The kinetics of browning measured during the storage of onion and strawberry

Summary The kinetics of non-enzymatic browning of onion and strawberry during storage at different temperature (5, 15, 25, 35, 45 °C) and equilibrium relative humidities (33%, 44%, 53%) was measured. Colour formation in onion was observed by measuring absorbance versus time in aqueous extract solutions. Experimental results of colour formation of onion as a function of time for each level of water activity were best represented by a zero order kinetics, while anthocyanin degradation in strawberry followed a second order kinetics. Rate coefficients obtained in both cases showed an increase in the rate of the reactions with both temperature and water activity. With regard to temperature dependence of rate coefficients, statistical evidence suggest that in the case of colour formation in onion, the Williams-Landel-Ferry model is a better representation than Arrhenius. In the case of strawberry it was not possible to reach such conclusion in spite of a lower summation of residuals obtained with the WLF model.     

DYNAMIC AND STEADY-STATE RHEOLOGY OF AUSTRALIAN HONEYS AT SUBZERO TEMPERATURES

The rheology of 10 Australian honeys was investigated at temperatures ?15C to 0C by a strain‐controlled rheometer. The honeys exhibited Newtonian behavior irrespective of the temperature, and follow the Cox–Merz rule. G″/G′ and ω are quadratically related, and the crossover frequencies for liquid to solid transformation and relaxation times were obtained. The composition of the honeys correlates well (r² > 0.83) with the viscosity, and with 247 data sets (Australian and Greek honeys), the following equation was obtained: The viscosity of the honeys showed a strong dependence on temperature, and four models were examined to describe this. The models gave good fits (r ² > 0.95), but better fits were obtained for the WLF model using T_g of the honeys and µ_g= 10¹¹ Pa.s. The WLF model with its “universal values” poorly predicted the viscosity, and the implications of the measured rheological behaviors of the honeys in their processing and handling are discussed.     

On modeling changes in food and biosolids at and around their glass transition temperature range

Temperature‐induced mechanical and other changes in biosolids are regulated by three types of kinetics, depending on whether the material is in the glassy state, undergoing a transition, or fully plasticized. The transition itself can take place over a considerable temperature range, which in many food and biological systems happens to be the most pertinent to their functionality and stability. At the transition onset, the plot of stiffness vs. temperature has a downward concavity. It is reversed only at an advanced stage of plasticization after much of the stiffness has already been lost. Consequently, the WLF, Arrhenius, or any other model that implies a continuous upward concavity cannot account for changes in the transition region, and it is unsafe to use them to predict properties through extrapolation.

The mechanical changes in the transition region can be described by a model with the mathematical structure of Fermi's function. Its applicability has been demonstrated with published data on a variety of foods and biosolids. Because the plot of stiffness vs. moisture, or water activity, has the same general shape as that of the stiffness vs. temperature plot, it too can be described by a model with the same mathematical format.

Because moisture lowers the transition center temperature in a manner that can be described by a simple algebraic expression, the combined effects of temperature and moisture can be incorporated into a single general model. The latter can be used to create three‐dimensional displays of the stiffness‐temperature‐moisture characteristic relationships of biosolids at and around their transition. At temperatures well above that of the transition, though, where a plot of log stiffness vs. temperature has a clear upper concavity, this model is no longer applicable, and the changes are better described by the WLF or an alternative model.     

A kinetic model for whey protein denaturation at different moisture contents and temperatures

The denaturation of whey protein samples that had previously undergone heat-treatment for different times at different temperatures and moisture contents was analysed by differential scanning calorimetry (DSC), using the DSC enthalpy as a measure of residual undenatured protein. Data were fitted to first order irreversible or reversible kinetic expressions, and the resulting rate constants were found to increase with both temperature and moisture content. The whole data set was then fitted as a function of time, temperature and moisture content, with rate constants varying according to either Arrhenius or Williams-Landel-Ferry (WLF) kinetics and with selected fit parameters made empirical functions of moisture content. The best fits were obtained using reversible WLF kinetics, which could be further slightly simplified without loss of accuracy. The model provides a platform for single- and multi-objective drying trajectory optimisation with respect to protein denaturation in dairy products.     

The Arrhenius equation revisited

The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T(reference), the plot of Ln k(T) vs. 1/(T+b) will always appear almost perfectly linear. Both the modified Arrhenius model version having the arbitrary constant b, Ln[k(T)/k(T(reference)) = a[1/ (T(reference)+b)-1/ (T+b)], and the exponential model can faithfully describe temperature dependencies traditionally described by the Arrhenius equation without the assumption of a temperature independent "energy of activation." This is demonstrated mathematically and with computer simulations, and with reprocessed classical kinetic data and published food results.     

