Development and experimental validation of a mathematical model for fluoride-removal filters comprising chemically treated mineral rich carbon

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.