TMRC: Chemically Treated Mineral-Rich Carbon
- TMRC is an aluminium hydroxide-coated derivative of mineral-rich carbon that enhances fluoride removal via a dominant ion-exchange reaction.
- It exhibits a capacity nearly 10 times greater than untreated MRC, making it the key reactive component in mixed-bed filters.
- Design trade-offs include balancing improved fluoride uptake against increased cost and clogging risk, guiding optimal water treatment strategies.
Chemically treated mineral-rich carbon (TMRC) is an aluminium-hydroxide-coated derivative of mineral-rich carbon (MRC) used for fluoride removal from drinking water. In the modeling literature on defluoridation filters, TMRC is treated as the dominant reactive component in mixed MRC–TMRC beds, despite a typical filter composition of approximately MRC:TMRC by mass. The recent mechanistic treatment of the subject develops a single chemically grounded framework that links batch isotherm and kinetic measurements to fixed-bed column breakthrough behavior, with the practical objective of improving fluoride-removal performance in resource-limited settings where excessive fluoride intake can lead to dental and skeletal fluorosis (Auton et al., 16 Jul 2025).
1. Material identity and relation to MRC
MRC is carbonised bone meal, also described as carbonised mammalian or avian bone meal or bone char. The later validation study states that about of MRC is hydroxyapatite, which is largely responsible for fluoride uptake. TMRC is produced by grinding down MRC and coating it with aluminium hydroxide, . The earlier model paper likewise treats TMRC as a derivative of MRC whose dominant chemistry is no longer controlled by bone-mineral sites, but by the aluminium-hydroxide coating (Auton et al., 16 Jul 2025, Auton et al., 2023).
The two materials differ in both adsorption performance and filter engineering constraints. TMRC has a much smaller grain size than MRC, with TMRC reported at mm and MRC at mm. TMRC is also more expensive because of the aluminium coating. The smaller grain size raises clogging concerns, which is one reason a pure-TMRC filter is described as undesirable in practice (Auton et al., 16 Jul 2025).
| Material | Composition or treatment | Reported grain size |
|---|---|---|
| MRC | Carbonised bone meal; hydroxyapatite-based | mm |
| TMRC | MRC ground down and coated with | mm |
The literature consistently characterizes TMRC as the higher-capacity sorbent. The 2023 paper cites prior experimental capacities of about $150$ mg/g for TMRC and about $14$ mg/g for MRC, while the 2025 study reports a fitted TMRC adsorption capacity about ten times larger than that of MRC (Auton et al., 2023, Auton et al., 16 Jul 2025). This suggests that “treated” in TMRC denotes not merely a surface modification, but a change in the dominant adsorption chemistry and effective capacity class of the material.
2. Fluoride-removal chemistry and mechanistic interpretation
For TMRC, the dominant fluoride-removal mechanism is modeled as ion exchange, also described as ligand exchange or chemisorption, between fluoride and surface hydroxyl groups on the aluminium-hydroxide coating. The 2025 study represents this globally as
0
while the 2023 paper writes the same chemistry in species form as
1
In both formulations, TMRC is modeled as a single dominant reversible ion-exchange process (Auton et al., 16 Jul 2025, Auton et al., 2023).
The TMRC model explicitly neglects physisorption and dissolution–precipitation under the operating conditions considered. Physisorption is taken to be too weak under alkaline conditions, and dissolution–precipitation is omitted because the pH is near neutral to alkaline and the fluoride concentrations used are below thresholds for significant precipitation at 2. The later paper notes that some fluoride uptake may involve complexation or ligand exchange, but represents such effects globally through the single reversible reaction above. It also notes that released hydroxide may partly appear as 3 and partly as hydroxylated aluminate species such as 4, but does not include those dissolution effects in the model (Auton et al., 16 Jul 2025).
By contrast, MRC is modeled with two distinct mechanisms. The first is chemisorption or ion exchange with hydroxyapatite hydroxyl groups, written in the 2023 paper as
5
The second is physisorption via hydrogen bonding or electrostatic interactions, written as
6
This distinction is central to the literature’s rejection of a simple one-step Langmuir description as chemically incomplete for the mixed MRC–TMRC system (Auton et al., 2023).
