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DEVELOPMENT OF A MODEL FOOD FOR MICROWAVE PROCESSING AND THE PREDICTION OF ITS PHYSICAL PROPERTIES K. Knoerzer1, M. Regier1, U. Erle2, K.K. Pardey1 and H. Schubert1 Institute of Food Process Engineering, University of Karlsruhe, Germany 2 Nestlé Product Technology Centre, Singen, Germany

1

Although microwave processes in the food industry such as microwave pasteurisation or microwave drying are already in use, most of their optimisation is still based on trial-and-error. To model these processes, knowledge of different physical properties of the food material is indispensable. In order to guarantee constant product properties a model food was developed imitating real food properties and showing physical and microbial stability over several months. In this manuscript the prediction of these physical properties and the comparison of the model food with a real food will be shown. Submission Date: December 29,2004 Acceptance Date: September 19, 2005

INTRODUCTION In scientific investigations of microwave food processing, the fluctuating composition of the natural or biological matter is often problematic. Different contents of water, sugars and salts result in a shift of dielectric, heat and mass transport properties and thus a change of heating or drying curves. In order to guarantee constant product properties, a model food was developed imitating real food properties and showing physical and also microbial stability over several months. Furthermore, the physical properties important for microwave modeling have been determined as functions of temperature and humidity. Of particular relevance are the following properties: • dielectric properties for modeling the interaction of electromagnetic waves with the material, • thermal conductivity and heat capacity for modeling heat transfer, • boiling temperature and diffusion coefficients of the liquid phase for modeling mass transfer, Keywords: Modeling, Food Applications, Food Properties

International Microwave Power Institute

•

density of the liquid phase and the solid matter (for determination of the corresponding volume fractions).

MATERIALS AND METHODS Composition of the Model Food For imitating real food properties and creating an advantageous structure and texture similar to real foods, the model food (Figure 1) consists of the following components: • water (as the only volatile component), • fructose (as representative of the saccharides), • NaCl (for adapting the dielectric loss factor to real food) • CuSO4 (to reduce the NMR-relaxation time of the protons, thus enhancing measurement speed), • cellulose (mixture of microcrystalline cellulose and cellulose fibers; for building a framework) • agar-agar (danish, pulverized; for building a quasi-solid gel) • and potato starch (in order to avoid strong shrinkage during drying).

167

Measurement of Dielectric Properties in the Microwave Frequency Range

Figure 1: Inner structure of model food as determined by MRI

Among many possible methods for the measurement of dielectric properties in the microwave frequency range (Rost, 1978), a widely employed method for food materials was chosen: the open-ended coaxial line probe. The set-up consists of a network analyser (HP 8753D, Hewlett Packard), as the source and the detector of electromagnetic waves of defined frequency. It is coupled by a coaxial line to an open-ended probe (HP 85070b, Hewlett Packard), which has to be in direct contact with the investigated sample (Regier and Schubert, 2001). Measurement of Heat Capacity

Production of the Model Food The first step of the production of the model food is dissolving the salts and sugar in a specific amount of distilled water. After heating up, the insoluble contents have to be added to the solution (with continuous mixing). This suspension has to be heated up to the melting temperature of agar-agar and then molded into an arbitrary form. After cooling, the model food becomes solid and can be shaped further.

For the measurement of heat capacity a differential scanning calorimeter (DSC 2920 CE, TA Instruments) was selected. The principle of the DSC measurement is to determine the temperature changes of the sample while using a well-known heat flux as a function of time and temperature. Measurement of Self-diffusion Coefficients To determine self-diffusion coefficients, nuclear magnetic resonance was used. The underlying

Figure 2: Typical observation time dependence of self-diffusion coefficient of solution in food to free solution (D/D0) 168

