Liquid-bridge breakup in contact-drop dispensing: Liquid-bridge stability with a free contact line
Bibliographic record
Abstract
The static stability of weightless liquid bridges with a free contact line with respect to axisymmetric and nonaxisymmetric perturbations is studied. Constant-volume and constant-pressure stability regions are constructed in slenderness versus cylindrical volume diagrams for fixed contact angles. Bifurcations along the stability-region boundaries are characterized by the structure of axisymmetric bridge branches and families of equilibria. A wave-number definition is presented based on the pieces-of-sphere states at branch terminal points to classify equilibrium branches and identify branch connections. Compared with liquid bridges pinned at two equal disks, the free contact line breaks the equatorial and reflective symmetries, affecting the lower boundary of the constant-volume stability region where axisymmetric perturbations are critical. Stability is lost at transcritical bifurcations and turning points along this boundary. Our results furnish the maximum-slenderness stability limit for drop deposition on real surfaces when the contact angle approaches the receding contact angle.
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How this classification was reachedexpand
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 | 0.001 |
| 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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".