HEATING BEHAVIOR STUDY OF LOW MOISTURE FOODS IN
RADIO FREQUENCY TREATMENTS
By
YANG JIAO
A dissertation submitted in partial fulfillment of
the requirements for the degree of
DOCTOR OF PHILOSOPHY
WASHINGTON STATE UNIVERSITY
Department of Biological Systems Engineering
AUGUST 2014
© Copyright by YANG JIAO, 2014
All Rights Reserved
© Copyright by YANG JIAO, 2014
All Rights Reserved
To the Faculty of Washington State University:
The members of the Committee appointed to examine the dissertation of
YANG JIAO find it satisfactory and recommend that it be accepted.
___________________________________
Juming Tang, Ph.D., Chair
___________________________________
Shaojin Wang, Ph.D.
___________________________________
Shyam S. Sablani, Ph.D.
___________________________________
Girish Ganjyal, Ph.D.
ii
ACKNOWLEDGEMENT
I’d like to thank my major advisor, Dr. Juming Tang, for his guidance and instruction throughout
my research at Washington State University. He is a model for me to learn to work professionally and
conduct good research as a scientist. I also express my sincere appreciation to my research committee
members: Drs. Shaojin Wang, Shyam Sablani and Girish Ganjyal. Their encouragement and suggestions
throughout my research were very much helpful. Special thanks to Dr. Shaojin Wang, who introduced me
into this research area, directed me to conduct experiments and wrote manuscripts in detail.
I acknowledge Drs. Shunshan Jiao, Bandar Alfaifi and Gopal Tiwari, from whom I received
valuable suggestions and research experiences. My sincere gratitude also gives to Dr. Martin Buehler from
Decagon Device, Dr. Robert Olsen from Electrical Engineering Department of WSU, Dr. Caleb Nindo from
University of Idaho, and Tony Koral from Koral Associates England for their selfless dedication in my
research. I thank Stewart Bohnet, Vince Himsl, Frank Liu, Zhongwei Tang, Frank Younce, Huimin Lin,
and Galina Mikhaylenko for their assistance and support in my research. Thank John Anderson, Joan
Hagedorn, Joanna Dreger and Dorota Wilk for their patient help in administrative works. Thank my fellow
graduate students Rossana Villa-Rojas, Donglei Luan, Jing Peng, Wenjia Zhang, Sumeet Dhawan, Roopesh
Shalamaldevi, Ofero Caparino, Fermin Resurreccion, Ellen Bornhorst, Shuxiang Liu, Ravi Tadapaneni and
all Food Engineering Club members for their kindly help and sharing the happy and sad moments with me
in both work and life. I also thank Boying Liu, Meng Wang, Xiaonan Liu, Yi Lu, Juan Wang and Shuai
Zhou for being with me and my family all the way through my Ph.D. life. I wish our friendship last forever.
Finally, I express my deepest gratitude to my parents for their endless love and support. My deepest
appreciation goes to my beloved husband, Feng Li, for his accompaniment and love. He is always sharing
my happiness and sticking on my side when I am frustrated and depressed. I would not have made it this
far without his mortal support. Special thanks to my dear son, Joey Li, who brings me so much joyfulness
and let me know one more meaning of the word “love”.
iii
HEATING BEHAVIOR STUDY OF LOW MOISTURE FOODS IN
RADIO FREQUENCY TREATMENTS
Abstract
by Yang Jiao, Ph.D.
Washington State University
August 2014
Chair: Juming Tang
Radio frequency (RF) heating is considered as a promising technology for pathogen control in low
moisture foods because of its advantages of volumetric and fast heating. However, the non-uniform heating
problem hinders its application in food industry. It is important to thoroughly understand the RF heating
mechanisms and propose solutions to improve heating uniformity of food in RF pasteurization. Peanut
butter was selected as a major example of a low moisture food in this study.
Firstly, the physical, thermal, dielectric properties of peanut butter samples were determined at
different frequencies (10–1800 MHz) and temperatures (20–90 ºC). Results showed RF energy was
applicable for peanut butter pasteurization since its penetration depths at 27.12 MHz were >10 cm. The
relationship between dielectric properties of foods and the heating rate in RF systems was expressed in a
mathematical model and validated by experiments. Results indicated that the maximum heating rate in
foods can be reached when the values of dielectric constant and loss factor were close to each other.
As a next step, a computer model was developed with COMSOL Multiphysics®. The model
described peanut butter in a cylindrical jar subjected into a 6 kW 27.12 MHz RF system with appropriate
initial and boundary conditions to predict the heating pattern in foods.
