Bibliographic record
Abstract
Abstract Wicking flow inside capillary tubes can attain considerable momentum so as to produce a liquid jet at the end of the tube. Auto-ejection refers to the formation of droplets at the tip of such a jet. Experimental observations suggest that a tapering nozzle at the end of the capillary tube is necessary for auto-ejection; it has never been reported for a straight tube. Besides, most experimental realizations require microgravity, although it is possible under normal gravity if the nozzle has a sufficiently sharp contraction. This computational study focuses on two related issues: the critical condition for auto-ejection, and the hydrodynamics of the liquid meniscus as affected by geometric parameters. We adopt a diffuse-interface Cahn–Hilliard model for the moving contact line, and allow the dynamic contact angle to deviate from the static one through wall energy relaxation. From analyzing the dynamics of the meniscus in the straight tube and the nozzle, we establish a critical condition for the onset of auto-ejection based on a Weber number defined at the exit of the nozzle and an effective length that encompasses the geometric features of the tube–nozzle combination. In particular, this shows that capillary ejection is not possible in straight tubes. With steeper contraction in the nozzle, we predict two additional regimes of interfacial rupture: rapid ejection of multiple droplets and air bubble entrapment. The numerical results are in general agreement with available experiments.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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".