Equilibrium shapes of two-phase rotating fluid drops with surface tension
Bibliographic record
Abstract
While rotating single phase fluid drops have been thoroughly investigated, the determination of the shape of a drop consisting of two immiscible liquid phases has not been previously considered. Recently, experiments using rotating micron-scale droplets of liquid helium have been carried out where the liquid can be in a normal or superfluid state depending on the isotope of helium used. Two phases can be present if the helium is a mixture of He3 and He4. Classical results have been very useful in aiding the analysis of single phase liquid helium drops and are similarly needed for two phase drops. In this contribution, the Navier–Stokes equations with surface tension are solved numerically using the finite-element method with surface tension effects on the inner and outer interfaces. The numerical models are time-dependent but are run to a steady state to determine equilibrium shapes. It is found that with an appropriate scaling of the density and surface tension coefficient, the relationships between the angular velocity and the angular momentum and of the outer surface dimensions with angular momentum become very similar to those of a single phase fluid for a broad range of parameters. However, the shapes of the inner drops vary significantly, particularly when the volume of the inner fluid is significantly less than that of the outer fluid. Increasing the relative magnitude of the interfacial surface tension coefficient or decreasing the relative density of the inner region leads to less deformation of the inner drop relative to the outer one.
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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 | 0.000 | 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".