Dynamic Interaction between a Millimeter-Sized Bubble and Surface Microbubbles in Water
Bibliographic record
Abstract
The coalescence between microbubbles and millimeter-sized bubbles is an elementary process in various industrial applications such as froth flotation and wastewater treatment. Fundamental understanding of the coalescence behavior between two colliding bubbles requires knowledge of water drainage from the thin liquid film between the deformable air-water surfaces, a simple phenomenon with high complexity in physics because of the interplay of surface forces, hydrodynamic drainage, and surface rheology. In this work, we performed simultaneous measurements of the interaction force and spatial thin-film thickness during the collision between a millimeter-sized bubble (radius 1.2 mm) and surface microbubbles (radii between 30 and 700 μm) using our recently developed dynamic force apparatus. The interaction force during the collision agrees well with the prediction from the Stokes-Reynolds-Young-Laplace model with the tangentially immobile boundary condition at the air-liquid interface. However, the measured coalescence times for different bubble sizes are shorter than the model predictions, possibly caused by a rapid drainage behavior along with the loss of symmetry of the thin liquid film. In dozens of experimental runs, the bubbles coalesced at a critical film thickness of 25 ± 15 nm, which agrees reasonably well with the predicted rupture thickness using attractive van der Waals interaction force. These results suggest that the nonsymmetric drainage process, rather than the rupture thickness, contributes to the scattering of the experimental coalescence time between two fast-colliding air bubbles. Furthermore, our results suggest that smaller surface bubbles (30-100 μm) are more effective for the attachment onto a large bubble as the coalescence time decreases considerably when the microbubbles are smaller than 100 μm.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".