The validated model was used to explore heating uniformity improvement methods for low
moisture foods. Surrounding the peanut butter sample with polyetherimide (PEI) sheets, which has a closer
iv
dielectric constant to peanut butter but a smaller loss factor, was found to be an effective method in heating
uniformity improvement. The method was also validated on wheat flour. Another heating uniformity
improvement strategy was tested by placing a pair of PEI blocks at the cold spots of peanut butter samples
to aggregate electromagnetic energy and improve heating uniformity. Computer simulations were
conducted to find the optimum size of PEI blocks. A combination of the two methods was found to be more
efficient than any single one in heating uniformity improvement.
This research contributes knowledge to improve low moisture foods heating uniformity in RF
treatments for designing RF pasteurization process.
v
TABLE OF CONTENTS
ACKNOWLEDGEMENT ................................................................................................................... iii
ABSTRACT .....................................................................................................................................iv-v
LIST OF TABLES ................................................................................................................................ x
LIST OF FIGURES ............................................................................................................................ xii
CHAPTER ONE: INTRODUCTION .................................................................................................. 1
1. Background of current issues ................................................................................................ 1
2. Introduction of RF heating and its advantages ...................................................................... 2
3. Current research directions in RF heating uniformity improvement .................................... 3
4. Justifications and objectives.................................................................................................. 5
5. Outline of the dissertation ..................................................................................................... 5
References .................................................................................................................................... 7
CHAPTER TWO: POTENTIAL OF APPLYING RADIO FREQUENCY HEATING IN LOW
MOISTURE FOODS PASTEURIZATION: A LITERATURE REVIEW ............................................... 15
1. Introduction ......................................................................................................................... 15
2. RF fundamentals ................................................................................................................. 15
2.1. Dielectric properties ........................................................................................................ 15
2.2. Radio frequency heating ................................................................................................. 17
2.3. RF equipment .................................................................................................................. 19
3. RF heating in low moisture foods pasteurization/sterilization ............................................ 20
4. Mathematical modeling approaches in determining RF heating pattern of foods .............. 22
References .................................................................................................................................. 25
CHAPTER THREE:
DIELECTRIC, PHYSICAL AND THERMAL PROPERTIES OF
PEANUT BUTTER WITH DIFFERENT WATER CONTENT................................................................ 33
1. Introduction ......................................................................................................................... 34
2. Materials and Methods ........................................................................................................ 36
vi
2.1.
Samples preparation .................................................................................................... 36
2.2.
Water content and water activity................................................................................. 36
2.3.
Density ........................................................................................................................ 37
2.4.
Specific heat ................................................................................................................ 38
2.5.
Thermal conductivity .................................................................................................. 38
2.6.
Dielectric Properties .................................................................................................... 38
2.7.
Statistical analysis ....................................................................................................... 39
3. Results and discussion ........................................................................................................ 39
3.1.
Physical properties ...................................................................................................... 39
3.2.
Thermal properties ...................................................................................................... 41
3.3.
Dielectric properties .................................................................................................... 42
3.4.
Penetration depth......................................................................................................... 45
4. Conclusion .......................................................................................................................... 45
References .................................................................................................................................. 47
CHAPTER FOUR: INFLUENCE OF DIELECTRIC PROPERTIES ON THE HEATING RATE
IN FREE-RUNNING OSCILLATOR RADIO FREQUENCY SYSTEMS............................................... 63
1. Introduction ......................................................................................................................... 64
2. Materials and methods ........................................................................................................ 66
2.1.
Theoretical model ....................................................................................................... 66
2.2.
Experiment validation I – salt solution ....................................................................... 69
2.3.
Experiment validation II – peanut butter samples ....................................................... 71
3. Results and discussions ....................................................................................................... 74
3.1.
Salt solution – salt concentration dependence............................................................. 74
3.2.
Peanut butter ............................................................................................................... 74
3.3.
Determination of heating rate from dielectric properties plot ..................................... 76
4. Conclusions ......................................................................................................................... 76
vii
References .................................................................................................................................. 78
CHAPTER FIVE: A NEW STRATEGY TO IMPROVE HEATING UNIFORMITY OF LOW
MOISTURE FOODS IN RADIO FREQUENCY TREATMENT FOR PATHOGEN CONTROL .......... 93
1. Introduction ......................................................................................................................... 94
2. Materials and methods ........................................................................................................ 96
2.1.
Sample preparation ..................................................................................................... 96
2.2.
Physical properties of food material ........................................................................... 97
2.3.
Surrounding material selection ................................................................................... 97
2.4.
Temperature profiles of peanut butter in hot water and RF heating ........................... 97
2.5.
Computer simulation ................................................................................................... 98
2.6.
Model validation - RF experiments........................................................................... 101
2.7.
Heating uniformity of wheat flour ............................................................................ 103
2.8.
Heating uniformity of multiple containers under RF treatment ................................ 103
2.9.
