1. No category

Journal of Food Engineering 116 (2013) 315–323
Contents lists available at SciVerse ScienceDirect
Journal of Food Engineering
journal homepage: www.elsevier.com/locate/jfoodeng
Microwave inactivation of Escherichia coli K12 CIP 54.117 in a gel medium:
Experimental and numerical study
Mohamad Mazen Hamoud-Agha, Sébastien Curet ⇑, Hélène Simonin, Lionel Boillereaux
LUNAM Université, ONIRIS, CNRS, GEPEA, UMR 6144, Site de la Géraudière, Nantes F-44322, France
a r t i c l e
i n f o
Article history:
Received 29 July 2012
Received in revised form 30 October 2012
Accepted 26 November 2012
Available online 20 December 2012
Keywords:
Microwave pasteurization
Thermal inactivation
Predictive microbiology
Finite element
Escherichia coli K12 CIP 54.117
a b s t r a c t
This study evaluates the efficiency of the inactivation of Escherichia coli K12, entrapped within calcium
alginate gel, by microwave processing compared to a conventional approach i.e. by heating in a water
bath. Microbial thermal inactivation equations coupled with heat transfer and Maxwell’s equations are
integrated into a 3D Finite Elements model under dynamic heating conditions. Water bath microbial
inactivation experimental data are exploited for performing parameter identification of a non-linear
microbial model, and the Calcium alginate gel’s dielectric properties were numerically estimated. The
coupled model provides a very good fitting to the experimental results. The simulation have shown
uneven temperature distribution during microwave heating which may interpret its lower inactivation
efficiency comparing to the conventional water bath treatment. This study also demonstrates the reliability of the coupled modeling approach to estimate the efficiency of the microbial inactivation, despite the
thermal heterogeneity inherent in the microwave treatment.
Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Microwave heating is increasingly used for several processes in
the food industry e.g. drying, thawing, meat tempering, pasteurization, sterilization and blanching of foods (Tang et al., 2008; Venkatesh and Raghavan, 2004). In fact, there are several advantages
of microwave heating compared to conventional heating methods
due to the different ways the energy is delivered. In particular,
microwave heating can provide a rapid rise in temperature within
materials of low thermal conductivity such as food products. Thus,
microwave heating reduces the processing time, which may enhance overall food quality (Cinquanta et al., 2010; Guan et al.,
2002; Lau and Tang, 2002; Sun et al., 2007).
Microwave pasteurization has been tested on several food products, either liquid like fruit juices and milk (Cañumir et al., 2002;
Kindle et al., 1996) or solid like meat (Huang and Sites, 2007; Yilmaz et al., 2005) and vegetables (Lau and Tang, 2002). Moreover,
microwave heating has been shown to be effective in inactivating
both gram positive and gram negative bacteria (Fujikawa et al.,
1992; Giuliani et al., 2010; Guan et al., 2003; Zhou et al., 2010).
The existence of non-thermal effects of microwaves on microorganisms is subject to debate. On the one hand, several publications
suggest that microwave irradiation can cause non-thermal effects
(Barnabas et al., 2010; Bohr and Bohr, 2000; Hong et al., 2004;
Kozempel et al., 1998) while, on the other hand, some studies have
⇑ Corresponding author. Tel.: +33 2 51 78 54 63; fax: +33 2 51 78 54 67.
E-mail address: [email protected] (S. Curet).
0260-8774/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.jfoodeng.2012.11.030
found that microwaves inactivate microorganisms exclusively by
heat (Fujikawa et al., 1992; Heddleson and Doores, 1994; Shaman
et al., 2007).
The most important limiting factor associated with microwave
pasteurization is the non-uniform temperature distribution, resulting in hot and cold spots in the heated product. This can lead to the
survival of pathogenic microorganisms in the less heated zones,
which can be a major obstacle to the widespread development of
microwave heating in industrial food pasteurization (Vadivambal
and Jayas, 2010). This is particularly critical for solid food products
where convection does not occur. For example, a recent study indicates that short time exposures of chicken portions to microwave
heating did not eliminate Escherichia coli O157:H7 because of the
non-homogeneous heating and wide temperature variations ranging from 66.7 to 92.0 °C (Apostolou et al., 2005).