Viscosity and Specific Heat of Vegetable Oils as a Function of Temperature: 35°C to 180°C

The viscosities and specific heat capacities of twelve vegetable oils were experimentally determined as a function of temperature (35 to 180°?C) by means of a temperature controlled rheometer and differential scanning calorimeter (DSC). Viscosities of the oil samples decreased exponentially with temperature. Out of the three models (modified WLF, power law, and Arrhenius) that were used to describe the effect of temperature on viscosity, the modified WLF model gave the best fit. The specific heat capacity of the oil samples however increased linearly with increase in temperature. The equations developed in the study could be valuable for designing or evaluating handling and processing systems and equipment that are involved in the storage, handling and utilization of vegetable oils.     

Rheology of supersaturated sucrose solutions

Sucrose solutions, with concentrations near or superior to saturation, present high potentialities for the candy and pastry industries. Creep measurements under small stresses were done to obtain the rheological properties of highly concentrated sucrose solutions, since such solutions could be in a metastable state and tend to crystallise. The viscosities of these solutions, from 70.0% to 85.2% (w/w), were determined experimentally at different temperatures, from 0 to 90 °C. The temperature dependence of viscosity was studied using experimental and published data for, respectively, high and low concentrations (<70% (w/w)). Results showed that the Arrhenius model describes better the temperature dependence of viscosity for concentrations under saturation and in the high concentration regime the WLF model had a better predicting ability. The effect of concentration on viscosity was observed and included in the Arrhenius and WLF models’ parameters. The proposed models were able to successfully describe the data in the corresponding concentration range. These results can be used in predicting the viscosities of syrups for either process design or new products formulation.     

Viscosity Prediction of Starch Hydrolysates from Single Point Measurements

A mathematical model is presented which allows the accurate prediction of the viscosity-concentration-temperature relationship of starch hydrolysates. The model is valid in a dry substance range between 60% and 85% and in a temperature range between 20°C and 80°C. The only input the model requires is a single viscosity value at a defined concentration and temperature or the composition of the sample up to a degree of polymerization of 10. The model is based on the fact that the temperature dependence of the viscosity of a glass forming material, just above its glass transition temperature, can be descibed using the WLF kinetics. Hence, the viscosity is only dependent on the difference between the actual temperature and the glass transition temperature of each starch hydrolysate.     

Non‐Arrhenius and non‐WLF kinetics in food systems

The classic Arrhenius and WLF equations are commonly used to describe rate–temperature relations in food and biological systems. However, they are not unique models and, because of their mathematical structure, give equal weight to rate deviations at the low‐ and high‐temperature regions. This makes them particularly useful for systems where what happens at low temperatures is of interest, as in spoilage of foods during storage, or where the effect is indeed exponential over a large temperature range, as in the case of viscosity. There are systems, however, whose activity is only noticeable above a certain temperature level. A notable example is microbial inactivation, for which these two classical models must be inadequate simply because cells and spores are not destroyed at ambient temperature. For such systems a model that identifies the temperature level at which the rate becomes significant is required. Such an alternative model is Y = ln{1 + exp[c(T ? T _c)]} ^m, where Y is the rate parameter in question (eg a reaction rate constant), T_c is the marker of the temperature range where the changes accelerate, and c and m are constants. (When m = 1, Y at T ? T_c is linear. When m ≠ 1, m is a measure of the curvature of Y at T ? T_c.) This model has at least a comparable fit to published rate–temperature relationships of browning and microbial inactivation as well as viscosity–temperature data previously described by the Arrhenius or WLF equation. This alternative log logistic model is not based on the assumption that there is a universal analogy between totally unrelated systems and simple chemical reactions, which is explicitly assumed when the Arrhenius equation is used, and it has no special reference temperature, as in the WLF equation, whose physical significance is not always clear. It is solely based on the actual behaviour of the examined system and not on any preconceived kinetics. © 2002 Society of Chemical Industry     

纸塑包装中PCBs的迁移模型及效果评价

多氯联苯化合物种类繁多,无法逐一进行冗长的迁移试验,迁移模型不仅可以简化迁移研究,而且概括性强,适用范围广。文章基于"有限包装-有限食品"模型,考虑纸层与塑料层间的扩散系数,忽略其间分配系数的差异,建立迁移预测模型。并以Brandsch模型估算扩散系数,以定义式粗算分配系数,并分析迁移试验值与模拟预测情况的差异。对比结果显示,试验值变化的整体趋势与模型预测结果相符。迁移量均随着时间的延长而增加,且平衡时的迁移量随着温度的升高而加大,大多预测值明显略高于试验值。     

Dynamic mechanical thermal analysis of aqueous sugar solutions containing fructose, glucose, sucrose, maltose and lactose