Statistical analysis ..................................................................................................... 103
3. Results and discussion ...................................................................................................... 104
3.1.
Dielectric and thermal properties of peanut butter .................................................... 104
3.2.
Heating rate comparison among peanut butter in hot water in RF treatments .......... 104
3.3.
Determination of cold spot location in a sample container ....................................... 105
3.4.
Model validation ....................................................................................................... 105
3.5.
Overall heating uniformity improvement evaluation ................................................ 106
3.6.
Heating uniformity of wheat flour ............................................................................ 107
3.7.
Heating uniformity of multiple peanut butter samples.............................................. 107
4. Conclusion ........................................................................................................................ 108
References ................................................................................................................................ 109
CHAPTER SIX: IMPROVEMENT OF RF HEATING UNIFORMITY ON LOW MOISTURE
FOODS WITH POLYETHERIMIDE BLOCKS ..................................................................................... 129
viii
1. Introduction ....................................................................................................................... 130
2. Materials and methods ...................................................................................................... 132
2.1.
Sample preparation ................................................................................................... 132
2.2.
Block material and size selection .............................................................................. 132
2.3.
Sequence of the study ............................................................................................... 132
2.4.
Computer simulation ................................................................................................. 133
2.5.
Simulation procedure ................................................................................................ 135
2.6.
RF experiments ......................................................................................................... 136
2.7.
Heating uniformity evaluation of different uniformity improvement methods ........ 136
2.8.
Height optimization of PEI blocks ............................................................................ 137
3. Results and discussion ...................................................................................................... 138
3.1.
Predicted electric field distribution ........................................................................... 138
3.2.
Heating rate of peanut butter with different size of PEI blocks ................................ 138
3.3.
Voltage estimation .................................................................................................... 138
3.4.
Computer model validation ....................................................................................... 139
3.5.
PEI blocks height optimization ................................................................................. 140
3.6.
Heating uniformity comparison of uniformity improvement methods ..................... 140
4. Conclusion ........................................................................................................................ 141
References ................................................................................................................................ 143
CHAPTER SEVEN: CONCLUSIONS AND RECOMMENDATIONS ........................................ 162
1. Conclusions ....................................................................................................................... 162
2. Contributions to knowledge .............................................................................................. 163
3. Recommendations ............................................................................................................. 164
ix
LIST OF TABLES
Table 1.1 Comparison between RF and microwave characteristics in food processing application
.................................................................................................................................................................... 13
Table 2.1 Comparison of open circuit and 50 ohm RF systems .................................................... 28
Table 2.2 Literature review of RF sterilization/pastuerization effect on pathogens in low moisture
food products .............................................................................................................................................. 29
Table 3.1 Water activity, density and thermal conductivity of peanut butter with 5 different water
contents at 22 °C ......................................................................................................................................... 51
Table 3.2. Dielectric constant and loss factor of peanut butter samples with five water contents at
eight temperature and four frequencies ....................................................................................................... 52
Table 3.3 Binary statistical regression equations of dielectric properties with temperature (T, °C)
and water content (M, g water/g sample) at three interested frequencies (valid in T = 20–90 °C, M = 1.3–22
g/100g sample) ............................................................................................................................................ 54
Table 3.4 Penetration depth of peanut butter with five water contents at eight temperatures and four
frequencies .................................................................................................................................................. 55
Table 4.1 Dielectric properties (mean ± SD of two replicates) of NaCl solutions with 10 electric
conductivities at 22 ºC and 27.12 MHz ...................................................................................................... 81
Table 4.2 Properties of peanut butter with 5 selected moisture content levels at temperature 20–80
ºC and 27.12 MHz (dielectric properties presented in mean ±SD of two replicates) ................................ 82
