Journal of Food Engineering 98 (2010) 398–407

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Journal of Food Engineering

journal homepage: www.elsevier .com/locate / j foodeng

Design of an ohmic reactor to study the kinetics of thermal reactionsin liquid products

Stéphanie Roux a, Mathilde Courel b, Laëtitia Picart-Palmade a, Jean-Pierre Pain a,*

a Université Montpellier II, UMR 95 Qualisud, cc 023, Place Eugène Bataillon, 34095 Montpellier, Franceb AgroParisTech, INRA, UMR 1145 Ingénierie Procédés Aliments, 1 Avenue des Olympiades, 91300 Massy, France

a r t i c l e i n f o

Article history:Received 24 July 2009Received in revised form 30 November 2009Accepted 8 January 2010Available online 25 January 2010

Keywords:High temperature short timeMilkInfant formulaMaillard reactionHeat transferModel

0260-8774/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.jfoodeng.2010.01.013

* Corresponding author. Tel.: +33 4 67 14 33 18; faE-mail address: jppain@polytech.univ-montp2.fr (

a b s t r a c t

An ohmic reactor was developed at a laboratory-scale to study the kinetics of thermal reactions in liquidproducts such as milk and infant formula in the UHT domain. Temperature mapping revealed good ther-mal homogeneity with a maximum difference of 3 �C in the treatment cell. The ohmic reactor enableddetermination of the electrical conductivity of the product under the real thermal conditions with a pre-cision of ±15%. Reproducible thermal profiles were obtained with a 2.3% relative variation for the heatingphase, 1% for holding and 20% for cooling. The FAST index, giving a global measurement of the extent ofthe Maillard reaction in dairy products, was used to estimate the reproducibility of a thermal reactionwith an average standard deviation of 3.8%. Finally, a semi-empirical model was developed to predictproduct temperature history during a complete thermal treatment with good adjustment for heatingand holding and acceptable adjustment for cooling.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

A majority of food products require thermal treatment fortransformation or conservation purposes. These thermal treat-ments are generally associated with chemical reactions that gener-ate quality attributes such as taste, flavor, color etc., as well asundesirable chemical compounds. The Maillard reaction is one ofthe thermal reactions that have been most extensively studied infood during the past century (Gerrard, 2006). Historically, milkhas been the focus of considerable attention as it was one of thefirst foods to be sterilized. In addition, liquid dairy products consti-tute an interesting matrix for the study of thermal reactions be-cause of their composition in highly reactive substrates such aslactose and lysine. Food scientists have played an important rolein elucidating the underlying reaction mechanisms; indeed, mucheffort has been made to unravel the reaction pathways in order toenhance knowledge and predict the extent of reactions (Martinset al., 2001; Van Boekel, 2001). Numerous studies have also beendedicated to evaluating the impact of different reaction parameters(pH, temperature, time, sugar reactivity, reagent concentration,water activity and glass transition temperature) on food qualityduring processing (Finot, 2005). However, because of the complexcomposition of foods, most of these have been carried out on sim-

ll rights reserved.

x: +33 4 67 14 42 92.J.-P. Pain).

plified model solutions or solid matrices and it is difficult toextrapolate the results to real food products.

Many authors have tried to identify the most relevant chemicalmarkers that can qualify the intensity of a thermal process and itsconsequences in terms of the degradation of food quality. Claeyset al. (2002, 2004) proposed the use of specific indicators that wereeither present (enzymes, microorganisms, constituents, etc.) orformed in milk (Maillard products) and would enable the directand quantitative measurement of a process impact without knowl-edge of the actual thermal history. Maillard reaction products suchas furosine and carboxymethyllysine are frequently used for suchpurposes (Erbersdobler and Somoza, 2007). However, Feinberget al. (2006) found that the most discriminative markers werethose which globally measure structural modifications to milk pro-tein rather than those which specifically quantify Maillard reactionmetabolites. These include the FAST index (Fluorescence of Ad-vanced Maillard products and Soluble Tryptophan) obtained usinga fluorimetric method, that can quantify the progress of a Maillardreaction (Birlouez-Aragon et al., 1998). This index has been provedto be linked to the nutritional quality of a food (Birlouez-Aragonet al., 2001) and has been used successfully to optimize a micro-wave pasteurization treatment for milk (Tessier et al., 2006).

Temperature appears to be one of the key operating variablesthat influence the Maillard reaction in milk (Van Boekel, 1998).Paradoxically, very little information can be found in the literatureon the thermal treatments that are applied and their characteriza-tion. In most cases, the Maillard reaction is studied in thermostatic

Nomenclature

a product characteristic constant (�C�1)A contact surface of product (m2)b0 constant of Eq. (19)b1 constant of Eq. (19)c0 constant of Eq. (20)c1 constant of Eq. (20)cp specific heat capacity (J/kg/K)e distance between electrodes (m)E electrical field (V/m)I current (A)IF infant formulak rate of fast cooling (�C/s)K global exchange coefficient (W/K/m2)m product parameter (�C�1)n number of repetitionsP power (W)Q energy (J)RRMSE relative root meat square error between experimental

and modeled valuesS surface area of electrodes (m2)t time (s)

T temperature (�C)U voltage (V)V product volume (m3)

Greek symbolsa constant involved in ohmic heating equations (s�1)q density (kg/m3)r electrical conductivity (S/m)s time constant involved in conductive heat losses equa-

tions (s)X electrical resistance (ohm)

Subscriptsc coldm mean0 initialref reference temperature value20 �C value for a reference temperature of 20 �Cu1 first phase of cooling: fast cooling

