Mass Advection–Diffusion in Creeping Flow Through an Orifice Plate: A Model for Nanoporous Atomically Thin Membranes
Bibliographic record
Abstract
Abstract Continuum transport equations are commonly applied to nanopores in atomically thin membranes for simple modeling. Although these equations do not apply for nanopores approaching the fluid or solute molecule size, they can be reasonably accurate for larger nanopores. Relatively large graphene nanopores have applications in small particle filtration and appear as unwanted defects in large-area membranes. Solute transport rates through these nanopores determine the rejection performance of the membrane. Atomically thin membranes commonly operate in a regime where advection and diffusion both contribute appreciably to transport. Solute mass transfer rates through larger nanopores have previously been modeled by adding continuum estimates for pure diffusion and pure advection through an infinitesimally thick orifice plate, as if the separate contributions were independent. We show here that estimating the transport rate in this way is accurate to within 30%. We further derive an expression for the net mass transfer rate in advection–diffusion through an infinitesimal thickness orifice plate at low Reynolds numbers that is accurate to within 1% for positive Péclet numbers (where diffusion is in the same direction as advection) and applies for negative Péclet numbers as well. Based on our expression, we devise an equation for the net mass transfer rate in creeping flow through orifice plates of arbitrary thickness that matches finite volume calculations to within 3% for positive Péclet numbers. These simple but accurate analytical equations for mass transfer rates in creeping flow through an orifice plate are useful tools in constructing approximate transport models.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.002 |
| 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 source (direct Gemma or distilled Codex), 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".