The glass transition of glucose, fructose, lactose, maltose and sucrose solutions at maximum cryo-concentration was studied by Dynamic Mechanical Thermal Analysis (DMTA), using the disc bending technique. The glass transition temperatures were determined from the peaks in the loss modulus E ', which corresponds theoretically to the resonance point (Maxwell model) for several input frequencies. The frequency dependence was well described by both an Arrhenius-type model and by the WLF (Williams, Landel and Ferry) equation, yielding glass transition temperatures for an average molecular vibration time of 100 s, which were similar to published midpoint temperatures determined by DSC scans. Some sugar mixtures were studied, yielding results that were well described by the Gordon–Taylor equation, using literature data. The frequency dependence of the viscoelastic ratio was also well approximated by an Arrhenius-type equation, with activation energies similar to those of the glass transition temperature and corresponded well to published values of the endset of glass transition.     

Glass Transition and Food Technology: A Critical Appraisal

ABSTRACT: Most low water content or frozen food products are partly or fully amorphous. This review will discuss the extent to which it is possible to understand and predict their behavior during processing and storage, on the basis of glass transition temperature values (Tg) and phenomena related to glass transition. Two main conclusions are provisionally proposed. Firstly, glass transition cannot be considered as an absolute threshold for molecular mobility. Transport of water and other small molecules takes place even in the glassy state at a significant rate, resulting in effective exchange of water in multi-domains foods or sensitivity to oxidation of encapsulated materials. Texture properties (crispness) also appear to be greatly affected by sub-Tg relaxations and aging below Tg. Secondly, glass transition is only one among the various factors controlling the kinetics of evolution of products during storage and processing. For processes such as collapse, caking, crystallization, and operations like drying, extrusion, flaking, Tg data and WLF kinetics have good predictive value as regards the effects of temperature and water content. On the contrary, chemical/biochemical reactions are frequently observed at temperature below Tg, albeit at a reduced rate, and WLF kinetics may be obscured by other factors.     

APPLICATION OF WLF AND ARRHENIUS KINETICS TO RHEOLOGY OF SELECTED DARK-COLORED HONEY

The rheological properties of Common Black Horehound, Globe Thistle, and Squill types of dark‐colored Jordanian honey were examined. The types of honey used were identified via assessing the source of nectar using pollen analysis (Melissopalynology). The apparent viscosity, η, was measured as a function of the shear rate, γ. In addition, the apparent viscosity was measured, at constant shear rate (6.12 s^?1), as a function of shearing time. Newton's law of viscosity (i.e., τ=ηγ) was found to adequately (R²～ 0.99) describe the flow behavior of honey samples. The apparent viscosity was found to decrease with temperature, and the temperature dependence of viscosity was contrasted versus both Arrhenius model (η=η_oe^Ea/RT) and WLF model (η/η_G= 10 (C₁(T–T)/C₂+(T–T_G))). Although Arrhenius kinetics may fit the viscosity versus temperature data for the examined types of honey, nevertheless, it gives a relatively high value of activation energy that is quite comparable with, if not even larger than, that of a typical chemical reaction. On the other hand, WLF‐model was found to adequately describe the data while at the same time it gives quite reasonable values of both T_G and η_G, which are in agreement with those cited in literature.     

Optimal temperature input design for estimation of the square root model parameters: parameter accuracy and model validity restrictions

As part of the model building process, parameter estimation is of great importance in view of accurate prediction making. Confidence limits on the predicted model output are largely determined by the parameter estimation accuracy that is reflected by its parameter estimation covariance matrix. In view of the accurate estimation of the Square Root model parameters, Bernaerts et al. have successfully applied the techniques of optimal experiment design for parameter estimation [Int. J. Food Microbiol. 54 (1-2) (2000) 27]. Simulation-based results have proved that dynamic (i.e., time-varying) temperature conditions characterised by a large abrupt temperature increase yield highly informative cell density data enabling precise estimation of the Square Root model parameters. In this study, it is shown by bioreactor experiments with detailed and precise sampling that extreme temperature shifts disturb the exponential growth of Escherichia coli K12. A too large shift results in an intermediate lag phase. Because common growth models lack the ability to model this intermediate lag phase, temperature conditions should be designed such that exponential growth persist even though the temperature may be changing. The current publication presents (i) the design of an optimal temperature input guaranteeing model validity yet yielding accurate Square Root model parameters, and (ii) the experimental implementation of the optimal input in a computer-controlled bioreactor. Starting values for the experiment design are generated by a traditional two-step procedure based on static experiments. Opposed to the single step temperature profile, the novel temperature input comprises a sequence of smaller temperature increments. The structural development of the temperature input is extensively explained. High quality data of E. coli K12 under optimally varying temperature conditions realised in a computer-controlled bioreactor yield accurate estimates for the Square Root model parameters. The latter is illustrated by means of the individual confidence intervals and the joint confidence region.     

