Analytical Determination of Viscous Permeability of Fibrous Porous Media
Bibliographic record
Abstract
In this study, the permeability of ordered fibrous media towards normal and parallel flow is determined analytically. In this approach, porous material is represented by a “unit cell” which is assumed to be repeated throughout the media. Several fiber arrangements including: touching and non-touching arrays are considered. Modeling 1D touching fibers as a combination of Channel-like conduits, a compact relationship is proposed to predict permeability. Employing an integral technique and assuming a parabolic velocity profile within the unit cells, analytical relationships are developed for pressure drop for rectangular arrangements. The developed models are successfully compared with existing experimental data collected by others for square arrangement over a wide range of porosity. Due to the random nature of the porous micro structures, determination of exact permeability of real fibrous media is impossible. However, the analyses developed for ordered unit cells enable one to predict the trends observed in experimental data. Moreover, it is shown that the proposed normal flow permeability of square unit cell serves as a lower bound for the permeability of fibrous media. The effects of unit cell aspect ratio and fibers diameter on the permeability are also investigated. It is noted that with an increase in the aspect ratio the normal permeability decreases while, the parallel permeability remains constant. It is also shown that the permeability of fibrous media is related to the diameter of fibers squared.
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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".