Transient coating flow of a thin non-Newtonian fluid film
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Bibliographic record
Abstract
The interplay between non-Newtonian effects, gravity, and substrate topography is examined in this theoretical study for the transient two-dimensional flow of a thin non-Newtonian film. The study is a continuation of the previous work by Khayat and Welke [Phys. Fluids 13, 355 (2001)], which focused on the influence of inertia on a Newtonian film. The fluid emerges from a channel and is driven by a pressure gradient maintained inside the channel. The substrate is assumed to be stationary and of arbitrary shape. 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 in the transverse direction and using the Galerkin projection, combined with a time-stepping implicit scheme, and integration along the flow direction. Gravity and substrate topography can have a significant effect on transient behavior, but this effect varies significantly, depending on whether the fluid is Newtonian, shear thinning or shear thickening. Wave formation and propagation, as well as steady film flow are examined. It is found that shear-thickening fluids tend to accumulate near the channel exit, exhibiting a standing wave that grows with time. This behavior clearly illustrates the difficulty faced with coating shear-thickening fluids at any level of inertia. The influence of the substrate topography has been explored in the case of undulated substrate.
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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