Reliable thermal processing calculations require an understanding of the thermal inactivation kinetics of microorganisms
throughout the heating process and in each part of the treated
samples. As a result, the microbial inactivation kinetics has to be
coupled with the heat transfer phenomena to calculate the survival
of bacteria, especially in the microwave non-uniform heating process. These relationships are commonly expressed in terms of
mathematical models. To our knowledge, there is a lack of coupled
modeling studies to understand the microwave pasteurization
process.
Inactivation of vegetative bacterial cells, whether due to a thermal or non-thermal food processing technique, can exhibit one of
eight shapes (Geeraerd et al., 2005). As a consequence, various
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Nomenclature
a, b
dimensions of the wave guide (m)
AsymDref asymptotic decimal reduction time (min)
critical component represents physiological state of the
Cc
cells (-)
Cp
apparent specific heat (J kg1 K1)
E
electric field intensity (V m1)
amplitude of the electric field (V m1)
E0
Elocal
electric field intensity at every point (V m1)
h
convective heat transfer coefficient (W m2 K1)
H
magnetic field intensity (A m1)
k
thermal conductivity (W m1 K1)
kmax
specific inactivation rate (min1)
L
sample length (m)
N
microbial population (CFU/g)
N0
initial microbial population (CFU/g)
Nsimul
simulated microbial population (CFU/g)
Nexp
experimental microbial population (CFU/g)
volumetric heat generation term (W m3)
Qabs
r
radial distance (m)
R
radius (m)
models have been proposed to describe the non-linear curves (Albert and Mafart, 2005; Geeraerd et al., 2000; Linton et al., 1995;
Mafart et al., 2002; Peleg, 1999; Xiong et al., 1999). The dynamic
non-linear model (Geeraerd et al., 2000) overcomes the disadvantages of several previous models (Daugthry et al., 1997; Sapru
et al., 1992; Whiting, 1993; Xiong et al., 1999). This model has been
successfully applied to the inactivation data of different microorganisms under various experimental conditions (Marquenie et al.,
2003; Valdramidis et al., 2005; Velliou et al., 2011).
Microwave heating can be modeled using two main approaches: Lambert’s law, which assumes an exponential decay of
microwave absorbed power as a function of penetration depth
within the sample, or a method based on the complete resolution
of Maxwell’s equations, which govern the electromagnetic field
propagation. In the case of thin samples, i.e. much smaller than
the microwave penetration depth, Maxwell’s equations need to
be solved (Chen et al., 2008; Curet et al., 2008). Furthermore, for
cylindrical geometries, the Lambert’s law approach provides a less
accurate temperature distribution during microwave heating compared to the Maxwell’s equations approach (Yang and Gunasekaran, 2004).
There is no study which highlights both experimental and
numerical data concerning the microbial inactivation in solid matrix during a microwave heating treatment.
In this paper, the microbial inactivation effect of microwave
heating is compared with a conventional water bath inactivation.
Furthermore, in order to interpret the microwave inactivation results, Maxwell’s equations and heat transfer are coupled to microbial inactivation equations, and integrated into a 3D Finite Element
model under dynamic heating conditions.
2. Materials and methods
2.1. Culture and preparation of cell suspensions
E. coli K12 CIP 54.117 was obtained from the Pasteur Institute,
France. The stock culture was kept at 80 °C in Brain Heart Infusion (BHI) broth (Fluka-53286 Sigma–Aldrich, 38297 St. Quentin
Fallavier, France) with 30% (v/v) glycerol (104094 Merck, Darmstadt, Germany). A pre-culture was prepared by transferring a loopful of the stock culture into 10 mL Tryptic Soy Broth (TSB)
T
T0
T1
Tref
x, y, z
z value
temperature (°C)
initial temperature of product (°C)
ambient temperature (°C)
microbial inactivation reference temperature (57 °C)
spatial coordinates in the three dimensions (m)
thermal resistance constant (°C)
Greek letters
e
complex permittivity (F m1)
e0
permittivity of vacuum (8.85 1012 F m1)
e0r
relative dielectric constant
e0r 0
relative dielectric loss factor
l
magnetic permeability of the material (H m1)
l0
magnetic permeability of vacuum (1.256 106 H m1)
q
density (kg m3)
r
electrical conductivity (S m1)
x
pulsation of the microwave radiation (rad s1)
(9100461, 30 g/L Biokar, Grosseron, 44819 St. Herblain, France)
and incubating it at 30 °C for 24 h on a rotary shaker at 175 rpm
(Excella E24, New Brunswick Scientific, Edison, New Jersey, USA).
