Critical entry pressure of a droplet pinning over multitude of pore openings
Bibliographic record
Abstract
Porous membranes filter by the virtue of their pore sizes in relation to the sizes of dispersals. While this is essentially true for solid dispersals, it needs to be reframed when dispersals are droplets. That is, without the existence of other selectivity criterion (other than pore sizes), droplets are prone to permeation, irrespectively. Fortunately, this extra criterion exists via the use of interfacial phenomena. That is, if the materials of the membrane are cast such that they are nonwetting with respect to droplets, interfaces are formed at pore openings that prevent droplets from permeation if the operating pressure is kept smaller than the entry pressure. Therefore, it is important to estimate such critical entry pressure under the different wettability conditions and droplet to pore ratios. Previous works have looked at droplets pining over single pore openings. In this work, the case in which relatively larger size droplets pin over multiple pore openings is investigated theoretically and via the tools of computational fluid dynamics. An exact formula is derived that account for the volumes of that part of the droplet hanging at the pore openings. An approximate formula is also highlighted that ignores this volume and compares very well with the exact formula. This derivation is based on the assumption that the droplets maintain their spherical shape, which is typically the case for smaller size droplets in produced water applications. The study shows that a pining droplet permeates first through the largest size pore until its size matches the critical size associated with the next larger pore opening when it starts to permeate.
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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 | 0.000 |
| 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 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".