Infinite series formulation for slip flow through a finite thickness orifice plate
Bibliographic record
Abstract
Liquid transport through membrane nanopores is often modelled as creeping flow through a finite thickness orifice plate. Experiments and molecular simulations have revealed the importance of slip in such pores, where the diameter can be orders of magnitude smaller than the slip length for materials such as carbon nanotubes and graphene. Approximate hydrodynamic resistance models considering access resistance to the pore and fully developed slip flow within the pore are sometimes applied to estimate flow rates. While this approach is very accurate without slip, it can result in large errors for long slip lengths. Even with large slip lengths, flow development in the entry/exit regions contribute significant pressure drops that should be accounted for. In this paper, we extend an infinite series formulation for no-slip creeping flow through a finite thickness orifice plate to slip flow through the same geometry. We develop an algebraic system of equations for the series coefficients that can be efficiently computed to determine the velocity and pressure fields for the selected pore aspect ratio and slip length. Accurate volume flow rates can be quickly calculated, and are tabulated for convenience. We refine the approximate hydrodynamic resistance model for this flow to include losses in the entry region and obtain a fit for the volume flow rate accurate to within 2.5% for all slip lengths and pore aspect ratios.
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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 | 0.001 | 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 | 0.001 |
| 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".