Bubbles and Drops on Curved Surfaces
Bibliographic record
Abstract
Surface curvature affects the shape, stability, and apparent contact angle of sessile and pendant drops. Here, we develop an approximate analytical solution for non-axisymmetric perturbations to small spherical drops on a flat substrate, assuming a fixed contact angle and fixed drop volume. The analytical model is validated using numerical solutions of the Laplace equation from the Surface Evolver software. We investigate the effects of surface curvature on drop shape, pressure, and surface energy, ascertaining the energy-gradient force that drives lateral drop migration. By balancing this force with the viscous resistance/drag force, in the lubrication approximation, we predict velocities of the order of 0.1 mm s(-1) for 1 mm diameter drops of water with a 30° contact angle on a substrate with a curvature gradient of 0.01 mm(-2), achieved, for example, on a harmonic surface with a wavelength of 4 cm and an amplitude of 4 mm.
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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 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.002 |
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; both teacher heads agree on what is shown here.
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".