Generalized Mechanical Equilibrium Condition for Multiphase Contact Lines and Multiphase Contact Points
Bibliographic record
Abstract
Multiphase contact lines are present in a number of practical cases, and they are also interesting from a theoretical perspective. The equilibrium relation for a multiphase contact line and multiphase contact point is presented using a thermodynamic free-energy formulation. Calculus of variation is applied to the free-energy functional of a multiphase system, and vectorial mechanical equilibrium conditions for contact lines and points are derived. The developed relation for the multiphase contact line could be regarded as the generalization of the classical Neumann triangle relation. It is shown that the mechanical equilibrium condition for a multiphase contact line may graphically be represented by a planar polygon, whose sides consist of the surface and line tensions. The stated mechanical equilibrium condition for a multiphase contact point can be regarded as the zeroth-order analogue of the Laplace equation (second order) and Neumann triangle relation (first order). It is also shown that the mechanical equilibrium condition for a multiphase contact point may graphically be represented by a nonplanar polygon, whose sides consist of the line tensions. To demonstrate the application of the above relations, a model lamina system is discussed in terms of the stability of the multiphase contact lines.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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".