Equilibrium shapes of two- and three-dimensional two-phase rotating fluid drops with surface tension: Effects of inner drop displacement
Bibliographic record
Abstract
The shapes of rotating fluid drops held together by surface tension are an important field of study in fluid mechanics. Recently, experiments with micrometer-scale droplets of liquid helium have been undertaken and it has proven useful to compare the shapes of the resultant superfluid droplets with classical analogs. If the helium is a mixture of He3 and He4, two phases are present. In a recent paper, the shapes of rotating two-phase fluid droplets were calculated where the inner drop was constrained to stay at the drop center. The outer shapes and dimensionless rotation rate–angular momentum relationships were shown to be similar to single-phase drops, providing that the density and surface tension scales were chosen appropriately. In the current paper, I investigate models in which the inner drop can displace from the center. In order to simplify the analyses, two-dimensional drops are first investigated. I show that the inner drop is unstable in the center position if its density is greater than the outer density and that the inner drop will move toward the outer boundary of the drop in these cases. When the inner drop has a higher density than the outer drop, the moment of inertia of displaced inner drops is increased relative to centered drops, and hence, the kinetic energy is decreased. Shapes of two- and three-dimensional drops, rotation rate–angular momentum, and kinetic and surface energy relationships are investigated for off-axis inner drops with parameters relevant to recent liquid He 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 | 0.002 |
| 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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".