Determination of Local Heat-Transfer Coefficients Around a Circular Cylinder Under an Impinging Air Jet

Heat transfer coefficients around a model food shaped as a circular cylinder placed on a flat surface and impinged by a slot air jet has been determined using an inverse heat transfer method. The determination was based on time-temperature data measured with a thermocouple in the cylinder and in the air jet. The cylinder was rotated around its horizontal axis to determine the heat-transfer coefficients at different locations around the cylinder. A sensitivity analysis using Monte Carlo simulations was also performed. The local heat-transfer coefficients determined, were compared to computational fluid dynamics (CFD) simulations using the k-ω SST and RSM models. The heat-transfer coefficients determined from temperature measurements was larger than predicted by the CFD simulations. The heat-transfer rates were in better agreement on the upper part of the cylinder, including the decrease along the cylinder due to flow separation, than on the lower part close to the wake recirculation area. The SST model predicted in general a slightly higher heat-transfer rate on the upper part of the cylinder and slightly lower on the lower part of the cylinder, as compared to the RSM model.     

Modeling cation diffusion in compacted water-saturated sodium bentonite at low ionic strength

Sodium bentonites are used as barrier materials for the isolation of landfills and are under consideration for a similar use in the subsurface storage of high-level radioactive waste. The performance of these barriers is determined in large part by molecular diffusion in the bentonite pore space. We tested two current models of cation diffusion in bentonite against experimental data on the relative apparent diffusion coefficients of two representative cations, sodium and strontium. On the "macropore/nanopore" model, solute molecules are divided into two categories, with unequal pore-scale diffusion coefficients, based on location: in macropores or in interlayer nanopores. On the "surface diffusion" model, solute molecules are divided into categories based on chemical speciation: dissolved or adsorbed. The macropore/nanopore model agrees with all experimental data at partial montmorillonite dry densities ranging from 0.2 (a dilute bentonite gel) to 1.7 kg dm(-3) (a highly compacted bentonite with most of its pore space located in interlayer nanopores), whereas the surface diffusion model fails at partial montmorillonite dry densities greater than about 1.3 kg dm(-3).     

Modeling of Respiration Rate of Litchi Fruit under Aerobic Conditions

Respiration of the produce and permeation of gas through the packaging films are the processes involved in creating a modified atmosphere inside a package that will extend shelf life of agricultural perishables. Thus modeling respiration rate of the selected produce is crucial to the design of a successful modified atmosphere packaging system. Two different models based on regression analysis and enzyme kinetics were developed with the help of respiration data generated at temperatures 0, 5, 10, 15, 20, 25, and 30 °C for litchi fruit using the closed system method. Temperature was found to influence the model parameters. In the model, based on enzyme kinetics, the dependence of respiration rate on O₂ and CO₂ was found to follow the uncompetitive inhibition. The enzyme kinetic model parameters, calculated from the respiration rate at different O₂ and CO₂ concentration were used to fit the Arrhenius equation against different storage temperature. The regression coefficients values were used for the prediction of respiration rate using regression model. The activation energy and respiration pre-exponential factor were used to predict the model parameters of enzyme kinetics at any storage temperature. The developed models were tested for its validity at 2 °C. The models showed good agreement with the experimentally estimated respiration rate.     

Kinetic modelling of non-enzymatic browning in honey and diluted honey systems subjected to isothermal and dynamic heating protocols

The kinetics of non-enzymatic browning (NEB) in honey and diluted honey systems was investigated. The effect of α_w (in the range of 0.54–0.99) on brown pigment formation in honey and its diluted solutions, differing in the concentration of reactant solutes was monitored upon heating at four temperatures (50, 60, 70 and 80 °C). The progression of the Maillard reaction was followed by spectrophotometric measurements at 420 nm (A₄₂₀) and the absorbance–time curves were fitted to the logistic model. The processing temperature and water activity, or the initial reactant concentration, had a significant impact on browning kinetics and the color change of honey. Secondary models, expressing the dependence of the best fitted primary model parameters on temperature and α_w, were further developed. In addition, an alternative method of expressing the temperature dependence of browning rate constants using the WLF kinetic formalism, based on the glass transition temperature, T_g, was applied. The main secondary models were validated by comparing the predicted model parameters with those obtained from isothermal experiments. Finally, the derived kinetic model was further evaluated against the observed browning responses of honey under dynamic heating conditions to examine the applicability of the developed model over fluctuating temperature–time protocols.