Snapshot 1: simulated vitamin C, AA and DHAA relative concentration versus time curves during a hypothetical conventional low-temperature, long-time (LTLT) pasteurization process

Snapshot 2: simulated vitamin C, AA and DHAA relative concentration versus time curves during storage at a constant temperature

Snapshot 3: simulated vitamin C, AA and DHAA relative concentration versus time curves during hypothetical food storage under fluctuating rising temperature

Snapshot 4: simulated partially oxidized vitamin C, AA and DHAA relative concentration versus time curves during hypothetical food storage under fluctuating falling temperature

In fresh foods, particularly fruit juices, vitamin C is naturally occurring ascorbic acid (AA), which is also an antioxidant. Upon oxidation, which is accelerated by high processing and storage temperatures, the AA is converted into dehydroascorbic acid (DHAA), which subsequently degrades to other compounds. Since DHAA is biologically active as a vitamin, being converted back to AA in the body, the effective or total vitamin C content of a processed or stored food is the sum of its AA and DHAA contents.

Assuming that all three underlying processes follow fixed order kinetics, the relative AA and DHAA concentrations are the solutions of the two rate equations

and

where

is the instantaneous temperature, the

are the corresponding rate constants and the

are the corresponding reactions' orders, assumed to be temperature independent. In most cases, based on experimental evidence, it can be assumed that

, which simplifies the model [1, 2]. The default boundary conditions are that the initial AA concentration is 1 and that of the DHAA is 0. For a partially oxidized system, the AA concentration will be less than 1 and that of the DHAA greater than 0. The rate constants' temperature dependence is assumed to follow the exponential model

,

where

is the rate constant at an arbitrary reference temperature

, in a pertinent temperature range. Both

and

are in °C. This model is a simpler substitute for the Arrhenius equation [3]. Once calculated, the effective or total vitamin C concentration is calculated as the sum of the AA and DHAA concentrations.

By clicking on the "mode of loss" setter, this Demonstration generates hypothetical temperature histories (profiles) similar to those encountered during food heat preservation or storage (top plot) and calculates and plots the corresponding vitamin C, AA and DHAA concentration curves (bottom plot).

The reference temperature

for the exponential model and the kinetic parameters AA and DHAA, namely the triplets

,

,

;

,

,

; and

,

,

, are selected with sliders. For a case where some DHAA is already present initially, the

slider is set to the appropriate fraction, for example, 0.1, in which case the initial AA concentration will be automatically set to

, that is, 0.9.

Set the plot time and temperature scales with the

and

sliders. By changing the position of the

slider, three black points are moved simultaneously on the three curves and the numerical values of the momentary vitamin C, AA and DHAA concentrations are displayed.

The emphasis of this Demonstration is to introduce the model and calculation procedure, not to describe any particular food or foods. Thus, not all parameter combinations and resulting generated vitamin C, AA and DHAA concentration versus time curves necessarily have a counterpart in reality, and conversely, there may be food systems that are not represented by the model.

[1] M. C. Vieira, A. A. Teixeira and C. L. M. Silva, "Mathematical Modeling of the Thermal Degradation Kinetics of Vitamin C in cupuaçu (

*Theobroma grandiflorum*) Nectar,"

*Journal of Food Engineering*,

**43**(1), 2000 pp. 1–7.

doi:10.1016/S0260-8774(99)00121-1.

[2] L. Verbeyst, R. Bogaerts, I. Van der Plancken, M. Hendrickx and A. Van Loey, "Modelling of Vitamin C Degradation during Thermal and High-Pressure Treatments of Red Fruit,"

*Food Bioprocess Technology*,

**6**(4), 2013 pp. 1015–1023.

doi:10.1007/s11947-012-0784-y.

[3] M. Peleg, M. D. Normand and M. G. Corradini, "The Arrhenius Equation Revisited,"

*Critical Reviews in Foods Science and Nutrition*,

**52**(9), 2012 pp. 830–851.

doi:10.1080/10408398.2012.667460.