Bounds on the spreading radius in droplet impact: the inviscid case
Bibliographic record
Abstract
We consider the classical problem of droplet impact and droplet spread on a smooth surface in the case of an ideal inviscid fluid. We revisit the rim–lamella model of Roisman et al. (Roisman et al . 2002 Proc. R. Soc. Lond. A 458 , 1411–1430 ( doi:10.1098/rspa.2001.0923 )). This model comprises a system of ordinary differential equations (ODEs); we present a rigorous theoretical analysis of these ODEs, and derive upper and lower bounds for the maximum spreading radius. Both bounds possess a W e 1 / 2 scaling behaviour, and by a sandwich result, the spreading radius itself also possesses this scaling. We demonstrate rigorously that the rim–lamella model is self-consistent: once a rim forms, its height will invariably exceed that of the lamella. We introduce a rational procedure to obtain initial conditions for the rim–lamella model. Our approach to solving the rim–lamella model gives predictions for the maximum droplet spread that are in close agreement with existing experimental studies and direct numerical simulations.
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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 | 0.002 | 0.014 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".