On the Applicability of the Grace Curve in Practical Mixing Operations
Bibliographic record
Abstract
Abstract Athough the Grace curve is often used to select the material components and optimal flow rates in blending operations, its validity for industrial mixing practice remains to be seen. Among other reasons, the flow field in industrial mixers is not homogeneous. This causes the actual shear/ elongation rate imposed upon a (moving) droplet to be time‐dependent. To investigate the importance thereof, analytical models are used which describe the droplet stretching rate as a function of the droplet shape, viscosity ratio and time‐varying capillary number. Both experiments and model predictions show that droplet breakup can be caused by inhomogeneous flow fields, even if the average capillary number is sub‐critical. Moreover, the model predicts how the critical capillary number is influenced by a non‐spherical initial shape. At higher aspect ratios the critical capillary number can be reduced significantly, especially for higher viscosity ratio droplets.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".