexpand
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 | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".