microwave inactivation of bacteria under dynamic heating ...€¦ · q abs e rms p f 0 r e rms 2...
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Microwave Inactivation of Bacteria under Dynamic Heating Conditions
in Solid Media S. Curet, M. Mazen Hamoud-Agha
LUNAM Université, ONIRIS, CNRS, GEPEA, UMR 6144, site de la Géraudière, Nantes, France
Excerpt from the Proceedings of the 2012 COMSOL Conference in Milan
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
2
The microwave pasteurization process
Application for prepacked food (yoghurt, pouch-packed meals, milk…)
Difficulty in monitoring and predicting the microwave heating pattern during processing
Few literature reviews concerning microwave inactivation process within a solid food products
Objective: predicting microbial inactivation during microwave pasteurization
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
3
Microwave processing into a TE10 rectangular waveguide
Pin = 130 W
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
4
Governing equations
• Heat transfer equation (PDE from COMSOL®)
absp QTkdivt
TC
).(
Thermophysical properties of the Ca-alginate gel*
Microwave absorbed power (W.m-3)
Maxwell’s equations (kg.m-3) 1010
Cp (J.kg-1.K-1) 4120
k (W.m-1.K-1) 0.84
* Lin, Y. E., R. C. Anantheswaran, et al. (1995). "Finite element analysis of microwave heating of solid foods." Journal of Food Engineering 25(1): 85-112.
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
5
Governing equations
• Electric field propagation (RF module)
Maxwell’s equations for a TE10 rectangular waveguide (sinusoidal time-varying fields with w = 2p f)
²...2² ''
0 rmsrrmsabs EfEQ p
2
localrms
EE
Qabs : volumetric heating rate (W.m-3)
= Electrical conductivity (S/m)
f : frequency of microwaves (2.45×109 Hz)
0 : permittivity of free space (F.m-1)
r’’ : relative dielectric loss factor
Erms: root-mean-square average value of electric field at a location (V.m-1)
01'
'2
2
2
2
2
y
yyEj
z
E
x
E
w
w
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
6
Governing equations
• Dielectric properties of the sample (2.45 GHz)
r’ = 81.79-0.299×T(°C)
r’’ = 22.6-0.378×T+2.93×10-3×T2
* Lin, Y. E., R. C. Anantheswaran, et al. (1995). "Finite element analysis of microwave heating of solid foods." Journal of Food Engineering 25(1): 85-112.
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
7
Governing equations
• Boundary conditions
rLzandzRratHHn
zyxatHn
zyaxatandzxbyyatEE
ab
PZEyxzat
a
xExE
zyxtatE
sampleair
y
inTEy
,2/,0
,00
,2/,2/,00
4;,cos
00
tan
00
p
rLzandzRratTThTk
zyxtatTT
,2/,
,00
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
8
Governing equations
• Microbial inactivation of E. Coli K12 (2 ODE equations)
Dynamic model from Geeraerd et al.* (2000)
Inactivation kinetics during dynamic heating (Bigelow, 1921)
Dref is estimated at Tref within the lethal temperature range
cc
c
Ckdt
dC
NC
kdt
dN
.
.1
1.
max
max
).(
10ln
max
10ln)(
refTTz
ref
eD
Tk
N = microbial population (CFU/g) Cc = physiological state of the cells (-)
* Geeraerd, A. H., C. H. Herremans, et al. (2000). "Structural model requirements to describe microbial inactivation during a mild heat treatment." International Journal of Food Microbiology 59(3): 185-209.
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
9
Mesh generation
• 26750 tetrahedral elements
sample
Air surrounding medium
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
10
Dynamic temperature profile
Dref = 234 s at 57°C, z = 6.28°C tprocess = 270 s
Estimation of D and z values from water bath experiments (9°C/min)
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
11
Local inactivation Global inactivation
(3D numerical integration)
Microbial inactivation during microwave heating
t = 270 s
H =
10
mm
r = 4 mm waves
water bath heating with 9°C/min
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
12
thermal heterogeneities at the end of microwave processing (DTmax = 5°C between the hot and cold spots)
local electric field concentrations around sample edges
Temperature and electric field distribution
t = 270 s
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
13
Highlights
• Modelling microwave pasteurization process: Non-uniform temperature distribution into a 0.5 mL cylindrical sample
(prediction of the cold point),
Lower bacteria inactivation compared to conventional water bath thermal treatment,
The global inactivation of bacteria under microwaves is successfully predicted from D and z values obtained from water bath experiments,
Cells death during microwave heating is mainly due to a thermal effect.
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
14
Future prospects
• Validation of the numerical model with a time-temperature controlled loop:
In order to insure better cells inactivation during microwave heating:
Study on the inactivation efficiency by maintaining the temperature within the lethal range (T > 55 °C)
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Context Model Design
Microbial inactivation
Thermal modelling
Conclusion/ Perspectives
15
Thank you for your attention,
any questions ??