Modelling of cross‐flow microfiltration of dye‐loaded activated carbon in a ceramic tubular membrane module
Bibliographic record
Abstract
A hybrid process involving adsorption followed by microfiltration is a less energy‐intensive alternative for treatment of textile effluent. Modelling of microfiltration of dye‐loaded activated carbon in a tubular module is important for design and scale‐up. In this work, a simple kinetic model for cake removal during microfiltration in a tubular module is derived from first principles.. Reactive black dye exhibits the highest flux decline rate among the four different dyes. Cake layer thickness is less than 1 % of the channel diameter for different operating conditions. The mathematical analysis is extended to predict the limiting pressure. Cake removal rate is in the range of 0.01–0.05 Pa−1 · s−1for different dyes, lowest for reactive black and highest for reactive brown. The cake is thickest (14 μm) for reactive black, compared to other dyes at 104 kPa and 100 L/h cross‐flow rate. Cake resistance of black dye is 1.5 times the membrane hydraulic resistance at a 50 L/h crossflow rate and 104 kPa, and it is the highest among all the dyes analyzed. Simulation shows that steady state permeate flux increases with Reynolds number at higher transmembrane pressure whereas it varies insignificantly at lower pressure. Attainment of steady state is delayed for a lower cake removal constant. For yellow dye, steady state is achieved at 15 min forkr = 0.1 Pa−1 · s−1and beyond 1 h forkr = 0.1 Pa−1 · s−1. Cake compressibility has a stronger influence on limiting transmembrane pressure compared to cake removal rate at higher Reynolds numbers.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.002 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".