A comprehensive model for predicting droplet freezing features on a cold substrate
Bibliographic record
Abstract
Water droplet freezing affects many aspects of our daily lives, although there is no comprehensive model which retrieves all of the experimentally observed features when a liquid water droplet deposited on a cold substrate turns to ice. In this paper, we present general governing equations to describe water droplet freezing on a solid substrate by accounting for the physical properties of each phase present, namely the liquid and ice, in addition to the solid substrate. The approach, which takes advantage of the full mean curvature expression of both the droplet–air and liquid–ice interfaces, disjoining pressure, the Gibbs–Thomson effect, natural convection and the substrate thermal and physico-chemical properties, enables us to model a more realistic frozen droplet shape, without a prior assumption for the freezing growth angle. In addition to correctly predicting the freezing time, we capture both qualitatively and quantitatively the key experimentally observed features during water droplet freezing such as volume expansion, concave ice front and the cusp singularity. Furthermore, the proposed equation for the tip angle seems to explain its experimentally observed variability.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| 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".