S. Roux et al. / Journal of Food Engineering 98 (2010) 398–407 399

water baths to achieve low temperature treatments below 100 �C,or in an oil bath where the temperature exceeds 100 �C. Because oflow heat exchange coefficients, this type of equipment is inappro-priate when trying to mimic the high temperature short time treat-ments (HTST) applied in industry. Moreover, the respectivecontributions of heating and cooling to the global thermal historyof a product, and thus to thermal reactions, are implicitly ne-glected. The objective of this study was therefore to design a reac-tor that would allow study of the kinetics of Maillard reactionsunder HTST conditions and provide access to a fully characterizedthermal history. Ohmic heating is an efficient technology based onthe Joule effect that enables the heating of a product in its entirevolume at high levels (Goullieux and Pain, 2005). It is a direct heat-ing method without thermal inertia and is easy to control at theelectrical source. Model systems using milk and milk-based infantformula were used to characterize the performances of the ohmicreactor thus developed in terms of temperature homogeneity, ther-mal history, the reproducibility of thermal profiles and the extentof the Maillard reaction.

Table 1General composition and thermal and physical properties of the milk and infantformula used during this study.

Milk Infant formula

Composition (g/L)Water 902 890Sugar 49 84Protein 32 14Lipids 16 36Minerals 9 4.6Thermal and physical propertiesa

Densityb (kg/m3) 990.7 ± 35.4 995.0 ± 35.3Specific heat capacityb (J/kg/K) 3970 ± 49 3895 ± 49Thermal conductivityb (W/m/K) 0.611 ± 0.038 0.595 ± 0.035

2. Materials and methods

2.1. Model dairy solutions

Two liquid dairy products were used during the experiments:commercial, semi-skimmed, micro-filtrated milk and liquid infantformula (IF) specially designed for the ICARE Project.1 Both prod-ucts were supplied by an industrial partner in the project. The gen-eral composition of the products is shown in Table 1. Their thermaland physical properties, i.e. density, specific heat capacity andthermal resistance, were calculated from composition data usingthe model developed by Singh and Heldman (2001). The values gi-ven in Table 1correspond to the thermal and physical propertiescalculated for an interval around the median value within theexperimental range of 20–140 �C.

1 ICARE ‘‘Impeding neoformed Contaminant Accumulation to Reduce their healthEffects” (EU 6th Framework Programme, Grant No. COLL-CT-2005-516415).

2.2. Analytical method

The FAST method was that described by (Birlouez-Aragon et al.,2002). One milliliter of sample was completed to 50 mL with so-dium acetate buffer (0.1 M, pH 4.6) in order to precipitate insolubleproteins. 4 mL of supernatant was then filtered through a 0.45 lmnylon filter (VWR, France) and placed in a disposable 4-sided acrylcuvette (Sarstedt, France). Fluorescence was measured with a spec-trofluorimeter (CaryEclipse Varian, France) at excitation/emissionwavelengths of 290/340 nm for tryptophan (Ftrp) and 330/420 nm for advanced Maillard products (Famp). The FAST indexis given by the ratio:

FAST index ¼ FampFtrp

� 100 ð1Þ

Maximum reproducibility variation coefficients of 3.5% wereobtained for Ftrp, Famp and the FAST index.

2.3. Design of the prototype

The thermal treatments were carried out in a laboratory-scalestatic batch ohmic reactor. A diagram of the complete installation

a Estimated from the composition using the Singh and Heldman model (Singhand Heldman, 2001).

b Median, maximum and minimum values over the range 20–140 �C.

400 S. Roux et al. / Journal of Food Engineering 98 (2010) 398–407

is shown in Fig. 1. The treatment cell was made of ULTEM�, anamorphous thermoplastic polyetherimide material, chosen for itssolidity and electrical insulation properties. During some of theexperiments, the ULTEM� material was reinforced by fiberglassto enable better resistance to temperature and pressure (180 �C;6 bars). The characteristics of the two treatment cells are shownin Table 2. The electrodes (Magneto, BA Schiedam, The Nether-lands) were made of titanium coated with a specific DSA alloy(Dimension Stable Anode), specially patented for not being affectedby electrolysis during ohmic heating at 50 Hz (Berthou et al., 1998,1999). The ohmic cell was equipped with a pressure control sys-tem: nitrogen was injected continuously into the bottom of the celland exited at the top of the cell via a pressure valve maintaining apressure of 0–6 bars within the system. An inert gas was preferredto air so as to ensure that no oxygen could interfere with the chem-ical reactions. Nitrogen sparkling had an additional homogenizing

Fig. 1. Schematic representation of the batch ohmic heating reactor.

Table 2Characteristics of the two ohmic treatment cells.

Cell no. 1 Cell no. 2

Material ULTEM� ULTEM� + fibreglassVolume (mL) 124 100Internal diameter (cm) 3.95 3.55External diameter (cm) 4.75 4.15Length (cm) 10.1 10.1Thermal conductivity (W/m/K)* 0.12 0.20

* Mean values obtained from different suppliers’ websites (www.k-mac-plas-tics.net; www.plasticsintl.com; www.eiecomprod.shopforplastics.com).

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5 3 3.5Left to right (cm)

Bot

tom

to to

p (c

m)

5

1

2

3

4

Fig. 2. Position of the five thermocouples in the central section of the ohmic cell.

effect on the temperature within the reactor. A voltage generator(5 kW power set) provided the energy necessary to heat the prod-uct, supplying the electrodes with 50 Hz alternative current. Volt-age and current varied, respectively between 0 and 320 V and 0and 20 A, creating a steady electrical field at between 0 and 3 kV/m. The heating rate was affected by the electrical conductivity ofthe product and could be adjusted by modifying the voltageapplied.

