The Role of Concentration Polarization with Concentration Dependent Diffusion Coefficient in Polymeric Membrane During Pervaporation
Bibliographic record
Abstract
The increase of the diffusion coefficient, due to its concentration dependency, can strongly increase the mass transfer rate through the membrane. Accordingly, the negative effect of the mass transfer resistance of the polarization layer can essentially be increased on the separation efficiency, especially in the case of low solute concentration in the feed phase. This effect can also exist at high solute concentration at extremely high pervaporation rate as it is illustrated by the case study. The simultaneous effect of the concentration polarization and membrane layers is discussed in this paper in case of exponentially or linearly concentration dependent diffusion coefficient. Mass transfer rate, enrichment and the polarization modulus are expressed in implicit, closed mathematical equations involving the transport parameters of the two layers, i.e.the kL, Pe, km, H values. How the increasing diffusion coefficient affects the concentration distribution in the polarization and the membrane layers and due to it, the mass transfer rate, enrichment or the polarization modulus, indicating the effect of the polarization layer, is discussed. It is shown how strongly the dimensionless plasticizing coefficient can decrease the polarization modulus and can affect the concentration distribution in the polarization and the membrane layers as well as the ratio of the diffusion dependent mass transfer rate to that without plasticizing effect, namely if . The case study illustrates the effect of the external mass transfer resistance on the mass transfer rate and on the concentration distribution in the case of high value of a plasticization coefficient.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 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".