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principles can be found, for example, in (Hills, 1998). The measurements were done in a 200MHz-BrukerTMsuper wide bore Avance spectrometer with variable bore diameter of up to 6.4 cm. The measured data were analysed with the help of a self-developed PVWaveTM-programme, yielding the local observation time dependent self-diffusion coefficients. Tortuosity and pore radius The self-diffusion coefficients of liquids in porous matter depend on the observation time (time between gradient pulses) during pulsed field gradient NMR measurements. For short observation periods, the self-diffusion coefficient corresponds to the pure solution (water molecules are free and not limited by pore boundaries). Longer periods lead to decreasing self-diffusion coefficients (see Figure 2). By fitting a theoretical curve to the measured values (Hürlimann, et. al, 1994) the tortuosity (ratio of quadratic length of the real way of a molecule through a porous structure to the quadratic length of the direct way) and the ratio of surface to volume S/V (pore radius = 2/(S/V), for cylindrical pores) can be determined (Badolato, et. al, 2001). Measurement of viscosity of the liquid phase To determine the viscosity of the liquid phase of the model food, a falling ball viscosimeter (Falling ball viscosimeter B, HAAKE) was chosen to measure viscosities in the viscosity range of water. In this setup, a glass tube containing the fluid sample is surrounded by a jacket to allow an accurate temperature control. A ball falls through the fluid sample. The time Δt required for the ball to pass between a defined distance is measured. The value Δt can be used to calculate viscosity. Measurement of Water Activity Gravimetrical and manometrical methods exist to determine sorption isotherms (Loncin and Weisser, 1977). We used gravimetrical measurements: small amounts of the investigated sample were introduced in an atmosphere with constant relative humidity. After reaching equilibrium, the water content of the sample was determined. To regulate the relative humidity of the atmosphere, saturated salt solutions with known water activities were used. Investigation of Microbial Stability In order to test the potential of the model food to


be used as a standard for microwave heating or drying experiments, a series of experiments on the storage stability were conducted. Vegetative microorganisms (E. coli K12) as well as spore-formers (Bacillus subtilis, Geobacillus stearothermophilus) and bakers yeast (Saccharomyces cerevisae) were surface-spread on the model food with a spiral plater (EDDYJET, IUL, Germany) and incubated at their preferred growth temperatures. Controls were run with standard complex media-plates. Additionally, typical spoilage molds were cultivated on standard media, and spores and mycelium transferred to a model food surface. Analyses were performed according to standard procedures of microbial testing of foods (Baumgart, 1999). RESULTS AND DISCUSSION Dielectric properties For modeling the dielectric properties of the model food, it was subdivided into three phases (the liquid phase, the solid matter and the air as gaseous phase). The dielectric properties of the solution were determined with varying water content (complete model food basis) and temperature. The measured values were fitted by a function of third order (for both water content and temperature, see Figure 3). The shape of the curves of the solutions was as anticipated for solutions of salts (and sugar) (Nelson and Datta, 2001). The temperature dependence of the permittivity and the loss factor of the solid matter was negligible compared to the solution, so that the values (εʻ=4.89, ε“=0.21, measured at room temperature) can be seen as constants. The values of air are also constant (εʻ=1, ε“=0) (Nelson and Datta, 2001). To calculate the dielectric properties of the complete model food starting from the properties of the three phases, a model from the literature was adopted, the Landau and Lifshitz, Looyenga equation (Nelson and Datta, 2001): ε1/3 =

V Vsolid 1/3 ⋅ ε solid + gas ⋅ ε1/3gas Vtotal Vtotal

(1)

This equation had to be adapted for three phases taking the liquid phase and the solved agar-agar and starch into account. ε'1/3 = a1 ⋅

V Vsolution 1/3 V ⋅ ε' solution + solid ⋅ ε'1/3solid + gas ⋅ ε'1/3gas Vtotal Vtotal Vtotal (2) 169

Figure 3: The dielectric permittivity and loss factor as a function of humidity (kg water / kg wet basis) and temperature

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ε"1/3 = a 2 ⋅

Vsolution 1/3 V ⋅ ε" solution + solid ⋅ ε"1/3solid Vtotal Vtotal

(3)

a1 = 0.57 ⋅ X W + 0.51

(4)

a 2 = −0.9 ⋅ X W + 2.02

(5)

The comparison of the measured dielectric properties with those calculated show a maximum deviation of less than five percent. Thermal Conductivity The data and fitting equations for thermal conductivity were taken from literature. For calculating the thermal conductivity of the solution, the following equation, describing the thermal conductivity of fructose solutions (dissolved salts have almost no influence on the thermal conductivity (VDI Wärmeatlas, 2002)), was used (Physical Properties of Food, 2002): λ(X W ,υ) = 0.0012

2 υ  υ W  ⋅  486 + 1.55 ⋅ − 0.005 ⋅     °C   m⋅K  °C

  60 ⋅ 1 − 0.54 ⋅ XW  60 + 272 ⋅  1 − XW 

     

For the thermal conductivity of the solid matter a constant value of λ = 0.17 W/(m⋅K) was chosen, being the corresponding value for solids with similar density and composition (VDI Wärmeatltlas, 2002). For the gaseous phase (pores surrounded by humid walls) the following model (heat pipe effect, Schlünder and Tsotsas, 1988)) can be used: 1.81