The temperature was monitored using a K-type (NiCr/NiAl)thermocouple (diameter 1.5 mm, precision ±1.5 �C) placed at thebottom of the cell (position 2 in Fig. 2) so that it would remain im-mersed in the product. The calibration of the thermocouple waschecked with boiling water. The temperature signal was comparedwith and without application of the electrical field and no devia-tion was found regarding the sensor. This sensor controlled themonitoring equipment (Simulator Control And Data Acquisition –SCADA) which, via a LabVIEW� program, acted on the voltage ap-plied between the electrodes in order to regulate the holding tem-perature at a targeted value. During the holding stage, thetemperature was thus maintained at a constant level by providingenough power to compensate for the energy lost at the cell walls.The process control system enabled the accurate management oftime/temperature conditions and on-line data collection (volt-age ± 0.25%, current ± 0.5% and a maximum of five temperatureswith a minimum delay of 0.2 s).

A sampling device provided for the collection of five, 15 mLsamples at different time points during a treatment. This was madeof stainless steel cylinders immersed in an ice bath and linked tothe ohmic cell by a capillary tube closed with a valve. When thevalve was opened, the pressure difference (5 bars) enabled the cyl-inder to be almost instantaneously filled with the product. Whileremaining pressurized, the sampling cylinder was subjected to fastcooling by contact with melting ice, before extraction of the liquidsample at a temperature of around 20 �C. The volume reductioncaused by sampling was compensated for by the nitrogen coun-ter-pressure, resulting in stable pressure and temperature withinthe treatment cell. During cooling, the product temperature wasmonitored by a K-type thermocouple (NiCr/NiAl) connected tothe data acquisition device.

2.4. Determination and expression of electrical conductivity

Ohmic heating is based on Ohm’s law. Electrical conductivity (rin S/m) could thus be calculated from the process parameters:

rðTÞ ¼ eS� IðTÞ

Uð2Þ

where e (m) is the distance between the two electrodes, S (m2) thecontact surface area between the product and an electrode, I (A) thecurrent and U (V) the voltage.

Furthermore, electrical conductivity was also related to the foodproduct under study, and a convenient way of expressing thisdependence was proposed by introducing a reference conductivityvalue rref for a reference temperature Tref and a product parametermref (Goullieux and Pain, 2005; Khalaf and Sastry, 1996):

rðTÞ ¼ rref � ½1þmref � ðT � TrefÞ� ð3Þ

Moreover, the mref parameter was also temperature-dependent:

mref ¼a

1þ a � Trefð4Þ

where a (�C�1) is an intrinsic characteristic of the product, corre-sponding to m value at a reference temperature of 0 �C.

S. Roux et al. / Journal of Food Engineering 98 (2010) 398–407 401

2.5. Heat transfer mechanisms

2.5.1. Joule effectAccording to ohm’s law, the power P (W) delivered by an elec-

trical generator to a volume V (m3) of product is proportional to theelectrical field E (V/m) and the electrical conductivity of a productr (S/m):

P ¼ E2 � rðTÞ � V ð5Þ

The heat transfer rate received by the product is given by theelectrical power P which can also be expressed as:

PðTÞ ¼ q � cp � V �dTdt

ð6Þ

where q (kg/m3) is the density and cp (J/kg/K), the specific heatcapacity.

Combining Eqs. (5) and (6) gives a first expression of a thermalprofile as a function of operating parameters and productcharacteristics:

dTdt¼ E2 � rðTÞ

q � cpð7Þ

Replacing r(T) by its expression as a function of temperature(Eq. (3)) gives:

dTdt¼ E2 � rref � ½1þmref � ðT � TrefÞ�

q � cpð8Þ

The integration of Eq. (8) can be simplified by using the initialtemperature of the product as a reference temperature (Tref = T0)and by grouping the constant terms in a new one, a:

dTdt¼ a T þ 1

m0� T0

� �ð9Þ

a ¼ E2 � r0 �m0

q � cp¼ U2 � r0 �m0

e2 � q � cpð10Þ

Indeed, within the temperature range considered during thisstudy of 20–140 �C, q and cp could be assumed to be constant withrelative variations of 3.6% and 1.2%, respectively (Table 1).

The boundary conditions are given by T0 at t = 0 and the integra-tion of Eq. (9) gives the temperature kinetic of ohmic heating:

Table 3Experimental design applied during each part of the study.

Tension duringheating

N(

Temperature mapping 315 V 05

Electrical conductivity measurements 315 V 5

Reproducibility of a thermal profile 315 V 05

Reproducibility of a reaction during holding 315 V 5Analysis of heat transfers within the product Heating 190 V 0

272 V 5315 V

Holding 315 V 5

Cooling 315 V 5

TðtÞ ¼ 1m0� ½expða � tÞ � 1� þ T0 ð11Þ

The ohmic heating rate can then be expressed as:

dTdt¼ a

m0� expða � tÞ ð12Þ

2.5.2. Conductive heat transferHeat could be lost by conduction through the walls of the reac-

tor (ULTEM� cylinder and electrodes) during heating and holdingor through the walls of the sampling cylinder during cooling. Be-fore writing the equations for heat losses, some assumptionsneeded to be made regarding the reactor: (i) uniform temperatureand (ii) constant volume; and with respect to the product: (iii) con-stant q and cp over the temperature range.