A common misconception is that TMRC should be understood as merely “better MRC.” The mechanistic papers instead treat it as an aluminium-hydroxide-coated adsorbent whose governing reaction pathway differs qualitatively from the two-pathway hydroxyapatite-based picture used for MRC. The practical consequence is that TMRC’s role in a filter is not simply additive with MRC; it can dominate the overall fluoride-removal front.
3. Batch modeling of TMRC
The batch model for TMRC is the IE-TMRC model. It is formulated as a mass-action kinetic system: 7
8
Here 9 is the fluoride concentration in solution, 0 is the hydroxide concentration, 1 is the moles of adsorbed 2 per gram TMRC, 3 is the maximum adsorption capacity, 4 is bulk density, 5 is porosity, and 6, 7 are the forward and reverse rate constants. The initial conditions are
8
The study uses 9 g/l for isotherm experiments and 0 g/l for kinetic experiments (Auton et al., 16 Jul 2025).
The equilibrium isotherm is obtained by setting the ODE to steady state, yielding
1
with
2
and
3
For kinetics, the same study rewrites the ODE as a quadratic-form Riccati equation,
4
with
5
6
7
A closed-form solution is then given for 8, and the integrated constraint
9
is used to infer 0 from kinetic data (Auton et al., 16 Jul 2025).
The importance of this formulation is not merely algebraic. It makes TMRC a chemically specific adsorbent model with explicit hydroxide coupling, rather than a generic single-site sorption fit. That specificity becomes central when the same intrinsic parameters are propagated into the column model.
4. Fixed-bed filter model and reconciliation of batch with column behavior
For practical fluoride-removal filters, the literature extends the batch chemistry to a one-dimensional advection–diffusion–reaction model for a mixed MRC–TMRC bed. The governing equations for fluoride and hydroxide in the 2025 paper are
1
2
with
3
4
5
The column is treated as a homogeneous porous medium with plug flow, and the transport equations use Danckwerts inflow and zero-flux outflow boundary conditions (Auton et al., 16 Jul 2025).
The earlier paper presents the same mixed-bed concept under the combined chemically based model, denoted CB-MT, with transport governed by advection and effective diffusion or dispersion, and with MRC entering through 6 and 7 while TMRC enters through 8 (Auton et al., 2023). Across both papers, the key conceptual step is the same: batch experiments identify intrinsic reaction parameters and capacities, and those same parameters are then inserted into the column transport–reaction PDEs. The resulting breakthrough behavior is therefore interpreted as an emergent consequence of transport combined with the same underlying chemistry measured in batch systems (Auton et al., 16 Jul 2025).
The 2025 paper also proposes a reduced model that sets 9 and retains only TMRC chemistry. This reduction is significant because it preserves the dominant reactive pathway while collapsing the breakthrough fit to a single fitting parameter. A plausible implication is that the mixed-bed system is, to leading order, transport-limited around a chemically dominant TMRC front, with MRC providing corrections mainly outside the central breakthrough regime.
5. Experimental basis, parameter estimation, and validation
The empirical basis for the TMRC literature comprises both batch and column experiments. In the 2025 validation study, batch isotherms used an adsorbent dose of 0 g/l and initial fluoride concentrations from 1 to 2 mol/l, corresponding to 3 to 4 mg/l. Kinetic experiments used 5 g/l adsorbent, with 6 mol/l 7 mg/l for MRC and 8 mol/l 9 mg/l for TMRC. No competing ions were present, the pH was 0, and the temperature was about 1 K. Column experiments used a glass cylinder of internal diameter 2 m and length 3 m, packed to a bed height of 4 m with an approximately 5 MRC:TMRC mass ratio. Flow rates were 6, 7, and 8 l/day; inlet fluoride concentrations were 9, 0, and 1 mg/l with 2 mg/l uncertainty; and outlet fluoride was measured over time by ion-selective electrode (Auton et al., 16 Jul 2025).