 υ  + 273  λ calculated 2.252  °C = ⋅  W p  273   m⋅K Pa 

2

 υ  3 p* ) 18.01 ⋅ 10 ⋅ (2501.6 − 2..34 ⋅  °C  ⋅ ⋅ Pa 3 p*  2  υ 1− 8314.3 ⋅  + 273 p  °C  (7)

(8)

In the case of p* ¶ p the thermal conductivity approaches infinity λcalculated ¶ ∞ , the heat transport is limited by the Maxwell velocity: λ max =

w ⋅ Λ ⋅ ρgas ⋅ c P,gas

(9)

3

To calculate the thermal conductivity of the complete model food, the model of Krischer (Krischer and Kast, 1978), extended to three phases, was used: -1

 V  λ V  0.2 ⋅  solut.+gas + solid ⋅ solut./gas  Vtotal λ solid   Vtotal   λ = λ solut./gas ⋅  0.8 +   Vsolut.+gas + Vsolid ⋅ λ solid   V  V λ   total solut./gas total

(10) with: -1

λ solut./gas (6)


   p* 3978.205  = exp  23.462 − with:  υ  Pa  233.349 +  °C 

    V  0.2 ⋅  Vsolution + gas ⋅ λ solution  +  Vtotal λ gas     Vtotal   = λ solution ⋅ 0.8   λ gas  Vsolution Vgas  + ⋅   Vtotal λ solution  Vtotal  (11)

Heat Capacity For describing the specific heat capacity of the model food, the three-phase-model (solution, solid matter, air) was used. The heat capacity of the solution was determined with varying water contents (complete model food basis) and temperatures. The measured values fit a function of third order (for both water content and temperature, see Figure 4). The heat capacity of the solid matter was determined as a function of temperature:   kJ υ c P =  6.7·10 -3 · + 1.42  ⋅   kg ⋅ K °C

(12)

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Figure 4: The specific heat capacity of the solution as function of humidity (kg water / kg wet basis) and temperature

Figure 5: The viscosity of the liquid phase as a function of humidity (kg water / kg wet basis) and temperature

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Figure 6: The self-diffusion coefficient of the liquid phase as a function of the water content and temperature For the gaseous phase the value of the heat capacity is constant (cP = 1 kJ/(kg⋅K), (VDI Wärmeatlas, 2002)). To calculate the heat capacity of the complete model food, the following equation (13) can be used (VDI Wärmeatlas, 2002):

cP =

V Vsolution V ⋅ c P,solution + solid ⋅ c P,solid + gaseous ⋅ c P,gaseous Vtotal Vtotal Vtotal (13)

Viscosity of the Liquid Phase

Tortuosity and Pore Radius Tortuosity and pore radius of the model food were determined at initial water contents ranging from 0.75 to 0.95 using the observation time dependence (see Figure 2) of the self-diffusion coefficient of water in the model food (Hürlmann, et al., 1994). The results show that the tortuosity decreases linearly (14) and pore radius increases exponentially (15) with increasing inital water content.


(15)

Self-diffusion Coefficient Self-diffusion coefficients were determined for the free solution at 25°C. Regarding the water content a third order polynomial was fit: D*(X W, 20°C) = (X W 3 + 0.5 ⋅ X W 2 + 2.5 ⋅ X W ) ⋅ m 2 /s (16) By using the Stokes-Einstein relation:

The viscosity of the liquid phase was determined at water contents between 0.15 to 0.90 and a temperature range of 20°C to 80°C. The results show the expected exponential decrease of viscosity with increasing temperature (Figure 5).

t = -5.03 ⋅ X W,initial + 6.19

rPore = 4.3 ⋅ 10 -4 im ⋅ exp (12.3 ⋅ X W,initial )

(14)

D(T) =

k⋅T 6 ⋅ π ⋅ η(T) ⋅ r

(17)

and taking the viscosity into account, the following equation can be used for calculating the self-diffusion coefficient depending on the water content and temperature (see Figure 6). The deviation between the measured and the calculated values was found to be less than three percent. D∗ (X W ,T) = D∗ (X W ,20°C) ⋅

η(X W ,20°C) (T + 273.15K) ⋅ η(X W ,T) 298.15 K (18)

By taking the tortuosity into account (see Figure 2) the self-diffusion coefficient in the model food can be calculated:

173

Figure 7: The water activity of the model food as function of humidity (kg water / kg wet basis) D*model food = D*free solution /τ = f(X W,initial ,X W ,T)

(19)

The Fickian diffusion coefficients can be calculated using the Darken-equation (Kuhn and Lechert, 1990): D F = D* ⋅

X W da W ⋅ a W dX W

(20)