The elementary heat exchange in the product is given by:

dQ ¼ q � V � cp � dT ð13Þ

The heat lost by the product through the walls of the cell couldbe expressed using the thermal resistances of the system:

dQ ¼ K � A � ðTc � TÞ � dt ð14Þ

where K (W/m2/K) is a global exchange coefficient, A is the contactsurface area of the product and Tc (�C) the temperature of the coldfluid. Combining Eqs. (13) and (14) gives:

dTTc � T

¼ K � Aq � V � cp

� dt ð15Þ

The constant terms could be grouped into a time constant s be-fore integrating with the boundary conditions given by T0 at t = 0:

T ¼ Tc þ ðT0 � TcÞ � exp � ts

� �ð16Þ

s ¼ q � V � cp

K � A ð17Þ

2.6. Experimental design

Thermal treatments comprise three phases: heating, holdingand cooling. During this study, the heating rate was controlledvia the voltage delivered during the heating and holding phases.In order to ensure thermal homogeneity, nitrogen was circulated

itrogenmL min�1)

Pressure(bars)

Product Temperature/holding time

Recordingfrequency

5 Milk 15 �C ? 100 �C 0.5 s0 100 �C/2 min

110 �C/2 min120 �C/2 min130 �C/2 min140 �C/2 min

0 5 Milk 15 �C ? 140 �C 0.2 sIF

5 Milk 15 �C ? 100–140 �C 0.5 s0 IF 100–140 �C/2–30 min

100–140 �C ? 20 �C0 5 Milk 110–138 �C/0–50 min 1 s

5 Milk 20 �C ? 100–140 �C 0.5 s0 IF

0 5 Milk 100–140 �C/2–30 min 0.5 sIF

0 5 Milk 100–140 �C ? 20 �C 0.5 sIF

402 S. Roux et al. / Journal of Food Engineering 98 (2010) 398–407

in the cell at a rate of 0 or 50 mL/min. The different sets of param-eters used during the experiments are shown in Table 3.

2.7. Statistical procedures

The precision of the model was determined by calculating therelative root mean square error (RRMSE) between experimental(yi) and predicted values ðyiÞ:

RRMSEð%Þ ¼ 100 � 1�y�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn1ðyi � yiÞ2

n

sð18Þ

where �y is the average of the predicted values yi.Good model precision corresponded to a low RRMSE.The 95% confidence interval was built by allowing 95% of the

experimental points to fit within the limits around a predicted va-lue. A broad interval could result from a high dispersal of experi-mental points or poor adjustment of the model.

3. Results and discussion

3.1. Thermal homogeneity of the reactor

Temperature mapping during ohmic heating was achieved byinstalling five K-type thermocouples (NiCr/NiAl) at different posi-tions in the central area of the cell (Fig. 2). Because of the axialsymmetry of the ohmic reactor, similar maps could be expectedfor all parts of the cell. Relatively high temperature differenceswere observed – ranging from 7 �C to 10 �C – between the bottom

Table 4Temperature mapping of the central section of the ohmic reactor with or withoutnitrogen bubbling for five different levels of holding temperature.

Holdingtarget(�C)

Temperature (�C) measured by thermocouple in position

1 (top) 2 (bottom) 3 4 5

Nitrogen flow rate = 0 mL/min (n = 2)100 100.4 ± 0.0 93.3 ± 1.8 96.4 ± 1.8 99.7 ± 1.5 96.7 ± 1.7110 110.5 ± 0.0 101.4 ± 2.0 104.5 ± 1.9 109.0 ± 1.4 104.9 ± 1.8120 120.5 ± 0.0 110.8 ± 1.8 114.3 ± 1.3 118.8 ± 1.4 114.5 ± 1.7130 130.5 ± 0.0 120.4 ± 2.0 124.0 ± 1.7 129.0 ± 1.5 124.3 ± 1.9140 140.5 ± 0.1 129.9 ± 2.5 133.7 ± 2.2 139.1 ± 1.9 134.1 ± 2.3Nitrogen flow rate P 50 mL/min (n = 6–8)100 100.2 ± 0.2 97.7 ± 1.6 100.8 ± 1.4 101.9 ± 0.9 100.6 ± 1.5110 110.4 ± 0.5 108.0 ± 1.2 111.1 ± 1.2 112.0 ± 1.1 110.7 ± 1.5120 120.5 ± 0.7 117.8 ± 1.2 120.7 ± 1.5 121.8 ± 1.1 120.5 ± 1.6130 130.5 ± 0.7 127.6 ± 1.2 130.2 ± 2.3 131.8 ± 1.0 130.6 ± 1.5140 140.5 ± 0.6 136.9 ± 0.9 140.1 ± 3.0 141.8 ± 0.9 140.8 ± 1.7

A

0

0.5

1

1.5

2

0 50 100 150Temperature (°C)

Con

duct

ivity

(S/m

)

n = 64

Mean

Limits

Fig. 3. Electrical conductivity vs. temperature as measured in the ohmic reactor by meaInfant formula.

and the top of the device (Table 4). A nitrogen bubbling system wasthus introduced at the bottom of the ohmic reactor to compensatefor thermal heterogeneity due to natural convection in the hot li-quid. An optimum flow rate of 50 mL/min was determined: in thisway, the greatest temperature differences measured between thebottom and top of the cell could be reduced to about 3 �C.