x
Table 5.1 Dielectric properties of common plastic materials at 1 MHz and room temperature .. 113
Table 5.2 Properties of peanut butter, polyetherimide and air for mathematical modeling (dielectric
properties of peanut butter averaged at temperature 20–80 ºC at 27.12 MHz) ......................................... 114
Table 5.3 Infrared picture analysis of top and side surfaces of a peanut butter jar with and without
PEI assistance after RF treatment ............................................................................................................. 115
Table 5.4 Uniformity index (UI) comparisons between two spatial arrangements of 9 peanut butter
samples and the centrally located sample under RF treatment with and without PEI assistance ............. 116
Table 6.1 Properties of peanut butter, polyetherimide and air for mathematical modeling (adapted
from Jiao et al., 2014b) ............................................................................................................................. 148
Table 6.2 Number of different type of mesh generated in all domains in computer simulation .. 149
Table 6.3 The heating conditions and voltages for peanut butter with various size of PEI blocks in
a 6 kW 27.12 MHz RF system .................................................................................................................. 150
Table 6.4 Temperature distribution analysis on the top surface of peanut butter from experiment
with various size of PEI blocks (T, °C) .................................................................................................... 151
Table 6.5 Uniformity index of peanut butter with various size of PEI blocks in RF treatment in
computer simulation.................................................................................................................................. 152
Table 6.6 Simulation conditions and uniformity comparison of peanut butter treated with PEI
surrounding, PEI blocks addition and a combination methods ................................................................. 153
xi
LIST OF FIGURES
Figure 1.1 Microbial stability as affected by environmental water activity (Adapted from Buechat,
1981) ........................................................................................................................................................... 14
Figure 2.1 Contribution of various mechanisms to the loss factor of food materials as functions of
frequency and temperature (Tang, Feng, & Lau, 2002, Chapter 1, based on Harvey & Hoekstra, 1972;
Kuang & Nelson, 1998; Metaxas & Meredith, 1993; Roebuck & Goldblith, 1972) .................................. 30
Figure 2.2 Scheme of a typical open circuit RF system (adapted from Zhao et al., 2000) ............ 31
Figure 2.3 Composition of a 50 ohm RF system ........................................................................... 32
Figure 3.1 Water activity of peanut butter samples as a function of water contents at room
temperature (22°C)...................................................................................................................................... 57
Figure 3.2 Specific heat of peanut butter samples measured by DSC as a function of water content
(a) and temperature with heat flow chart at 1.3 g/100g water (b) ............................................................... 58
Figure 3.3 Dielectric constant of peanut butter with water content levels of 1.3 (a), 4 (b), 10 (c), 16
(d), and 22 (e) g/100g at four selected temperatures ................................................................................... 59
Figure 3.4 Loss factor of peanut butter with water content levels of 1.3 (a), 4 (b), 10 (c), 16 (d), and
22 (e) g/100g at four selected temperatures ................................................................................................ 60
Figure 3.5 Dielectric properties of peanut butter with five water contents and eight temperatures at
27 MHz ....................................................................................................................................................... 61
Figure 3.6 Dielectric properties of peanut butter with five water contents and eight temperatures at
915 MHz ..................................................................................................................................................... 62
xii
Figure 4.1 Scheme of RF heating system with parallel plate electrodes ....................................... 83
Figure 4.2 Electrical conductivity regression curve for NaCl solutions with various salt
concentrations ............................................................................................................................................. 84
Figure 4.3 Experimental setup for foods with a temperature measurement system in radio frequency
heating ......................................................................................................................................................... 85
Figure 4.4 Temperature-time histories for NaCl solutions with different electrical conductivity
levels of 0.03 (◊), 0.05 (□), 0.1 (Δ), 0.15 (×), 0.2 (♦), 0.3 (○), 0.5 (●), 1 (▲), 2 (+) and 3 (■) S/m (dash
for 0.03–0.1and bold for 0.15–3) subjected to RF heating at 27.12 MHz for 3 min (mean of 2 replicates)
.................................................................................................................................................................... 86
Figure 4.5 Final temperatures after 3 min RF treatment of salt solutions with 10 different electric
conductivities at 27.12 MHz obtained by experiments (○) and theoretical prediction (Δ). ..................... 87
Figure 4.6 Temperature-time histories for peanut butter with 5 moisture contents, 1.3% (×), 4%
(○), 10% (□), 16% (Δ) and 22% (◊) w.b. during 4 min RF heating at 27.12 MHz.................................. 88
Figure 4.7 Final temperature comparison of peanut butter samples with five water contents after 4
min RF heating at 27.12 MHz between experiments (○) and prediction (Δ)........................................... 89
Figure 4.8 Time-temperature curve for peanut butter with 22% (w.b.) moisture content with 48 min
27.12 MHz RF heating (mean of 2 replicates) ............................................................................................ 90
Figure 4.9 Tendency comparison between heating rate for a 48 min RF heating at 27.12 MHz (a)
and heating rate coefficient (b) calculated from the dielectric properties of peanut butter with 22% (w.b.)
