A general form of capillary rise equation in micro-grooves
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Bibliographic record
Abstract
Micro-grooves are a crucial feature in many applications, such as microelectro-mechanical systems, drug delivery, heat pipes, sorption systems, and microfluidic devices. Micro-grooves utilize capillary action to deliver a liquid, with no need for an extra pumping device, which makes them unique and desirable for numerous systems. Although the capillary action is well studied, all the available equations for the capillary rise are case-specific and depend on the geometry of the groove, surface properties, and the transport liquid. In this study, a unified non-dimensional model for capillary rise is proposed that can accurately predict the capillary rise for any given groove geometry and condition and only depends on two parameters: contact angle and characteristic length scale, defined as the ratio of the liquid-vapor to the solid-liquid interface. The proposed model is compared against data from the literature and can capture the experimental results with less than 10% relative difference. The effect of the grooves' height, width, and contact angle is investigated and reported. This study can be used for a unified approach in designing heat pipes, capillary-assisted evaporators for sorption systems, drug delivery micro-fluidic devices, etc.
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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 it