Parameter estimation differs between batch and column models. For batch fitting, GlobalSearch in MATLAB was used with an objective function equal to the absolute difference between model predictions and data points. Because GlobalSearch is stochastic, multiple runs of order 3 were performed and the best SSE or highest 4 solution was reported. For columns, lsqcurvefit was used, with manually constrained physically reasonable bounds. For varying inlet concentration, 5 values were fitted globally across the three breakthrough curves; for varying flow rate, 6 values were fitted separately because rate constants depend on hydrodynamics (Auton et al., 16 Jul 2025).
| Model or dataset | Key fitted values | Reported accuracy |
|---|---|---|
| MRC batch | 7, 8 mol/g, 9, $150$0 | Isotherm: SSE $150$1, $150$2; kinetic: SSE $150$3, $150$4 |
| TMRC batch | $150$5 mol/g, $150$6, $150$7 | Isotherm: SSE $150$8, $150$9; kinetic: SSE $14$0, $14$1 |
| Full mixed-bed column | For varying inlet concentration: $14$2, $14$3, $14$4 | $14$5, SSE $14$6 |
| Reduced TMRC-only column | For varying inlet concentration: $14$7 | $14$8, SSE $14$9 |
For varying flow rate, the full model fitted 00, 01, and 02, while the reduced model fitted 03 (Auton et al., 16 Jul 2025). The earlier 2023 paper, using GlobalSearch throughout, likewise concluded that the chemically based model fits column breakthrough well, whereas Langmuir fits poorly (Auton et al., 2023).
These results establish two separate points. First, TMRC’s fitted maximum capacity is substantially larger than MRC’s. Second, the predictive success of the reduced TMRC-only breakthrough model shows that a chemically specific simplification can remain accurate without reverting to a chemically agnostic Langmuir law.
6. Dominance of TMRC, design trade-offs, and open directions
The principal physical conclusion is that TMRC dominates fluoride removal even though it is present at only about 04 of the filter mass. The papers give several mutually reinforcing reasons. TMRC has a much larger capacity, with 05 about an order of magnitude greater than 06. Its forward reaction rate is also much larger than the MRC rates in the fitted column model. The equilibrium constant is large, with 07, which the 2025 paper interprets as strongly forward-favored, quasi-irreversible chemisorption. Spatial and temporal analysis further shows that TMRC saturates first and controls the breakthrough front, while MRC contributes at early and late times (Auton et al., 16 Jul 2025).
The reported outlet quantities provide a particularly sharp illustration. At about 08 hours, 09 is already at approximately 10 of equilibrium, 11 is above 12, but 13 is only about 14 utilized; 15 approaches full saturation only after roughly 16 hours. The 2025 paper also notes that the TMRC ion-exchange mechanism may suppress the MRC ion-exchange pathway, which helps explain why the effective MRC rates become small in the mixed bed (Auton et al., 16 Jul 2025). This suggests that TMRC is not simply the stronger of two parallel adsorbents, but the adsorbent that sets the filter’s operational timescale.
The filter-design implications are correspondingly mixed. A small TMRC fraction can deliver most of the fluoride-removal performance. Increasing TMRC improves capacity, but raises cost and clogging risk because TMRC is finer-grained and more expensive. Optimal design is therefore framed as a balance among TMRC content, bed length, flow rate, and packing structure. The reduced TMRC-only model is described as straightforward and inexpensive to work with numerically, and as attractive for predicting filter lifespan and optimizing design in resource-limited settings such as rural West Bengal (Auton et al., 16 Jul 2025).
The literature also identifies several directions for further work: varying the MRC:TMRC ratio, changing filter length and area, periodic agitation or mixing to extend lifespan, and including competition from 17 and other ions at broader pH ranges (Auton et al., 16 Jul 2025). The earlier paper had already suggested studying varying filter length, varying flow rate, and simplified one-parameter prediction for lifespan and optimization (Auton et al., 2023). Taken together, these directions define TMRC not as a finished material platform, but as a mechanistically characterized sorbent whose practical deployment depends on coupled chemical, hydraulic, and economic constraints.