Modelling of porous core–shell adsorbent particles with various morphologies suspended in batch adsorber from analytical solutions of diffusion equations
Bibliographic record
Abstract
Abstract Considering both intra‐particle diffusion and film resistance for mass transfer, analytical solutions of transient concentration of adsorbate inside adsorbents with spherical, cylindrical, or slab‐type particles were derived for batch adsorbers by solving governing equations using the Laplace transform. Assuming Henry's or rectangular isotherm, the average concentration inside adsorbents as well as transient bulk concentration were also obtained for the particles with or without the inert core. Computations were performed to compare the results according to the shape of adsorbents by adjusting adsorbent loading, Biot number (Bi), and inert core thickness. Regardless of particle morphologies, steady‐state bulk concentration was only affected by adsorbent loading and inert core thickness, whereas the effect of Bi was confirmed from the decreasing reduction rate of adsorbate concentration with decreasing Bi. When diffusivity was dependent on time, time‐decaying diffusivity caused the increase in steady‐state concentration that was predicted by eigenfunction expansion. Experimental results using porous fibres by electrospinning were compared with the mathematical solution of a cylindrical adsorbent for the estimation of intra‐particle diffusivity. Using the solutions of the diffusion equation model, novel core–shell cylindrical adsorbents can be designed and synthesized as core–shell fibres by electrospinning with a coaxial nozzle to save the cost of the active shell layer. Such core–shell structured fibres can be adopted as adsorbents for novel batch adsorption processes and the present modelling results can be extended to other processes like fixed bed adsorbers.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| 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".