moisture content .......................................................................................................................................... 91
xiii
Figure 4.10 Dielectric properties of peanut butter samples (pb 1.3% (◊), 4% (□), 10% (Δ), 16%
(×) at room temperature, 22% (●) at 20–70 °C) and salty water (electric conductivity 0.03–0.2 S/m (○) at
room temperature) with a function curve of y = x at 27.12 MHz for estimating the maximum heating rate
.................................................................................................................................................................... 92
Figure 5.1 3-D Scheme (a) and dimensions (b) of the 6 kW 27.12 MHz RF system and a food load
(peanut butter) with PEI sheets (dimensions are in mm) .......................................................................... 117
Figure 5.2 Cold spot location determination method: comparison of top surface and cross sectional
surface temperature distribution................................................................................................................ 118
Figure 5.3 Cutting a cylindrical container in half for temperature distribution measurement at the
cross-sectional surface .............................................................................................................................. 119
Figure 5.4 Eighteen thermocouples (with labeled locations) connected to data logger for measuring
temperature distribution inside the food container after RF treatment ..................................................... 120
Figure 5.5 Two spatial arrangements of 9 peanut butter jars for RF treatment (top view):
Arrangement 1 (a) and Arrangement 2 (b)................................................................................................ 121
Figure 5.6 A typical measured temperature-time curve of peanut butter in a cylindrical container
(a) subjected to hot water heating and RF heating and (b) subjected to RF heating with and without PEI
assistance with an electrode gap 9 cm (temperature at the center of peanut butter) ................................. 122
Figure 5.7 Comparison of simulated and experimental results for top surface temperature
distributions of peanut butter without and with PEI assistance after 10.0 and 2.8 min RF heating with an
electrode gap of 9 cm ................................................................................................................................ 123
xiv
Figure 5.8 Simulated electric field (arrow) and electric potential (contour) plot for peanut butter (a)
without PEI and (b) with PEI assistance after 10.0 and 2.8 min RF treatment (electrode gap 9 cm) ....... 124
Figure 5.9 Comparison of simulated and experimental results for cross-sectional surface
temperature distributions of peanut butter without and with PEI assistance after 10.0 and 2.8 min RF heating
with an electrode gap of 9 cm ................................................................................................................... 125
Figure 5.10 Experimentally measured temperature at18 locations in peanut butter container after
10.0 min RF treatment without PEI and 2.8 min with PEI ....................................................................... 126
Figure 5.11 Thermal images of surface temperature distribution of wheat flour after 8.0 and 4.3
min RF treatment without and with PEI sheets (electrode gap = 9 cm) ................................................... 127
Figure 5.12 Simulated temperature distribution (middle layer) of two spatial arrangements of 9
peanut butter samples with and without PEI assistance under 6 min RF treatment with an electrode gap of
9 cm........................................................................................................................................................... 128
Figure 6.1 Scheme of a peanut butter sample in a cylindrical container with PEI blocks in a 6 kW
27.12 MHz RF cavity................................................................................................................................ 154
Figure 6.2 Electric field direction (arrow), electric field intensity (surface), and electrode potential
(streamline) of peanut butter treated by RF with and without PEI blocks ................................................ 155
Figure 6.3 Temperature-time history of peanut butter at the container center with different sizes of
PEI blocks in a 6 kW 27.12 MHz RF system with an electrode gap of 10.1 cm (mean of three replicates)
.................................................................................................................................................................. 156
xv
Figure 6.4 Temperature distribution on the top surface of peanut butter from experiment and
computer simulation and cross-sectional surface from simulation with various size of PEI blocks in RF
treatment (upper temperature scale: experiment; lower temperature scale: simulation)........................... 158
Figure 6.5 Uniformity index of peanut butter with various height of PEI blocks in RF.............. 159
Figure 6.6 Heating pattern of peanut butter with PEI blocks (a: height 0.1 cm, b: height 1.4 cm, c:
height 2.3 cm) in RF treatments ................................................................................................................ 160
Figure 6.7 Cross-sectional surface temperature distribution of peanut butter treated in RF with three
different methods (electrode gap is 10.1 cm) ............................................................................................ 161
Figure 7.1 An option for placement of RF pasteurization (in dash) in peanut butter industrial
processes ................................................................................................................................................... 165
xvi
CHAPTER ONE:
INTRODUCTION
Low moisture foods safety issues associated with Salmonella outbreaks have been a hot topic in
the area of food safety recently. In order to reduce the microbial hazard, radio frequency (RF) heating could
be introduced as a pasteurization technique. However, although RF provides a relatively uniform
temperature distribution in foods compared with a microwave, the edge over heating may still cause quality
deterioration while inactivating the bacteria. This study is to investigate the heating behavior of a low
moisture food in RF treatment and to explore heating uniformity improvement methods which are suitable
for packaged low moisture foods.
1. Background of current issues
Low moisture food can be defined as foods with a moisture content of less than 10% or water
activity below 0.60 (Gould, 1996). Many foods fall into the low moisture food category, most of which are
solid or semi-solid, e.g. dried noodles, crackers, roasted nuts, whole milk powder, dried spices, dehydrated
soup, cereals, agricultural seeds, wheat flour, beef jerky, chocolate syrup, peanut butter and paste.
Since the low water activity environment is not suitable for bacteria multiplication (Fig. 1.1), most
of the low moisture foods are not required to be pasteurized or sterilized before coming into the market.