1 mL of the pre-culture was then subcultured into 100 mL fresh
TSB in a 250-mL Erlenmeyer flask in the same conditions for
16 h. Early stationary-phase cultures were harvested by centrifuging the broth culture for 10 min at 8720g at 4 °C (Jouan, GR 20.22,
Thermo scientific, 91963 Villebon sur Yvette, France). The pellet
was resuspended to approximately 1.5 1010 cells per mL in
20 mL sterile Phosphate Buffered Saline (PBS).
2.2. Calcium alginate gel preparation
Calcium alginate (Ca-alginate) gel is widely used as an experimental material in food-related research (Yoo et al., 1996). Two
volumes of sterile 3% (w/w) sodium alginate solution (Algogel
3021, Cargill, 78100 St. Germain en laye, France) were mixed with
one volume of the cell suspension. By using a 3-mm diameter cutended micropipette, 0.5 mL of this mixture was then flowed gently
and constantly into a sterile 1% (w/w) CaCl2 solution. The resulting
cylindrical gels were hardened in this solution for 15 min, then
washed with sterile PBS to remove excess calcium ions and untrapped cells. The gels were then dried for 10 min inside the laboratory fume hood. The final gels (8 mm diameter, 10 mm height) of
0.53 ± 0.2 g with a cell concentration of 109 CFU/g were used
immediately.
2.3. Programmable water bath treatment
A dynamic heating experiment was designed to compare the
inactivation rate after conventional water bath heating and microwave heating. Glass test tubes (9 mm diameter, 150 mm height)
were filled with approximately 1 g of Ca-alginate gel, sealed by a
sterilized aluminum paper and then subjected to linear heating
in a programmable water bath (Hart Scientific 9105, American
Fork, UT, USA). The water bath temperature was programmed to
increase linearly from 20 °C to 64 °C at 9 °C/min, which was calculated by a linear regression of the microwave heating ramp for the
lethal range (i.e. 50–64 °C). The temperature of the gel was measured in the geometrical center of the tube by using a sterile thermocouple linked to a data logger (AOIP datalog, 91133 Ris Orangis,
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France). At specific temperatures (50, 55, 57, 59, 62, 64 °C), the
heating was ended by immersing the tube in iced water. Viable
cells were then enumerated. Results are the average of at least
three independents trails.
2.4. Microwave instrument and treatment
The experimental apparatus was a microwave system (Fig. 1),
supplying a monochromatic wave in the fundamental mode,
TE10, operating at a frequency of 2.45 GHz. Microwave energy
was transmitted along the z-direction of a rectangular waveguide
(cross-section 86 mm 43 mm). To ensure that only a minimal
amount of microwave was reflected back to the sample, a water
load was fixed at the end of the guide (at 450 mm under the sample, water flow rate of 0.23 L/min, DT 10 °C). Its efficiency in
absorbing microwaves was tested by measuring reflected power
in the waveguide using a directional coupler. Continuous microwave treatment was performed by putting one cylindrical gel per
sterile EppendorfÒ tube (11 mm diameter, 40 mm height), sealing
it tightly and then arranging two tubes on a polystyrene plate
(84 mm 41 mm 10 mm) placed perpendicular to the direction
of the irradiation. The incident microwave power was adjusted to
130 W and the samples were heated from ambient temperature
to 64 °C.
The effect of the polystyrene layer on the electric field was neglected. A preliminary test has been carried out to ensure that the
plastic EppendorfÒ tubes do not absorb microwave energy.
Due to the symmetrical condition for the electromagnetic field
distribution (TE10 mode), temperatures were measured in one tube
as illustrated in (Fig. 1) by using optical fiber sensors (T1 Neoptix,
Quebec, Canada) inserted at two geometrical central points and attached to a data logger (ReFlix-4, Neoptix, Quebec, Canada).
Like for the water bath treatment, one tube was removed at different temperatures (50, 55, 57, 59, 62, 64 °C), cooled immediately
in iced water and then the viable cells were enumerated. Results
are the average of at least three independents trails.
