Simulation of Time-Lag Permeation Experiments Using Finite Differences
Bibliographic record
Abstract
Membrane-based pressure driven processes are used in an increasing number of applications.To properly design membrane applications, it is necessary to have a good estimate of membrane properties.To characterize membrane permeation properties, the time-lag method is commonly used.A study has been undertaken to gain a deeper understanding on the accuracy of the time-lag method under realistic boundary conditions using numerical methods.Numerical simulations offer the opportunity to obtain a solution to the Fick's diffusion equation under various boundary conditions and for nonlinear sorption behaviour for which analytical solutions are difficult or impossible to obtain.This paper is mainly concerned with the selection of the optimal finite difference scheme for solving the Fick's diffusion equation that leads to the accurate determination of the membrane time lag.Pressure responses in the upstream and downstream reservoirs at both membrane interfaces are determined from the concentration gradients.The concentration gradient at the upstream side of the membrane is initially very steep and to accurately extract membrane properties, it is important to predict it very accurately.Simulation results for the prediction of concentration profiles and gradients at both interfaces are compared with known benchmark analytical equations to assess the precision of numerous numerical schemes where the effect of mesh size and time step is quantified.Results show that a variable mesh size is required to predict accurately the concentration gradient at the upstream interface.The choice of a variable mesh size scheme is important as a compromise must be struck between the smallest mesh size and the time step as it greatly impacts on the computation time.Results also showed that both the implicit and explicit finite difference schemes gave very similar results.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".