3.2. Electrical conductivity measurements

In the ohmic reactor, variables such as temperature, voltage andcurrent could be measured against time so that the experimentalelectrical conductivity could be acquired as a function of tempera-ture (Fig. 3). This electrical conductivity appeared to be a linearfunction of temperature:

rðTÞ ¼ b1 � T þ b0 ð19Þ

The slope and intercept were determined by linear regressionfor 64 and 21 experiments with mean determination coefficients,R2, of 0.987 and 0.992 for milk and infant formula, respectively (Ta-ble 5). This type of linear behavior has been reported by numerousauthors studying a variety of products under different experimen-tal conditions (Ayadi et al., 2004; Castro et al., 2004; Goullieuxet al., 1997; Icier and Ilicali, 2005; Legrand et al., 2007; Pongvira-tchai and Park, 2007; Sarang et al., 2007; Sulc and Novi, 2007; Zar-eifard et al., 2003). However, it remained difficult to find referencevalues for the electrical conductivity of milk or infant formula. Avery old study by Jackson and Rothera (1914) focused in part onthe electrical conductivity of various milks. Average values of0.5–0.6 S/m were reported for cow’s milk and 0.2–0.3 S/m for hu-man milk at 25 �C, which is quite close of the values found duringthe present study, i.e. 0.4 and 0.3 S/m for cow’s milk and infant for-mula, respectively.

The m parameter relative to the electrical conductivity of theproduct (Eq. (3)), was determined using the value of r at a refer-ence temperature of 20 �C estimated using Eq. (19), while a wascalculated from m using Eq. (4) (Table 5). A 95% confidence intervalwas applied to estimate a mean error on r20 �C and a, leading to rel-ative errors of 10–15% for r and 7–9% for a. Even though the pre-cision obtained for r could be improved, the possibility of directlymeasuring the electrical conductivity under real operating condi-tions was of considerable interest.

3.3. Thermal performances of the reactor

3.3.1. Reproducibility of a thermal profileThermal treatments can be broken down into three phases: (i)

during heating, the temperature increases from ambient to the

B

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150Temperature (°C)

Con

duct

ivity

(S/m

)

n = 21

MeanLimits

ns of Eq. (19). Linear regression is surrounded by 95% confidence limits. A: Milk; B:

Table 5Parameters of the electrical conductivity of the milk and infant formula as determinedby Eqs. (19), (3), and (4).

Milk Infant formula

Equation r(T) = b1.t + b0 r(T) = b1.t + b0

n 64 21Mean R2 0.987 0.992b1 0.01117 ± 0.00029 0.008142 ± 0.00022b0 0.1795 ± 0.0539 0.1082 ± 0.0271

r20 �C (S/m) 0.402 ± 0.062 0.270 ± 0.026a (�C�1) 0.0616 ± 0.0054 0.0760 ± 0.0057

S. Roux et al. / Journal of Food Engineering 98 (2010) 398–407 403

holding target; (ii) the temperature is then held at the target; (iii)the sample extracted from the reactor is quickly cooled in an icebath. An example of a time/temperature profile is given in Fig. 4for milk samples. In order to estimate the reproducibility of a ther-mal profile, the temperature kinetics were fitted with an exponen-tial model for the whole range of holding temperatures (100–140 �C) with the c1 coefficient set at zero for the holding phase:

T ¼ c0 � ec1 �t ð20Þ

c0 and c1 coefficients were determined by minimizing the sum ofthe squares of residuals with coefficients of determination above0.9 (Table 6). Reproducibility was then expressed as the statisticalvariability of c0 and c1 extracted from n = 57 to 81 heating or coolingprofiles. The holding temperature being constant, reproducibilitywas quantified by its statistical variability in n = 68 experiments.Excellent reproducibility was achieved for holding, since relativestandard deviations of less than 1% were obtained for holding tem-peratures. The reproducibility of heating profiles was also very sat-isfactory, with relative standard deviations lower than 2.3% for the

0102030405060708090

0 2 4 6Time (min)

FAST

and

Ftr

p/10

020406080100120140160

Temperature (°C

)

FAST Ftrp/10 Temperature

Fig. 4. Example of a three phase time/temperature profile superimposed on thekinetics of the FAST index and tryptophan fluorescence (Ftrp) obtained for infantformula treated in the ohmic reactor at 140 �C.

Table 6Reproducibility of thermal profiles for the whole range of holding temperatures (100–140 �C) expressed as the statistical variability of c0 and c1 coefficients in Eq. (20).

Heating Holding Cooling

Fitting model (Eq. (9)) T = c0.ec1.t T = c0 T = c0.ec1.t

n 57 68 81Mean R2 0.992 / 0.900Relative standard deviation on c0 1.8% 0.8% 8.2%

on c1 2.3% / 20.5%

c0 and c1 parameters. The cooling phase appeared to be less repro-ducible, with variations of 8.2% and 20.5% for c0 and c1, respectively.However, in view of the fact that heating and holding are the twophases which contribute most to the sterilization value, any vari-ability in the cooling phase is not expected to be a problem that willaffect kinetic studies using this reactor (Roux et al., 2009).

3.3.2. Reproducibility of a reaction during holdingThe extent of chemical reactions during a thermal treatment

was monitored using the FAST index, which is related to the forma-tion of Maillard reaction products, and the Ftrp which is propor-tional to the soluble protein concentration. An example of thekinetics obtained for a holding temperature of 140 �C is shown inFig. 4 for both markers. During a thermal treatment, Maillard prod-ucts accumulate with a pseudo-zero order under isothermal condi-tions. Soluble proteins tend to denature within the first twominutes of an ohmic treatment, and then stabilize. A detaileddescription of these reactions and their interpretation was pro-posed by Roux et al. (2009).

