Marangoni instabilities associated with heated surfactant-laden falling films
Why this work is in the frame
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Bibliographic record
Abstract
Investigated in this paper is the stability of the gravity-driven flow of a liquid layer laden with soluble surfactant down a heated incline. A mathematical model incorporating variations in surface tension with surfactant concentration and temperature has been formulated. A linear stability analysis is carried out both asymptotically for small wavenumbers and numerically for arbitrary wavenumbers. An expression for the critical Reynolds number has been derived which accounts for thermocapillary and solutocapillary effects, and reduces to known documented results for special cases. Also, a nonlinear reduced model has been derived using weighted residuals, and solved numerically to simulate the instability of the equilibrium flow and the development of permanent surface waves that arise. The nonlinear simulations were found to be in good agreement with the linear stability analysis.
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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