Mathematical modelling of coalescence of viscous particles: An overview
Bibliographic record
Abstract
Abstract Viscous particles of polymer melts and glasses coalesce under the action of surface tension. Resistance is due to viscosity, while inertia is not a contributing factor, with the Ohnesorge number being very high. Russian physicist Yakov Frenkel developed a model for neck growth during the initial stage of the merging process of two spherical particles, assuming uniform biaxial extensional flow. Frenkel's model was extended for prediction of neck size as a function of time to the completion of coalescence, expressed by an ordinary differential equation. The time t is expressed in dimensionless form as (tγ/ηR), where η, γ, and R denote the viscosity, surface tension, and particle radius, respectively. Models were also developed for viscoelastic effects, non‐isothermal conditions, and unequal diameter particles. For the coalescence of infinitely long cylinders, planar extensional flow is assumed. Other investigators presented numerical solutions of the Navier–Stokes equations, which include shear flow components, but the predictions of neck growth are not much different from those of the Frenkel‐based models. Comparisons to experiments are also discussed, involving polymers, glasses, animal tissue cells, and biomacromolecules. The models are also used in additive manufacturing applications for the determination of bonding and pore shrinkage.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".