The reproducibility of the thermal reactions occurring duringohmic heating of the milk solution was estimated from a broadvariety of thermal treatments with holding times that ranged from0 to 50 min and temperatures from 110 to 138 �C. Although eachexperiment could only be repeated twice, 25 different time/tem-perature treatments could be observed in terms of dispersion ofthe FAST index and its two components, Ftrp and Famp. This dis-persion was calculated from the standard deviation between tworepetitions of thermal treatment and the relative mean value ofthe 25 standard deviations was used to express the reproducibilityof the thermal reactions. Average relative standard deviations of3.8%, 6.4% and 2.5% were found for the FAST index, Ftrp and Famp,respectively. Such variations were independent of the time/tem-perature scale, thus demonstrating the excellent reaction repro-ducibility of the reactor during both short and longer holdingtimes.

3.4. Analysis of heat transfers within the product

It was necessary to be able to analyze heat transfer mechanismswithin the product so that the temperature profiles of UHT ohmictreatments could be predicted, thus enabling subsequent study ofthe thermal impact on chemical reactions. Two types of heat trans-fer mechanism occurred during the thermal treatment of a liquidproduct in the reactor: the Joule effect and conductive heat trans-fer. Both mechanisms were implicated during heating and holding,while cooling was based on flash volumetric expansion and con-ductive heat transfer.

3.4.1. HeatingDuring the heating period, the energy balance between ohmic

heating and conductive losses gave:

dTdt¼ E2 � rðTÞ

q � cp� 1

s� ðT � TcÞ ð21Þ

This equation could be integrated to extract a temperature ki-netic with the same boundary conditions as used previously:

T ¼ T0 þaa þ

Tcs

a�s�1s

!� exp

a � s� 1s

� t� �

�aa þ

Tcs

a�s�1s

ð22Þ

The values of most of the parameters used in this model aregrouped in Tables 1 and 5. The voltage applied was 314.8 ± 1.9 Vand the air temperature, Tc, was set at 20 ± 5 �C. The global ex-change coefficient K being unknown, the time constant s was usedas a fitting parameter to adjust Eq. (22) to the experimental heatingkinetics: nine different sets of operating conditions were used as a

404 S. Roux et al. / Journal of Food Engineering 98 (2010) 398–407

function of cell type, nitrogen flow, product type and heating rate(Table 7). Fitting of the ohmic/conductive model was evaluatedby calculating the relative root mean square error (RRMSE) be-tween experimental and modeled values (Fig. 5). Satisfactory re-sults were obtained with low RRMSE values of around 3% forelevated heating rates, while higher RRMSE (<8%) were found forthe lowest heating rate. The relative variation of the modeled tem-perature necessary to produce a 95% confidence limit is given forthe nine operating conditions in the last column of Table 7. Smallvariations of 3–7% were observed with heating rates higher than0.4 �C/s, which was promising when considering the high heatingperformances observed during UHT treatments. The adjusted time

Table 7Performances of the thermal ohmic/conductive model applied during the heating phase (Enitrogen flow, product and heating rate.

Cell Nitrogen (mL/min) Product Heating ratea (�C/s)

1 0 Milk 2.22 0 Milk 2.02 �50 Milk 2.12 �50 Milk 4.2d

2 0 IF 1.32 �50 IF 0.4e

2 �50 IF 0.9e

2 �50 IF 1.22 �50 IF 4.2d

a Mean experimental heating rate between 20 and 140 �C.b RRMSE: relative root mean square error between experimental and modeled values.c Relative variation of the modeled temperature necessary to produce a confidence lid NaCl was added in order to artificially increase conductivity and hence the heatinge These experiments were performed under a lower tension (i.e. 190 and 272 V) in or

020406080

100120140160

0 1 2 3

Time

Tem

pera

ture

(°C

)

HeatingEq. (22)

RRMSE = 2.9%

Holding Eq. (23)

RRMSE = 1

Fig. 5. Example of three phase thermal treatments at 140 �C obtained for IF. Fitting of thcorrespond to a 95% confidence interval.

20 °C 20 °C

Fig. 6. Sensitivity of the thermal models (Eqs. (22), (23), (25)/(27)) to operating variabrelative variation in the predicted temperature vs. the reference was calculated for a 10%phase (1 graduation = 20%); B: Holding phase (1 graduation = 100%); C: Cooling phase (

constant s appeared to be sensitive to both the heating rate and thematerial of the ohmic cell, probably because of the thermal inertiaof the system. Indeed, higher heat losses might have been expectedwith the ULTEM� + fiberglass material (cell no. 2) because it has ahigher thermal conductivity than ULTEM� (cell no. 1) (Table 1).

The sensitivity of the heating model (Eq. (22)) was tested byquantifying the impact on the final temperature of a 10% variationin eight variables (T0, a, U, Tc, r20 �C, s, q, cp) vs. the reference values.These reference values were calculated using the mean values foreach variable by adjusting the time necessary to achieve a holdingtemperature of 140 �C. The results presented in Fig. 6a show thatvoltage was potentially the most influential parameter, followed

q. (22)), for nine different sets of operating conditions as a function of the type of cell,

n s (s) RRMSEb (%) Variationc (%)

20 284.7 ± 80.6 1.9 4.015 125.6 ± 19.0 2.0 3.33 223.8 ± 28.9 2.7 6.12 48.0 ± 3.1 2.9 6.621 137.8 ± 11.7 2.9 4.06 191.3 ± 32.6 7.7 9.74 131.9 ± 4.5 3.1 4.84 115.8 ± 4.8 2.2 3.44 51.5 ± 5.5 3.1 5.3

mit of 95%.rate.der to reduce the heating rate.

