Capillary-Driven Ejection of a Droplet from a Micropore into a Channel: A Theoretical Model and a Computational Fluid Dynamics Verification
Bibliographic record
Abstract
In this work, the problem of re-ejection of a permeating droplet through a membrane pore back to the feed channel when the transmembrane pressure (TMP) becomes zero is investigated. This problem is important in the context of oily water filtration using membranes. In particular, in the novel periodic feed pressure technique (PFPT), which has been proposed to combat membrane fouling, the TMP alternates between the operating value and zero in a periodic manner. During the period in which TMP is high, filtration occurs, and when it is zero, cleaning commences. We are particularly interested in what happens to a droplet, initially undergoing permeation, when the TMP becomes zero. It is evident that when the TMP is zero the meniscus inside the pore reverses its motion toward the feed channel rather than toward the permeate side by the action of interfacial tension force. A theoretical model is built to determine the rate at which the meniscus inside the pore advances when the TMP is zero. The conservation of momentum equation is used to establish a one-dimensional model that updates the location of the meniscus with time. The derived model considers both quasi-static and dynamic scenarios. In addition, the model accounts for both the viscosity contrast between the two fluids, as well as the gravity. A computational fluid dynamics (CFD) simulation has been built to provide a framework for model verification and validation. The model, based on quasi-static conditions, provides an overall similar trend to that obtained via CFD analysis. Nevertheless, the quasi-static model predicts a more rapid meniscus advancement inside the pore than the CFD simulation. When the dynamic contact angle is incorporated, very good matching is observed.
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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) | 0.000 | 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".