Development and experimental validation of a mathematical model for fluoride-removal filters comprising chemically treated mineral rich carbon
Bibliographic record
Abstract
Excessive fluoride intake can lead to dental and skeletal fluorosis, among other health issues. Naturally occurring fluoride and industrial runoff can result in concentrations far exceeding the World Health Organization’s recommended limits in water supplies. In this study, we derive a model incorporating the dominant mechanisms governing fluoride removal from drinking water using the two adsorbents mineral-rich carbon (MRC) and chemically treated mineral-rich carbon (TMRC). Using both new and previously published experimental data, we validate the model for MRC, TMRC, and their mixture, using both batch and column data. Despite the filters containing approximately 40:1 MRC:TMRC ratio by mass, we find that TMRC dominates fluoride removal, while MRC contributes at early and late times. The full column model, which uses parameters from isotherm batch studies, achieves excellent agreement with experimental breakthrough data across varying inlet concentrations and flow rates (R 2 > 0 . 991 , SSE < 0 . 0632 ). Motivated by this, we propose a reduced model based solely on TMRC adsorption, with a single fitting parameter, which still performs well across all breakthrough curves (R 2 > 0 . 983 , SSE < 0 . 117 ). The simplicity of this model means that it is straightforward and inexpensive to work with numerically. In both models, batch and column behaviours are reconciled and, for the case of breakthrough curves with varying inlet concentrations, a set of globally optimised parameters is found. The strong agreement with experimental data supports the model’s robustness and reinforces the physical interpretability of its parameters. These models for MRC and TMRC provide a foundation for filter optimisation and future efforts aimed at improving fluoride removal in resource-limited settings.
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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 | 0.000 | 0.000 |
| 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".