Water Activity The water activity of the model food was determined between 0.11 < aW < 0.97 at temperatures between 25°C and 50°C. The results show, that in this temperature range the sorption isotherm is only a function of the humidity (dry basis; see Figure 7). The used fit equation type was: A X= (1 − aW )B

The boiling temperature of the liquid phase was calculated using the vapor pressure characteristics of water (VDI Wärmeatlas, 2002) and Clausius-Clapeyron equation (elevation of the boiling point) (Atkins, 1990):  5209 − 273.14 ÷ 1.9 ⋅ 10 −4 ⋅   p   20.91 − ln    mbar    2 Ts ( XW , p ) =      66 5209  ⋅  XW  p    20.91 − ln    66 ÷ 2623 ⋅ 1 − XW  mbar   

      ⋅º C     (22)

Measured and calculated values show a deviation of less than two percent.

(21)

Density of the Liquid Phase and the Solid Matter The density of the solution was determined as a

function of the water content (complete model food basis) and temperature. The measured values fit as a third order function (for both, humidity and temperature). In this case the maximum deviation between calculated and measured density was less than two percent. The density of the solid matter was found to be constant (ρ = 1561 kg/m³).

174

The Boiling Temperature of the Liquid Phase

Microbial Stability The spore-forming bacteria and yeasts tested

did not grow (within the investigated time) on the surface of the model food, and E. coli K12 was even inactivated in less than 10 hours. This is probably due to CuSO4 in the food, which is a known bacteriocidal agent (Wallhäusser, 1995). Mold spores and mycelium also failed to grow on the surface, whereas a control agar-plate containing a standard medium was quickly covered with fresh growth. Since the model food does


Vol. 39, No. 3 & 4, 2004

drying velocity dm/dt / g/s

water loading X / gwater/gdm

10 8 6 4 2 0

4 3 2 1 0

0

2

4

6

8

10

water loading X / gwater/gdm

blanched carrot model food 0

20

40

60

80

100

120

140

time t / min

Figure 8: Drying curves of microwave vacuum dried model food and carrots.

Figure 9: Semi-continuous microwave oven. not contain a nitrogen source (e.g. amino acids) it seems to be unsuitable for mold growth. A long term storage trial at 37 °C in an incubator did not result in spoilage or visible growth of microorganisms after more than one year. Thus the model food can be used as a standard for microwave drying without prior pasteurisation treatment and conveniently stored and handled. Drying curves of the Model Food and Carrots For evaluating the possibility of investigating


microwave processes by using the model food, drying curves of both the model food and carrots were compared (Figure 8). The drying experiments were done in a semicontinuous microwave oven simulating a microwave tunnel with industrial dimensions (see fig. 9, (Erle, 2000)). Although operating pressures of this device can be varied between 20 mbar and 5 bar, in this case the pressure was controlled to be 50 mbar and a microwave power of 300 W at 2450 MHz was chosen. The cylindrical slices of the model food and blanched carrots had a diameter of approximately 10175

15 mm and a thickness of 3-5 mm. The total mass at the beginning of each experiment was kept constant at approximately 140 g. CONCLUSION AND OUTLOOK In this paper the development of a model food was described (the so called Karlsruher MW model food) as well as the determination of equations for all physical properties that are important in microwave processing (the constituents and the physical data are available at the Institute of Food Process Engineering, University of Karlsruhe). It was demonstrated that the drying behaviour of the model food and a real food (carrots) is similar, so that in further research microwave processes can be investigated using the model food to avoid the fluctuations of composition and thus the physical properties in natural foods. Furthermore it is possible to imitate different kinds of real foods by changing initial water content and thus the physical properties. LIST OF SYMBOLS

D0

self-diffusion coefficient of the free solution

m²/s

DF

Fickian diffusion coefficient

m²/s

k

Boltzmann constant

p

pressure

Pa

p*

vapor pressure

Pa

r

mean molecule diameter

m

rPore

pore radius of the porous model food structure

µm

S

surface of the porous structure

m²

T

temperature

TS

boiling temperature

°C

V

volume of the porous structure

m³

Vgas

volume of the gaseous phase of the model food

m³

Vsolid

volume of the solid phase of the model food

m³

Vsolution

volume of the liquid phase of the model food

m³

Vtotal

volume of the complete model food (all three phases)

m³

1.38·10-23 J/K

K

A,B

fitting parameters

-

a1

correction factor of permittivity of solution

-

a2

correction factor of loss factor of solution

-

X

water load of the model food kgwater/kgdry basis

aW

water activity

-

XW

humidity of the model food

cP

heat capacity

kJ/(kg·K)

