Simulations of Droplet Coalescence in Simple Shear Flow
Bibliographic record
Abstract
Simulating droplet coalescence is challenging because small-scale (tens of nanometers) phenomena determine the behavior of much larger (micrometer- to millimeter-scale) droplets. In general, liquid droplets colliding in a liquid medium coalesce when the capillary number is less than a critical value. We present simulations of droplet collisions and coalescence in simple shear flow using the free-energy binary-liquid lattice Boltzmann method. In previous simulations of low-speed collisions, droplets coalesced at unrealistically high capillary numbers. Simulations of noncoalescing droplets have not been reported, and therefore, the critical capillary number for simulated collisions was unknown. By simulating droplets with radii up to 100 lattice nodes, we determine the critical capillary number for coalescence and quantify the effects of several numerical and geometric parameters. The simulations were performed with a well-resolved interface, a Reynolds number of one, and capillary numbers from 0.01 to 0.2. The ratio of the droplet radius and interface thickness has the greatest effect on the critical capillary number. As in experiments, the critical capillary number decreases with increasing droplet size. A second numerical parameter, the interface diffusivity (Péclet number) also influences the conditions for coalescence: coalescence occurs at higher capillary numbers with lower Péclet numbers (higher diffusivity). The effects of the vertical offset between the droplets and the confinement of the droplets were also studied. Physically reasonable results were obtained and provide insight into the conditions for coalescence. Simulations that match the conditions of experiments reported in the literature remain computationally impractical. However, the scale of the simulations is now sufficiently large that a comparison with experiments involving smaller droplets (≈10 μm) and lower viscosities (≈10(-6) m(2)/s, the viscosity of water) may be possible. Experiments at these conditions are therefore needed to determine the interface thickness and Péclet number that should be used for predictive simulations of coalescence phenomena.
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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 | 0.001 |
| 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".