Enter process and composition data
Sample scenario comparison
| Scenario | Temperature | pH | aw | Sugar (mol/L) | Amino (mol/L) | Apparent constant | BI after 60 min |
|---|---|---|---|---|---|---|---|
| Mild drying blend | 110 °C | 6.2 | 0.45 | 0.1 | 0.08 | 1.2854e-6 | 5.4386 |
| Roasted matrix | 140 °C | 7.2 | 0.62 | 0.25 | 0.18 | 1.9910e-4 | 53.6077 |
| High heat alkaline | 165 °C | 8.1 | 0.68 | 0.35 | 0.24 | 1.6578e-3 | 99.7569 |
These rows are illustrative only. They use the same model form included in this calculator.
Model equations
1) Temperature dependence
k(T) = A × exp( -Ea / (R × T) )
2) Apparent Maillard rate term
k_app = k(T) × [Sugar]^m × [Amino]^n × exp(β × (pH - 7)) × exp( -((a_w - a_w,opt)^2) / (2σ^2) )
3) Browning index projection
Linear: BI(t) = BI0 + k_app × t
Saturating: BI(t) = BImax - (BImax - BI0) × exp(-k_app × t)
Symbols
A is the pre-exponential factor, Ea is activation energy, R is the gas constant, T is absolute temperature, m and n are empirical orders, β controls pH sensitivity, and the Gaussian water activity term centers the rate around an optimum moisture range.
Workflow
- Enter temperature, time horizon, and the matching units.
- Provide Arrhenius constants from literature or fitted plant data.
- Enter reducing sugar and amino concentrations with empirical orders.
- Set pH, pH sensitivity, water activity, optimum water activity, and spread.
- Choose a linear or saturating browning model.
- Press Calculate reaction rate to show the result above the form.
- Review the summary cards, comparison table, and graph.
- Use the CSV or PDF buttons to export the run.
Common questions
1) What does this calculator estimate?
It estimates an apparent Maillard browning rate from temperature, composition, pH, moisture, and time. It is meant for comparative process design, screening, and teaching, not direct regulatory release decisions.
2) Is the Maillard reaction really first order?
Not always. Real systems can show mixed, shifting, or diffusion-limited behavior. This tool lets you tune empirical orders for sugar and amino reactants, then wraps them into an apparent kinetic model.
3) Why is water activity handled with an optimum curve?
Maillard browning often increases toward an intermediate moisture range and falls when systems are too dry or too wet. The Gaussian term is a practical way to represent that non-linear behavior.
4) What is a good source for A and Ea values?
Use literature for similar foods, model systems, or your own fitted pilot data. Values vary widely with sugars, amino acids, pH, matrix structure, and how browning is measured.
5) What does the Q10 value mean here?
Q10 is the predicted rate multiplier for a ten-kelvin rise near the selected temperature. It helps compare sensitivity to heating when you keep the same fitted activation energy.
6) Which browning model should I choose?
Choose linear for short runs or when browning stays far from saturation. Choose saturating when the browning signal approaches a practical ceiling or plateau during the process.
7) Can I use mass fractions instead of molar concentration?
You can, but only if you fit A, m, and n consistently to that basis. Mixing units between calibration and prediction will distort the apparent constant and projected browning index.
8) Does this include caramelization or lipid oxidation?
No. This calculator targets Maillard-type browning only. Caramelization, ascorbic acid degradation, enzymatic browning, and oxidation may contribute color too and should be modeled separately.