Bibliographic record
Abstract
Abstract We study the classical Landau–Levich dip-coating problem for the case in which the interface possesses both elasticity and surface tension. The aim of the study is to develop a complete asymptotic theory of the elastocapillary Landau–Levich problem in the limit of small flow speeds. As such, the paper also extends our previous study on purely elastic Landau–Levich flow (Dixit & Homsy J. Fluid Mech., vol. 732, 2013, pp. 5–28) to include the effect of surface tension. The elasticity of the interface is described by the Helfrich model and surface tension is modelled in the usual way. We define an elastocapillary number, $\epsilon $ , which represents the relative strength of elasticity to surface tension. Based on the size of $\epsilon $ , we can define three different regimes of interest. In each of these regimes, we carry out asymptotic expansions in the small capillary (or elasticity) numbers, which represents the balance of viscous forces to surface tension (or elasticity). In the weak elasticity regime, the film thickness is a small correction to the classical Landau–Levich law and can be written as $$\begin{eqnarray*}{\tilde {h} }_{\infty , c} = (0. 9458- 0. 0839~\mathscr{E}){l}_{c} C{a}^{2/ 3} , \quad \epsilon \ll 1,\end{eqnarray*}$$ where ${l}_{c} $ is the capillary length, $Ca$ is the capillary number and $\mathscr{E}= \epsilon / C{a}^{2/ 3} $ . In the elastocapillary regime, the film thickness is a function of $\epsilon $ through the power-law relationship $$\begin{eqnarray*}{\tilde {h} }_{\infty , ec} = {\bar {h} }_{\infty , e} L\hspace{0.167em} f(\epsilon )C{a}^{4/ 7} , \quad \epsilon \sim O(1),\end{eqnarray*}$$ where ${\bar {h} }_{\infty , e} $ is a numerical coefficient obtained in our previous study, $L$ is the elastocapillary length, and $f(\epsilon )$ represents the functional dependence of film thickness on the elastocapillary parameter.
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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 | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".