4 5 6

(min)

Experimental

Model

Limits

.2%

Cooling Eqs. (25) and (27)RRMSE = 23%

e heating, holding and cooling phases with Eqs. (22), (23), and (25)/(27). The limits

les, for a reference thermal history (T0 = 20 �C, Tm = 140 �C) in infant formula. Thevariation or one experimental standard deviations (sd) of each variable. A: Heating

1 graduation = 10%).

S. Roux et al. / Journal of Food Engineering 98 (2010) 398–407 405

by electrical conductivity. Fortunately, the generator used duringthese experiments was able to deliver a very stable voltage (U)with mean relative variations of 0.6%, whereas electrical conduc-tivity (r) remained the most influential variable with higher vari-ations of 15%. Finally, the heating model displayed very lowsensitivity to the time constant s, thus confirming the importantcontribution of ohmic heating to compensating for heat lossesthrough the cell walls.

3.4.2. HoldingDuring the holding phase, the voltage supply was regulated to

provide sufficient ohmic energy to compensate for heat lossesthrough the walls. The energy balance of the system equaled zero;there was no temperature variation (Fig. 5) and Eq. (21) thus gave:

T ¼ 1a� 1

s� a � Tm �

1mTm

� �� Tc

s

� �ð23Þ

where Tc is the air temperature (20 ± 5 �C) and Tm the mean holdingtemperature.

As for the modeling of heating, the time constant s was used asa fitting variable to adjust Eq. (23) to experimental holding kinetics(Table 8). The results show that similar s values were obtainedwith a single product and were comparable for milk and infant for-mula, which was certainly due to their very close composition andthermal-physical properties. During holding, the voltage U wassubjected to the major oscillations imposed by the regulationsystem in order to achieve a constant temperature. For this reason,the average voltage required for the expression of parameter a inEq. (10) could not be determined experimentally and was also usedas a fitting parameter in Eq. (23). It can be seen from Table 8 thatthe voltage increased linearly with temperature and differed formilk (U = 0.070*T + 44.1; R2 = 0.98) and infant formula (U =0.076*T + 50.8; R2 = 0.99). As IF is less conductive than milk, morevoltage is needed to maintain the same temperature. The precisionof the model given by Eq. (23) was good, with the RRMSE beinglower than 1.6%. The relative variation of the modeled holdingtemperature necessary to produce a 95% confidence limit is givenin Table 8. Such variations of 0.5–3.4% were of the same order ofmagnitude as the experimental variability: mean relative varia-tions of 0.3–1.5% were obtained for holding temperatures, thusdemonstrating the satisfactory performance of the regulation sys-tem. As for heating, the holding thermal model was highly sensi-tive to ohmic variables U and r20 �C but was also sensitive to thetime constant (s) (Fig. 6b). The fitting of U and s tended to generate

Table 8Performances of the thermal ohmic/conductive model applied to the holding phase (Eq. (2

T (�C) n s (s)

Experimental Mean

Infant formula99.9 ± 1.1 4 975.0109.7 ± 1.1 4 1004.1119.9 ± 1.8 4 1028.7 1010.3 ± 29.3129.7 ± 2.0 3 1049.7140.0 ± 1.7 3 993.9

Milk100.2 ± 0.5 3 975.9110.2 ± 0.5 12 968.5116.4 ± 0.3 8 1009.2120.2 ± 1.2 3 1053.8 951.1 ± 97.3123.3 ± 0.7 10 1019.8130.0 ± 1.6 3 826.9139.4 ± 1.3 3 803.5

a RRMSE: relative root mean square error between experimental and modeled values.b Relative variation of the modeled temperature necessary to produce a confidence li

little variation, while r20 �C was again the most influential param-eter during these experiments.

3.4.3. CoolingThe cooling profile initially displayed an abrupt drop in temper-

ature with a linear shape, followed by a more classical exponentialcurve (Fig. 5). A mechanism other than conductive heat loss thusoccurred during the first phase of the cooling (u1): on enteringthe sampling cylinder, the product was subjected to a drop in pres-sure from 4 to 5 bars to atmospheric pressure, which probably re-sulted in flash cooling (Joule Thomson effect). To take account ofthese two different mechanisms, the cooling kinetic equationwas thus divided into two parts:

For t 6 tu1: fast cooling could be modeled using an empirical lin-ear equation:

dTdt¼ �k ð24Þ

T ¼ T0 � k � t ð25Þ

where k is the rate of fast cooling (�C/s).For t > tu1: conductive cooling

dTdt¼ 1

s� ðTc � TÞ ð26Þ

Eq. (26) was integrated with the boundary conditions given byTu1 at t = tu1:

T ¼ Tc þ ðTu1 � TcÞ � exp � t � tu1

s

� �ð27Þ

where Tc corresponds to the ice bath temperature (2 ± 2 �C).k, tu1 and s were used as fitting parameters in Eqs. (25) and (27).

The values obtained for five different initial temperatures (T0) werevery close (Table 9). Indeed, there was no reason for k, tu1 and s tobe dependant on initial temperature, and the mean values ob-tained were therefore used for the model. The RRMSE and relativevariation of the predicted temperature necessary to produce a 95%confidence limit were quite high (14–48% and 20–140%). However,despite this poor adjustment, and as mentioned previously, thecooling phase was not expected to generate a significant error inthe complete thermal model.

