A Mathematic Model for Direct Causticization of Na<sub>2</sub>CO<sub>3</sub> with TiO<sub>2</sub> in a Semi‐batch Reactor
Bibliographic record
Abstract
Abstract A mathematic model was developed for direct causticization of sodium carbonate with titanium dioxide in a semi‐batch reactor. The model predictions of the titanate yield and pentatitanate yield showed a reasonable agreement with the experimental data from a pilot‐scale fluidized bed operating in semi‐batch mode. The rate constant of the present model was generally consistent with those obtained from the small‐scale batch experiments in the literature. A new rate constant considering carbonate conversion to pentatitanate was introduced. All the results provided support that the solid‐state direct causticization of sodium carbonate with titanium dioxide in a semi‐batch fluidized bed follows the shrinking‐core diffusion model.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 teacher head, 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".