Bubble growth from first principles
Bibliographic record
Abstract
We consider the simplest relevant problem in the foaming of molten plastics: the growth of a single bubble in a highly viscous Newtonian fluid without interference from other bubbles. This problem has defied accurate solution from first principles. Classical approaches from first principles have neglected the temperature rise in the surrounding fluid, and we find that this oversimplification greatly accelerates growth prediction. We use transport phenomena to analyze the growth of a solitary bubble, expanding under its own pressure. We consider a bubble of ideal gas growing without the accelerating contribution from mass transfer into the bubble. We find that bubble growth depends upon nucleus radius and nucleus pressure. We begin with a detailed examination of the classical approaches. Our failure to fit data with these approaches sets up the second part of our paper, a novel exploration of the essential decelerating role of viscous heating. We explore both isothermal and adiabatic expansions, and also the decelerating role of surface tension. The adiabatic analysis accounts for the slight deceleration due to the cooling of the expanding gas, which depends on gas polyatomicity. We explore the pressure profile, and the components of the extra stress tensor, in the surrounding fluid. These stresses can be frozen into foamed plastics. We find that our new theory compares well with measured size, when the nucleus radius, nucleus pressure, and melt viscosity are fitted. We include a detailed dimensional worked example to help process engineers with foam design.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".