However, recent Salmonella outbreaks associated with low moisture foods, e.g. pet food (2012), pine nuts
(2011), pepper (2011), pistachio (2009) and rice cereal (2008), and peanut butter (2007, 2009, 2012), show
that low moisture foods could also be contaminated by pathogens and cause illness (CDC, 2011; 2012). A
serious outbreak in peanut butter in 2009 resulted in 9 deaths and more than 714 illnesses among consumers
from 46 states, along with a huge economic loss from companies because of recalled products and legal
cases (Wittenberger, 2010). Another peanut butter contamination case, recently found in New Mexico, was
related to Salmonella and caused 38 sicknesses in 20 states (CDC, 2012). These outbreaks are mainly due
to the cross contamination of pathogens during multiple-step food processing; the introduced bacteria
1
survived in the low moisture environment and cause sickness in human beings without multiplication.
Kapperud et al. (1990) reported that only 1cfu/g of Salmonella in chocolate products caused 349 deaths in
Norway and Finland.
Thermal inactivation is one of the most effective means of pathogen control in food industries.
However, it has been reported that the heat resistance of bacteria is relatively higher in low water activity
(aw < 0.5) and high fat content food products (Barrile and Cone, 1970; Juneja and Eblen, 2000; Mattick et
al., 2000; Juneja et al., 2001; Mattick et al., 2001; Laroche et al., 2005; Villa-Rojas et al., 2013).
Furthermore, those traditional pasteurization methods (e.g. hot air, hot water, steam, etc.) are not suitable
for packaged foods since the packaging materials hinder heat transfer. Insufficient heating may result in
longer heating treatments, which usually damage the food quality and even increase the heat resistance of
bacteria (Chung et al., 2007). Therefore, novel post-packaging pasteurization technologies with fast heating
characteristic need to be developed to guarantee a desired log reduction of pathogens in the final food
product.
2. Introduction of RF heating and its advantages
Radio frequency (RF) falls in the range of 3 kHz and 300 MHz in the electromagnetic spectrum.
Federal Communication Commission (FCC) assigned 13.56 ±0.00668, 27.12 ±0.0160 and 40.68 ±0.0200
MHz for RF being uses in industrial, scientific and medical (ISM) applications. The principle of RF heating
is the molecules/ions in foods are rotating/vibrating to adapt to the alternating electric field, and the friction
during movements generates heat. Compared with microwave energy, RF energy has the advantage of
heating bulk food because of its relatively longer wavelength (7.4–22.1 m in vacuum). A comparison of
characteristics of microwave and RF energy was summarized in Table 1.1.
RF heating is proposed as a promising technology in the food industry due to its rapid and
volumetric heating, larger penetration depth and high energy efficiency. Because of these advantages, RF
heating technology has been found helpful in preventing loss of quality due to oxidative and non-oxidative
2
browning, protein and lipid oxidation, vitamins loss, dehydration, production of undesirable aromas and off
flavor compounds and loss of natural color (Wang et al., 2006). RF heating has been studied for being
applied in biscuits post-baking (Mermelstein, 1998, Piyasena, Dussault et al., 2003), meat thawing (Farag
et al., 2011), meat cooking (Laycock et al., 2003; Zhang et al., 2004; Guo et al., 2006), disinfestation of
walnuts (Wang et al., 2001; Wang et al., 2002; Wang et al., 2003; Mitcham et al., 2004; Wang et al., 2005;
Wang et al., 2006b; Wang et al., 2007a; Wang et al., 2007b; Wang et al., 2008c), beans (Jiao et al., 2011),
legumes (Guo et al., 2010; Wang et al., 2010), coffee beans (Pan et al., 2012), persimmons (Monzon et al.,
2007; Tiwari et al., 2008), apples (Ikediala et al., 2000; Birla et al., 2004; Wang et al., 2006a; Birla et al.,
2008), oranges (Birla et al., 2004; Birla et al., 2005), and cherries (Ikediala et al., 2002). For bacteria control,
the potentials of RF sterilization and pasteurization were investigated in egg products (Luechapattanaporn
et al., 2005), mashed potatoes (Wang et al., 2008a), meat (Byrne et al., 2010), white bread (Liu et al., 2011),
almonds (Gao et al., 2011) peaches and nectarines (Casals et al., 2010; Sisquella et al., 2014) and meat
lasagna (Wang et al., 2012). However, very little research has focused on RF pasteurization when applied
to low moisture foods.
RF heating has not been widely applied in low moisture foods pasteurization because of the
following reasons: (1) the cause of non-uniform heating is not well understood; (2) limited means of heating
uniformity improvement of low moisture foods have been reported; and (3) the potential of computer
simulation modeling has not been fully explored and applied for development of heating uniformity
optimization methods.
