Bibliographic record
Abstract
Abstract We study the classical Landau–Levich dip-coating problem in the case where the interface has significant elasticity. One aim of this work is to unravel the effect of surface-adsorbed hydrophobic particles on Landau–Levich flow. Motivated by recent findings (Vella, Aussillous & Mahadevan, Europhys. Lett., vol. 68, 2004, pp. 212–218) that a jammed monolayer of adsorbed particles on a fluid interface makes it respond akin to an elastic solid, we use the Helfrich elasticity model to study the effect of interfacial elasticity on Landau–Levich flow. We define an elasticity number, $\mathit{El}$ , which represents the relative strength of viscous forces to elasticity. The main assumptions of the theory are that $\mathit{El}$ be small, and that surface tension effects are negligible. The shape of the free surface is formulated as a nonlinear boundary value problem: we develop the solution as an asymptotic expansion in the small parameter ${\mathit{El}}^{1/ 7} $ and use the method of matched asymptotic expansions to determine the film thickness as a function of $\mathit{El}$ . The solution to the shape of the static meniscus is not as straightforward as in the classical Landau–Levich problem, as evaluation of higher-order effects is necessary in order to close the problem. A remarkable aspect of the problem is the occurrence of multiple solutions, and five of these are found numerically. In any event, the film thickness varies as ${\mathit{El}}^{4/ 7} $ in qualitative agreement with the experiments of Ouriemi & Homsy (Phys. Fluids, 2013, in press).
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".