2.5. Measurement of cell inactivation
An appropriate quantity of McIkaine buffer (0.2 M Na2HPO4,
0.1 M citric acid) was prepared to dissolve the gel in order to release the cells from the beads after the heat treatment.
For the programmable water bath assays, 3 mL of McIkaine buffer was added to the tube and the mixture was then drained into a
sterile stomacher bag. The test tube was rinsed with 3 mL of PBS
and again drained into the bag.
For the microwave tests, the gel was transferred, in aseptic conditions, into a sterile stomacher bag and the tubes were rinsed with
1.5 mL of PBS which was then drained into the bag. 1.5 mL of McIkaine buffer was finally added to the bag.
The mixture was homogenized by a Stomacher Lab Blender
(Interscience BagmixerÒ 400 B054300, Grosseron, 44819 St. Herblain, France) for 25 min.
The number of cells released was measured by plating appropriate decimal serial dilutions of the homogenized mixture on Tryptic
Soy Agar in duplicate then incubating them at 30 °C for 48 h. The
results are the average of at least three independent repetitions
for each of these treatments.
2.6. Modeling microbial inactivation under non-isothermal conditions
2.6.1. Modeling of microbial inactivation
Without incorporating the tailing effect, as it was not observed
in the experimental data, the reduced equations of the model were
adopted to describe the non-isothermal inactivation kinetics
(Geeraerd et al., 2000). It consists of two coupled ordinary differential equations as follows:
dN
1
N
¼ kmax dt
1 þ Cc
ð1Þ
dC c
¼ kmax C c
dt
ð2Þ
where N represents the microbial population (CFU/g), Cc (critical
component) relates to the physiological state of the cells (–), and
kmax is the specific inactivation rate (1/min).
Thermal inactivation parameters, i.e. the asymptotic decimal
reduction time (AsymDref) (Juneja et al., 2001) and the thermal
resistance constant (z value), which is the temperature change required to achieve a tenfold change in AsymD, were integrated into
the Bigelow model (Eq. (3)) to yield predictions for the specific
inactivation rate at a given temperature.
kmax ðTÞ ¼
ln 10 ðlnz10ðTT ref ÞÞ
e
AsymDref
ð3Þ
Within the lethal range of 50–64 °C, the heating ramp of 9 °C/
min was implemented in the numerical model with a linear regression of the experimental data.
The reference temperature, Tref, was chosen to be equal to the
middle of the lethal experimental temperature range (i.e. 50–
64 °C) in order to minimize the uncertainty of AsymDref (Poschet
et al., 2005).
2.6.2. Estimation of bacterial inactivation kinetics
The parameters implemented in the inactivation model
(AsymDref, z, and Cc(0)) were estimated by using the Levenberg–
Marquardt optimization method (available in MatlabÒ software)
This technique has already proved its reliability for estimating
the kinetic parameters of the inactivation model (Valdramidis
et al., 2008).
The criterion to minimize is defined following the root mean
square error between the water bath experimental data and the
numerical data:
J¼
Fig. 1. Microwave system.
t final
X
i¼t init
Nsimul ðiÞ
Nexp ðiÞ
log
log
N0
N0
!2
ð4Þ
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where N0 is the initial microbial population (CFU/g), Nsimul is the
simulated microbial population, and Nexp is the experimental
microbial population at the same time.
To our knowledge, there is no inactivation data available in the
literature for E. coli K12 in a gel media; therefore, the model
parameters were numerically calculated based on previous observations in the literature concerning E. coli (Juneja and Marmer,
1999; Juneja et al., 1997; Valdramidis et al., 2005). The initial estimates for the unknown parameters were: AsymD57 = 5 min,
z = 6 °C/min, Cc(0) = 0.82 (–). The optimization algorithm was also
tested with different initial parameters to reduce the risk of stopping on a local minimum. The 95% confidence interval of the optimized parameters was also calculated (nlparci function in MatlabÒ
software).
The maximum amplitude of the incident electric field was located
at the center of the sample. Due to the non-uniformity of the electric field along x and the symmetry considerations at the center, 1=4
of the rectangular waveguide was modeled. As a result, only one
half of the cylindrical sample was considered (Fig. 2).
Maxwell’s equations were solved in both air and the cylindrical
sample, and the microwave heat generation in the sample was deduced from the electromagnetic field distribution.