3. Current research directions in RF heating uniformity improvement
Non-uniform heating may cause overheating in foods, which degrades food quality. Researchers
have investigated several ways to improve the RF heating uniformity for post-harvest pest control in
agricultural commodities and pre-packaged military foods.
3
Ikediala et al. (2002) used saline water to match the dielectric properties of cherries to reduce the
localized overheating for controlling codling moth infestation. The temperature difference between the pit
and surface of cherries was reduced to 1 ºC. Based on the water immersion method, Birla et al. (2004; 2005)
developed a fruit mover to rotate oranges and apples which were immersed in tap water, and controlled the
temperature uniformity within 3.1 ºC when average temperature increases 30 ºC in 7.8 min. However, the
water immersion system and fruit mover setup were complicated and not easily scaled up for industrial use.
Wang et al. (2008b) also conducted a study for pre-packaged mashed potatoes heated in RF systems with
circulating water to remove the heat accumulation at the edges. Water with various electrical conductivities
was tested for heating rate, and the highest electrical conductivity (220 S/m) can reduce the hot and cold
spot temperature difference from 30.9 to 24.2 ºC, and 22.4 to 13.6 ºC on different mashed potato samples.
Wang et al. (2005) developed an intermittent stirring method during RF treatments to improve the
heating uniformity for in-shell walnut disinfestation. A mathematical model was developed to study the
influence of intermittent stirrings on heating uniformity. The results showed a minimum of two stirrings
were needed for desired uniformity and insect mortality. Another work from Wang et al. (2007a) tested
four methods with different combinations: washing, moving, mixing and hot air. The goal was to find which
combination had the best uniformity. Result showed the unwashed walnut with moving, mixing and hot air
assistance could achieve a satisfactory heating uniformity. Gao et al. (2010) developed an almond
disinfestation protocol using RF heating combined with hot air, movement and mixing, and achieved a good
heating uniformity. However, in the pasteurization protocol also developed by Gao et al. (2011), only hot
air was used since mixing would contaminate the almonds by potentially introducing pathogens. Several
researchers also used combination methods for improving the heating uniformity, e.g.: hot water and RF
combination heating method was used by Sosa-Morales (2009) for mango insect control, and hot air and
RF combination method was used by Liu et al. (2011) for white bread treatment.
Recently, Alfaifi et al. (2013) made a modification to the top electrode in the RF machine by adding
a bended angle and modifying setback distance, and found that a 90 ºC angle and a 2 cm setback can
4
optimize the heating uniformity of raisins in bulk. This method solved the non-uniform heating problem
for agricultural products treated in a rectangular box, and it can be extended to other food material with
different shapes and for different heating purposes.
4. Justifications and objectives
Although several means were developed for improving RF heating uniformity, very few of them
could be directly applied to pre-packaged low moisture foods. Systematical studies need to be conducted
to understand the fundamentals of low moisture food heating behavior in RF systems and the cause of nonuniform heating in order to develop better means for pre-packaged low moisture foods pasteurization.
The objectives of this study are to: (1) determine dielectric, physical and thermal properties of
peanut butter with a range of water activities at different temperatures (20‒90 ºC) and frequencies (10‒1800
MHz), and to find the relationship between dielectric properties and RF heating; (2) develop a computer
model to simulate foods in RF heating for heating pattern prediction and to validate the model with
experiments; and (3) explore heating uniformity improvement methods for low moisture foods in a 27.12
MHz 6 kW RF system with the assistance of the validated model.
5. Outline of the dissertation
This dissertation is divided into seven chapters:
Chapter one describes the current research directions and the objectives of this study. A general
introduction is provided on the current issues related to Salmonella outbreaks in low moisture foods. An
introduction to RF was provided and the research gap needed to be filled was specified.
Chapter two reviews the application of RF heating, the dielectric properties of low moisture foods,
mathematical modeling methods and heating uniformity improvement methods for RF heating.
Chapter three presents methodologies and results for thermal and dielectric properties of peanut
butter with different moisture contents in RF and MW ranges (10‒1800 MHz) and over different
temperature ranges (20‒90 ºC).
5
Chapter four establishes the relationship between dielectric properties and heating rate with a
mathematical model, and is validated by experiments with two different model foods with a wide range of
dielectric properties.
Chapter five explores the potential of using a set of PEI sheets surrounding peanut butter to improve
its heating uniformity in RF treatments. Temperature distribution on the surface and inside of the peanut
butter was measured after RF treatment with and without PEI sheets.
Chapter six provides computer simulation and optimization results for heating uniformity
improvement with PEI blocks on top and bottom of peanut butter. The optimized diameter and height of
PEI blocks were found, and the effectiveness of combining PEI surrounding and the additional method was
shown.
Chapter seven summarizes the main conclusions and contributions of the completed work and
provides recommendations for further research.