Δ

cP,gas

heat capacity of the gaseous phase of the model food

observation time (during NMR measurement)

kJ/(kg·K)

Λ

free length of path

cP,solid

heat capacity of the gaseous phase of the model food

kJ/(kg·K)

ε

complex permittivity

-

cP,solution

heat capacity of the liquid phase phase of the model food

εʼ

permittivity

-

kJ/(kg·K)

εʼʼ

loss factor

-

D

self-diffusion coefficient of the solution in the porous structure

m²/s

εʼʼgas

D*

self-diffusion coefficient

m²/s

loss factor of the gaseous phase of the model food

-

εʼʼsolid

loss factor of the solid phase of the model food

-

εʼʼsolution

loss factor of the solution (liquid phase of the model food)

-

εʼgas

permittivity of the gaseous phase

mean Maxwell velocity

D*free solution self-diffusion coefficient of the free solution

m²/s

D*model food self-diffusion coefficient in the model food

m²/s

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m/s kgwater/kgwet basis ms

Vol. 39, No. 3 & 4, 2004

of the model food

-

εʼsolid

permittivity of the solid phase of the model food

-

εʼsolution

permittivity of the solution (liquid phase of the model food) -

η

dynamic viscosity

λ

thermal conductivity

W/(m·K)

λcalculated

calculated thermal conductivity of the gaseous phase

W/(m·K)

λgas

thermal conductivity of the gaseous phase of the model food W/(m·K)

λmax

maximum thermal conductivity limited by Maxwell velocity

W/(m·K)

λsolid

thermal conductivity of the solid phase of the model food

W/(m·K)

λsolut./gas

thermal conductivity of combined liquid and gaseous phase of the model food W/(m·K)

λsolution

thermal conductivity of the liquid phase of the model food W/(m·K)

ρgas

density of the gaseous phase of the model food

τ

tortuosity (ratio of quadratic length of the real way of a molecule through a porous structure to the quadratic length of the direct way)

υ

temperature

Pa·s

kg/m³

-

Hürlimann, M., Helmer, K., Latour, L., Sotak, C., “Restricted Diffusion in Sedimentary Rocks. Determination of Surface-Area-to-Volume Ratio and Surface Relaxivity,” J. of Magnetic Resonance, A 111, 169-178, 1994. Krischer, O., Kast, W., 1978. Die wissenschaftlichen Grundlagen der Trocknungstechnik, Springer. Kuhn, K., Lechert, H., 1990. “Determination of Fickian Diffusion Coefficients of Water in Foods Using NMR-techniques and the DARKEN-equation,” Lebensm.-Wiss. u. Technol., 23, 331-335. Loncin, M. and H. Weisser, 1977. “Die Wasseraktivität und ihre Bedeutung in der Lebensmittelverfahrenste chnik,” Chem.-Ing.-Tech, 49, Nr. 4, 312-319. Nelson, S.O., Datta, A.K., 2001. “Dielectric Properties of Food Materials and Electric Field Interactions,” Datta, A.K., Anantheswaran, R.C. (Eds.): Handbook of Microwave Technology for Food Application, Marcel Dekker Inc., 69-114 Physical Properties of Food, DataBase, 2002. www.nelfood.com Regier, M., Schubert, H., 2001. “Microwave Processing,” Richardson, P. (Ed.), Thermal Technologies in Food Processing, Woodhead Publishing Limited, 178207, 2001. Rost, A., 1978. Messung dielektrischer Eigenschaften, Braunschweig, Vieweg Verlag Schlünder, E.U., Tsotsas, E., 1988. Wärmeübertragung in Festbetten, durchmischten Schüttgütern und Wirbelschichten, Georg Thieme Verlag VDI Wärmeatlas, 2002. 9. Auflage, Springer Wallhäusser, K.H., 1995. Praxis der Sterilisation, Georg Thieme Verlag

°C

REFERENCES Atkins, P.W., 1990. Physikalische Chemie, VCH. Badolato, G.G., Regier, M., Schubert, H., 2001. “Messung von Selbstdiffusionskoeffizienten an mikrowellenvakuumgetrockneten Lebensmitteln mittels PFG-NMR,“ Wiss. Abschlussber., 36. Internationales Seminar Univ. Karlsruhe, 2001. Baumgart, J., 1999. Mikrobiologische Untersuchung von Lebensmitteln. Behr´s Verlag Erle, U,, 2000. “Untersuchungen zur MikrowellenVakuumtrocknung von Lebensmitteln,“ Dissertation, Universität Karlsruhe Hills, B., 1998. Magnetic Resonance Imaging in Food Science, J. Wiley & Sons


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