For the TE10 mode (Ex = Ez = 0), the general governing equation
for electric field propagation after mathematical simplification
leads to (Curet et al., 2009):
@ 2 Ey @ 2 Ey
þ 2
@x2
@z
!
þ x2 le0 1 j
r
E ¼0
xe0 y
ð5Þ
With the associated initial and boundary conditions:
2.7. Modeling of heat transfer during microwave heating
E¼0
In order to analyze the heat transfer during microwave heating
of a cylindrical sample, the following assumptions were made:
Assumption 1: The product is surrounded by a medium with
zero dielectric losses (air). Thus, the heat transfer is not spatially
solved within the surrounding medium (air) due to the dielectric
characteristics being very close to a vacuum. However, natural
convection to the air is considered as a boundary condition.
Assumption 2: The product is homogeneous and isotropic.
Assumption 3: The thermophysical properties are constant and
the dielectric properties are temperature-dependent.
Assumption 4: The mass transfer is negligible.
Assumption 5: The walls of the waveguide are perfect electric
conductors.
Assumption 6: The initial temperature of the sample is
homogeneous.
Assumption 7: The shrinkage of the sample is neglected during
the thermal treatment.
2.7.1. Modeling of microwave propagation
In our case, the TE10 mode was considered and the electric field
was contained within the (xOy) plane with only one component Ey.
at t ¼ 0; 8x y z
Ein ¼ E0 cos
p x
a
at z ¼ þ1; 8x y; 8t i 0
n ðHair Hsample Þ ¼ 0
nH¼0
Ey ¼ 0
at r ¼ R; 8z and z ¼ L=2; 8r; 8t i 0
at x ¼ 0; 8z y; 8t i 0
at x ¼ a=2; 8z; y; 8t i 0
The heat generation due to microwaves was computed from the
local electric field strength at any point of the cylindrical domain.
Q abs ¼
1
x e0 e00r jElocal j2
2
ð6Þ
2.7.2. Modeling of heat transfer
Heat transfer is based on the generalized heat equation, which
depends on the thermo-physical properties of the product, as
follows:
qC p
@T
¼ div ðkrTÞ þ Q abs
@t
Fig. 2. Model design.
ð7Þ
M.M. Hamoud-Agha et al. / Journal of Food Engineering 116 (2013) 315–323
The local electromagnetic heat generation term Qabs quantifies
the amount of power dissipated into the gel by dielectric losses.
The associated initial and boundary conditions can be expressed
as follows:
T ¼ T0
k
at t ¼ 0; 8r 8z;
T 0 ¼ 20 C
@T ¼ 0 8z; 8t i 0
@r r¼0
@T k ¼ hðT T 1 Þ 8z; 8t i 0;
@r r¼R
k
@T ¼ hðT T 1 Þ
@z z¼L=2
319
COMSOLÒ Multiphysics 4.2a. The mesh consists of 26750 tetrahedral elements and is a good compromise between precision and
computation time. In order to simulate 270 s of the complete
microwave heating process, the total CPU time required was
approximately 30 min on a SUNÒ Microsystems U40 Workstation,
equipped with 2 AMDÒ Opteron processors, at 3 GHz, with 20 GB
of RAM, running on RedHatÒEnterprise LINUX 5, 64 bits.
2.8. Model validation
T 1 ¼ 18:5 C
8r; 8t i 0
The convective heat transfer coefficient is due to natural convection between the surrounding air medium and the surface of
the sample. As a first approximation, the convective coefficient
was calculated from empirical correlations for vertical isothermal
plates with a correction factor to make them applicable to vertical
isothermal cylinders (Cebeci, 1974). The local heat transfer coefficient from a vertical isothermal plate can be obtained from an
empirical correlation (Churchill and Chu, 1975).
2.7.3. Thermophysical and dielectric properties
The thermophysical properties of Ca-alginate gel were taken directly from the literature for a sodium alginate gel (Lin et al., 1995).
They were thus determined to be:
Density, q = 1010 kg m3
Specific heat, Cp = 4120 J kg1 K1
Thermal conductivity, k = 0.8374 W m1 K1
The key factor for the numerical modeling during microwave
heating is the knowledge of the dielectric properties of Ca-alginate
gel.