The cooling model was less sensitive to operating variables (T0,Tc, k, tu1, s) than the heating and holding models (Fig. 6c). The ini-tial temperature T0, and the time constant s, were the most influ-ential variables, with 10% variations inducing 15% relativevariations in the final temperature. However, because the temper-

3)) for infant formula and milk.

U (V) RRMSEa (%) Variationb (%)

58.2 ± 0.02 1.1 2.059.2 ± 0.01 1.0 1.760.0 ± 0.01 1.5 3.160.7 ± 0.03 1.6 3.461.3 ± 0.02 1.2 2.4

51.0 ± 0.01 0.5 0.852.0 ± 0.02 0.5 1.152.4 ± 0.01 0.3 0.552.7 ± 0.01 1.0 1.752.9 ± 0.01 0.6 1.253.3 ± 0.01 1.2 2.353.8 ± 0.03 0.9 2.0

mit of 95%.

Table 9Performances of the two-step thermal model applied to cooling (Eqs. (25) and (27)) with five different initial cooling temperatures (T0).

Initial temperature T0 (�C)

139.7 ± 1.6 129.8 ± 1.1 123.4 ± 1.0 116.3 ± 0.1 99.1 ± 0.6Experimentaln 14 11 15 8 8k (�C/s) 14997 ± 21.1 15000 ± 0.1 15000 ± 0.1 15000 ± 0.2 15000 ± 0.5tu1 (ms) 4.04 ± 0.63 3.62 ± 0.37 3.72 ± 0.28 3.27 ± 0.22 2.11 ± 0.44Tu1 (�C) 79.1 ± 9.3 75.5 ± 5.2 67.5 ± 4.2 67.3 ± 3.2 66.2 ± 6.5s (s) 72.6 ± 14.0 76.6 ± 10.6 91.0 ± 8.1 94.0 ± 6.2 89.9 ± 17.1

Modelk (�C/s) 15000 ± 0.9tu1 (ms) 3.20 ± 0.60Tu1 (�C) 91.6 81.8 75.3 68.2 51.1s (s) 58.8 ± 8.7RRMSEa (%) 23 17 14 16 48Variationb (%) 32 24 41 61 140

a RRMSE: relative root mean square error between experimental and modeled values.b Relative variation of the modeled temperature necessary to produce a confidence limit of 95%.

406 S. Roux et al. / Journal of Food Engineering 98 (2010) 398–407

ature was precisely recorded, s remained the parameter makingthe largest contribution, with 20% experimental variations.

4. Conclusion

The main objective when designing this ohmic reactor was todevelop a tool that would enable the study of Maillard reactionkinetics at high temperatures that would match the ultra-hightemperatures applied to industrial milk products. Because of itsvery interesting performances in terms of both the reproducibilityof thermal treatments and chemical reactions, the ohmic reactorcould be considered as a convenient and precise tool to study ther-mal reactions in liquid food products in the UHT domain. The re-sults showed that the extent of the Maillard reaction – asmonitored by the FAST index – was reproducible: the average rel-ative standard deviation of the FAST index between two test runswas 3.8%. This proves that a wholly-controlled thermal environ-ment allowed chemical reactions to be generally reproducible inthe ohmic reactor, thus attaining the objective targeted by thisstudy.

The three phases of the temperature kinetics – heating, holdingand cooling – could be modeled using semi-empirical equationsbased on the Joule effect and conductive heat losses. Althoughthe heating and holding models could certainly be refined (for in-stance, by taking account of other sources of heat transfer such asnitrogen bubbling, the fin effects of the sampling device and ther-mocouple etc.), their predictive performances were relatively satis-factory. The hypotheses determined for the reactor (temperatureuniformity and constant volume) and the product (constant den-sity and specific heat capacity) appeared to be appropriate. Thesemi-empirical model developed for cooling did not perform aswell as that designed for heating and holding, but the temperaturedropped rapidly, falling below 100 �C in less than 1 s, which was al-ready very interesting in terms of halting a thermal reaction. Thesemodels could therefore be used to predict instantaneous tempera-ture conditions and in a kinetic model of thermal reactions. Thisapproach should make it possible to combine heat transfer andchemical reaction kinetics in order to describe a complex reactionduring real food processing.

This work was based on the hypothesis that temperature is theonly processing parameter that directly influences the kinetics ofMaillard reactions in homogeneous fluid products such as infantformula. For this reason, extending the results to a continuous con-figuration requires identification of the temperature profiles in-duced by velocity profiles in a flowing fluid. Indeed, the shearvariable will induce temperature profiles adjacent to the walls of

a continuous installation, or local temperature heterogeneities ina steam injection device, that will indirectly affect the extent ofchemical reactions. Thus the shear variable only needs to be takeninto account at that stage. In that context, the present findings maybe of considerable value to the optimization of UHT technologies interms of the chemical safety of products.

There are however certain limitations to this method: the timerequired to attain a temperature of 140 �C is relatively long (1–1.5 min) when compared with the performance of industrial sys-tems. This means that thermal reactions are certainly initiated dur-ing this transient temperature step in the ohmic reactor. Thisproblem could be solved by using a more powerful generator toaccelerate the heating phase.

Acknowledgements

The authors wish to thank the ICARE European project for sup-porting this work (6th Framework Program, Grant No. COLL-CT-2005-516415). We are also particularly grateful to Mrs. G. Blaiseand L. Fuentes for their technical assistance.

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