Transient two-layer thin-film flow inside a channel
Bibliographic record
Abstract
The flow of two superimposed newtonian layers in a channel is investigated numerically in this study. The two-layer film flows inside a long channel due to a pressure gradient. The scaled conservation equations for two-layer incompressible newtonian film flow are first introduced. The weighted residual approach first proposed by Amaouche et al. [Phys. Fluids 19, 084106 (2007)] is used for finding the suitable weight functions before depth averaging. Subsequently, a linear stability analysis of thin-film equations for two-layer Poiseuille flow is carried out. The formulas which give the asymptotic stability with respect to long-wave perturbations obtained with Navier-Stokes equations [J. Non-Newtonian Fluid Mech. 71, 1 (1997)] are recovered with our averaging equations. In order to mimic the disturbance effect on the coextrusion flow, the steady flow, which is simply the uniform flow of two layers of fluid inside a channel, is then perturbed at inception. Following a finite difference based scheme, two types of boundary conditions are considered at the channel inception, namely a Dirac-type pulse and periodic forcing. The perturbation takes the form of a wave packet which may or may not be amplified as it moves downstream, depending on the values of the parameters involved in the problem. Furthermore, Gaster's relation is used to calculate the spatial growth rate of perturbation. The values obtained from this relation are in good quantitative agreement with those coming from the numerical simulations of thin-film equations. Then, our averaging equations also describe the nonlinear behavior of the interfacial instabilities occurring for the Poiseuille flow of two thin layers.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 |
| 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".