Due to experimental complexity, the dielectric properties were
numerically estimated, over the heating range (20–64 °C), based on
temperature dependant equations available in the literature for sodium alginate gel (Lin et al., 1995). During the optimization procedure, five numerical parameters related to linear or polynomial
functions were adjusted (Eqs. (8) and (9)). The Levenberg–Marquardt optimization method was used to minimize the error between
the temperature–time microwave experimental measurements at
the geometrical center of the sample and the simulated ones.
2.7.4. Computational details
Based on a Finite Element method, the three-dimensional
numerical model was solved with the computational code
After establishing the microwave coupled model and selecting
the appropriate parameters, the simulated temperature profile at
the geometrical center was compared with the experimental data.
The volumetric mean inactivation predicted from the model was
also compared to the experimental inactivation data.
3. Results and discussion
3.1. Inactivation of E. coli K12 during microwave and water bath
heating
The experimental temperature at the geometrical center of Caalginate gel exposed to 130 W microwave power and to a programmed water bath treatment is displayed in Fig. 3.a. The time–
temperature profile shows an almost linear come-up profile, previously reported for microwave heating (Pitchai et al., 2012;
Ramaswamy and Pilletwill, 1992).
Several studies have reported that thermal inactivation of a micro-organism not only depends on treatment temperature and
holding times, but also how fast the samples were brought to the
treatment temperature (Chung et al., 2007; Huang, 2009; Valdramidis et al., 2007). Based on microwave experiments, a heat ramp of
9 °C/min was reproduced by a programmable water bath to eliminate the effect of heating history on microbial death. The temperature of the water bath was automatically controlled to increase
linearly from 20 °C to a final temperature of around 64 °C. The
lag time at the beginning of the curve is due to the thermal conduction from the outside layers to the center of the tube. Nevertheless,
the global temperature profiles for the water bath and microwave
treatments show the same heating rates from 20 to 64 °C (Fig. 3a).
The experimental survival curves during conventional heating
of E. coli K12 within Ca-alginate gel was compared to the inactivation curves obtained with a microwave heating process (Fig. 3b).
No significant differences in microbial inactivation were observed for temperatures up to 59 °C. For higher temperatures, the
inactivation due to microwave heating was largely lower (more
than 5log) than that obtained for water bath heating.
Fig. 3. (a) Heating ramps under microwave (continuous line) and programmed water bath (dashed line) treatments, linear regression (dotted lines), and (b) experimental
inactivation of E. coli K12 in Ca-alginate gel during microwave (s) and water bath heating (d), standard deviations (|).
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M.M. Hamoud-Agha et al. / Journal of Food Engineering 116 (2013) 315–323
Table 1
Identification of parameters based on water bath inactivation data.
AsymD57 (min)
z (°C)
Cc(0) (–)
3.9 ± 0.7
6.28 ± 0.36
0.23 ± 0.23a
a
The sensitivity analysis reveals that the Cc(0) value does not significantly
influence the optimization results.
The experimental and predicted data of E. coli inactivation within water bath are presented in Fig. 4. The bacterial concentration
did not change significantly at the early stage of the heating process. However, the rate of bacterial inactivation accelerated above
59 °C.
Reliable microbial inactivation parameters were extracted. The
model was able to describe the inactivation of the bacteria under
water bath treatment.
It thus appears that the Geeraerd et al. (2000) model provides a
very good fit for our experimental results under dynamic
conditions. The relevance of this methodology during a microwave
inactivation process within Ca-alginate gel is now evaluated.
3.3. Simulation of heat transfer during microwave treatment
Fig. 4. Fit of the reduced Geeraerd et al. (2000) inactivation model (continuous line)
for water bath experimental data (d) (from 50 °C to 64 °C) with the use of a linear
temperature profile (dashed line), standard deviations (|).
To explain this lower microbial microwave inactivation, it was
assumed that the geometrical center of the sample may not be
the actual cold point despite the small volume of the gel. Due to
the difficulty in predicting experimentally the cold point location,
the numerical simulation remains a reliable tool. Thus, numerical
simulations were used to study the temperature distribution within the gel, and to explain the inactivation efficiency differences between the two treatments.
In order to predict the temperature profiles in the sample during microwave heating, a three-dimensional Finite Element model
of coupled heat transfer and electromagnetism was designed.
