The Critical Conditions for Coalescence in Phase Field Simulations of Colliding Droplets in Shear
Bibliographic record
Abstract
Simulations have been performed using the free-energy binary-liquid lattice Boltzmann method with sufficient resolution that the critical capillary number for coalescence was determined for collisions between droplets in simple shear with a small initial offset in the shear gradient direction. The simulations were used to study the behavior of the interacting interfaces and the film between them during collisions over a wide range of capillary numbers with emphasis on near-critical conditions. From these three-dimensional simulations with deforming interfaces, several features of the evolution of the film between the drops were observed. The critical film thickness was determined to be similar to the interface thickness, a power law described the dependence of the minimum film thickness on the capillary number in collisions without coalescece, and an inflection point was found in the dynamics of the minimum distance between drops that eventually coalesce. The rotation of the film and the flow in it were also studied, and a reversal in the flow was found to occur before coalescence. The mobility of the phase field was therefore important in the continued thinning of the film at the points of minimum thickness after the flow reversal. A comparison of the critical capillary number and critical film thickness in the simulations with the values for experiments in confined simple shear indicated that the effective physical radius of the simulated droplets was on the order of several micrometers. The results are significant for simulations of droplet interactions and emulsion flows in complex geometries and turbulence because they demonstrate the necessary scale of the computations and how parameters, such as the interface thickness and phase field mobility, should be selected for accurate results.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".