The convective heat transfer coefficient is obtained from an
empirical correlation dedicated to vertical isothermal cylinder.
The natural convection coefficient ranges from 7 to 13 W m2 K1
and is a function of temperature of the sample.
The temperature-dependent dielectric properties of Ca-alginate
gel needed to be accurately characterized. Based on literatures
equations, the numerically optimized dielectric properties of the
gel in this research were found to be similar to those of sodium
alginate gel (Fig. 5b), particularly for the dielectric loss factor for
which very close values were obtained. The influence of the dielectric constant on the heating was more remarkable. The difference
between the optimized Ca-alginate and the literature Na-alginate
values is due to the different salt content in the two studies (Stogryn, 1971). At the optimum, five parameters were adjusted and the
dielectric properties were expressed as functions of temperature,
as shown in Eqs. (8) and (9):
Dielectric constant;
3.2. Modeling microbial inactivation under water bath heating
Water bath inactivation data were used to predict the inactivation curves of E. coli K12 in Ca-alginate gel under dynamic heating
conditions from the Geeraerd et al. (2000) model.
The model used in this study was validated with a predefined
temperature profile with a heating rate of 9 °C/min.
The resulting parameters based on the Levenberg–Marquardt
optimization technique and their confidence intervals are shown
in Table 1.
e0r ¼ 86 0:27 T ð CÞ
Dielectric loss factor;
e00r ¼ 19:92 0:296 T þ 0:0025 T 2
ð8Þ
ð9Þ
The modeling of microwave absorbed power and temperature
distribution in microwave heating was highly reliable and the
numerical data fitted the experimental data very well. The evolution of the experimental temperature compared to the numerical
data is depicted at the sample center (Fig 5a)
Three-dimensional temperature contours obtained from the
numerical simulation (Fig. 6). The simulation highlights uneven
temperature distributions and a large temperature gap (more than
Fig. 5. (a) Measured temperature profiles (s) with standard deviations (|) at the sample center, simulated temperature profile with the optimized Ca-alginate dielectric
properties (continuous line) and simulated temperature profile with the Na-alginate dielectric properties (dashed line), and (b) comparison of the dielectric properties of Caalginate (continuous line) and Na-alginate (dashed line).
M.M. Hamoud-Agha et al. / Journal of Food Engineering 116 (2013) 315–323
Fig. 6. (a) 3D temperature distribution within the cylindrical Ca-alginate gel at the
end of microwave processing (Pin = 130 W, t = 270 s), (b) cross-section at the gel top
surface, (c) cross-section at the gel center, and (d) cross-section at the gel bottom
surface.
5 °C) is observed between the hottest and coldest points within the
heated sample. Confirming the focusing effect observed by previous studies for cylindrical objects (Vilayannur et al., 1998; Zhou
et al., 1995), the numerical simulation demonstrates that hot spots
occurred along the central axis whereas cold spots were located
near the surface. As a consequence, the bacteria located at the surface were not significantly affected by the heating temperature.
The natural convection at the surface and the heat generated by
microwaves tends to a local thermal equilibrium. This may explain
the difference between the water bath and microwave inactivation
results observed (Fig. 3). Thus, despite the small volume of the
sample, the large inactivation variability between the water bath
and microwave treatment is probably due to a significant non-uniform temperature distribution during the microwave treatment.
3.4. Simulation of microbial inactivation during microwave treatment
As the temperature inside the food product is not uniform, the
microbial evaluation is a function of space coordinates. Thus, the
overall destruction of bacteria during microwave heating was evaluated by implementing the coupled ordinary differential equations
of the Geeraerd et al. (2000) model into the 3D Finite Element
model over the entire course of the heating process. The previous
parameter estimation results during water bath treatment were taken as inputs for the microwave kinetic parameters. To accept this
321
Fig. 7. (a) 3D E. coli inactivation distribution within the cylindrical Ca-alginate gel
at the end of microwave processing (Pin = 130 W, t = 270 s), (b) cross-section at the
gel top surface, (c) cross-section at the gel center, and (d) cross-section at the gel
bottom surface.
application, the non-thermal effect of microwaves on microorganisms was neglected.
In this study, microbial inactivation is defined at any point as a
function of time. The 3D distribution of E. coli inactivation in the
gel was calculated using the simulation procedure during a microwave treatment of 270 s (Fig. 7). These results demonstrate a problem of non-uniform inactivation and agree with the uneven
temperature distribution. The inactivation efficiency varies a great
deal (more than 2log) between the different locations within the
sample.
The microbial survival data from the coupled model were integrated numerically over the whole geometrical volume. The mean
inactivation values predicted by the numerical model as a function
of temperature located at the center of the sample are presented in
Fig. 8. The results show very similar inactivation behavior for both
numerical and experimental points. This result also demonstrates
the accuracy of the kinetic parameter estimation and the successful
data extrapolation from water bath experiments to microwave
processing. As a result, the microwave treatment is a thermal process and no difference with the conventional treatment was
numerically confirmed.
It is clear that uncontrolled process conditions lead to the development of unacceptable uneven temperature distributions caused
322
M.M. Hamoud-Agha et al. / Journal of Food Engineering 116 (2013) 315–323
Fig. 8. Fit of the reduced Geeraerd et al. (2000) inactivation model for microwave
experimental data (s) (continuous line) and water bath data (d) (dashed line).
by a number of interacting factors. The most important factors that
influence the uniformity of temperature distribution are the dielectric and thermophysical properties of the food, the shape and size
of the product and the frequency and power of the incident electromagnetic wave (Datta, 1990). Uniform and effective heating depend on the proper integration of all these parameters at the same
time. One of the possible reasons for obtaining this heterogeneity
in our study is the use of continuous microwaves. Some studies
found that pulsed microwave heating provides more uniform heating within agar gel cylindrical samples comparing to continuous
microwave heating (Gunasekaran and Yang, 2007). Furthermore,
another study reported a more marked influence of pulsed waves
than continuous ones on the inactivation rate of E. coli K12 IF0
3301 (Sato et al., 1996). Thus, we can hypothesize that pulsed
microwaves are more reliable for microwave pasteurization.
In order to design a reliable microwave heating operation,
knowledge of the local temperature distribution during the treatment is required. Currently, there are a number of different methods for measuring temperatures in microwave fields; their
advantages and shortcomings are discussed in a recent study
(Knoerzer et al., 2009).
A three-dimensional temperature map dedicated to microwaveheated products is an essential requirement to ensure food safety
in microwave pasteurization processes. The spatial resolution
achievable by using fiber-optic sensors is often unsatisfactory
and the reliability of using fiber-optic sensors to ensure food safety
in microwave pasteurization processes can therefore be questioned. By the use of numerical modeling, our study clearly demonstrates the possibility of locating the coldest point inside the food
matrix and predicting the microwave inactivation of bacteria.
4. Conclusion
The objective of this research was to compare a microwave
inactivation of E. coli K12, entrapped within Ca-alginate gel, with
a conventional inactivation in dynamic heating conditions. Due
to non-uniform microwave heating, lower inactivation efficiency
was obtained by the microwave treatment.
By using a Finite Element method, a predictive modeling approach for microwave pasteurization is proposed. Governing equations for electromagnetic propagation, heat transfer and microbial
inactivation were successfully coupled to predict the temperature
distributions and microbial inactivation within the gel. The suitability of Geeraerd et al. (2000) models for describing the survival
of E. coli was confirmed for a solid medium during water bath and
microwave inactivation treatment.
The results also highlight the possibility of modeling the microwave process, provided that a good estimation of the dielectric
properties is available. Microwave heating differs from conventional heating in that measuring the temperature at a few locations
does not guarantee the real temperature distribution in the product, as the heating pattern can be uneven and difficult to predict.
Thus, volumetric measurement of temperature or accurate determination of the cold point within the product is mandatory. This
study clearly demonstrates that the differences between conventional and microwave inactivation processes are due to temperature heterogeneities.
As a perspective, the coupled model should now be tested with
new operating conditions in order to evaluate its robustness in predicting microbial inactivation for microwave pasteurization. A further development of this approach describes a feedback-control
loop in the simulation based on a combination of electromagnetism, heat transfer and microbial inactivation calculations, which
helps to optimize microwave processes to ensure their safety as
a reliable pasteurization method.
Acknowledgment
The authors acknowledge the financial support provided by the
Syrian Ministry of Higher Education and Scientific Research.
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