In this dissertation, chapter four and five were published. A list of articles published from this
research are shown below:
1. Jiao, Y., Tang, J., Wang, S., Koral, T., 2014. The influence of dielectric properties on the heating
rate in free running oscillator radio frequency heating. Journal of Food Engineering, 120: 197–203.
(Chapter Four)
2. Jiao, Y., Tang, J., Wang, S., 2014. A new Strategy to improve heating uniformity of low moisture
foods in radio frequency treatment for pathogen control. Journal of Food Engineering, 141: 128–138.
(Chapter Five)
6
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10
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11
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12
Table 1.1 Comparison between RF and microwave characteristics in food processing application
RF
Microwave
Working frequency
13.56, 27.12, 40.68 MHz
915, 2450 MHz
Wavelength (in vacuum)
22.1, 11.1, 7.4 m
0.33, 0.12 m
Penetration depth (in tap water)
1.58, 0.79, 0.53 m
0.02, 0.01 m
Major heating mechanism
ionic charge migration
dipole molecule rotation
System construction/cost
simple/low
complicate/high
13
Limit of bacteria growth
Osmophilic yeast
Xerophilic moulds
Halophilic
Moulds
Yeast
Bacteria
0
0.6
0.7
0.8
0.9
1.0
Water activity (aw)
Figure 1.1 Microbial stability as affected by environmental water activity (Adapted from Buechat,
1981)
14
CHAPTER TWO:
POTENTIAL OF APPLYING RADIO FREQUENCY HEATING IN LOW MOISTURE FOODS
PASTEURIZATION:
A LITERATURE REVIEW
1. Introduction
Bacterial inactivation in low moisture foods is an urgent need due to large scale outbreaks all over
the United States. Because of the distinct properties of low moisture foods, traditional thermal inactivation
methods are unable to eliminate the residual pathogens while still providing high quality foods. Radio
frequency (RF) heating has been considered as a possible novel pasteurization method because of its
volumetric heating property. The volumetric and fast heating process can potentially reduce the pathogen
population without damaging food quality. The objective of this review is to provide the basics of RF
heating, RF systems, dielectric properties of low moisture foods, approaches of RF heating process
modeling and strategies for heating uniformity improvement.
2. RF fundamentals
2.1. Dielectric properties
Dielectric properties, also called relative permittivity, are intrinsic properties of materials
describing the degree of a material’s interaction with an alternative electrical field, and quantifying its
ability for reflecting, storing and transmitting electromagnetic energy. The dielectric properties can be
expressed as:
 *  ‘ - j "
(1)
Where 𝜀 ∗ is the complex relative (to vacuum) permittivity; ε’ is the relative dielectric constant,
which is a measure of the ability of a material to store electromagnetic energy; ε” is the relative dielectric
loss factor, which is a measure of the ability of a material to dissipate electromagnetic energy into heat.
15
Many factors affect the dielectric properties of a material, such as frequency, temperature, food composition
and density.
Penetration depth (dp, m) is defined as the distance from the surface of a dielectric material when
the incident power is reduced to 1/e (e = 2.718) of the power while electromagnetic waves penetrate a
certain dielectric material. Penetration depth was calculated using the following equation (Von Hippel,
1954):
dp 
c
2
 

   
2 2 f    1     1 

 
  

 
(2)
1
2
where c is the speed of light in free space (3×108 m/s).
The dielectric properties of various low moisture foods including grains, pecans, walnuts, almonds,
peanuts and chestnuts with different water contents at various frequencies and temperatures have been
reported by many researchers (Nelson, 1981; Lawrence et al., 1992; Wang et al., 2003; Boldor et al., 2004;
Sacilik et al., 2006; Guo et al., 2011; Gao et al., 2012; Zhu et al., 2012). The results from the literature show
that both dielectric constant and loss factor increase with increasing water content and temperature, and
decrease with increasing frequency in low moisture foods.
Most of the low moisture material has relatively low dielectric property values (ε’, ε” < 20) at room
temperature and RF frequency. When the frequency is below 100 MHz (frequency falls into RF range), the
dominating mechanisms of energy loss become ionic conduction, bound water relaxation and MaxwellWagner effect (Fig 2.1) (Tang, Feng, & Lau, 2002, Chapter 1, based on Harvey & Hoekstra, 1972; Kuang
& Nelson, 1998; Metaxas & Meredith, 1993; Roebuck & Goldblith, 1972). In a low moisture food system,
ionic effects are not effective because of the lack of free water, so the other two mechanisms are dominating
the dielectric properties. Bound water is a form of water that has its mobility between ice and free water.
Since the relaxation frequency depends on the mobility of water molecules, bound water molecules have a
16
lower relaxation frequency that free water, at around 100 MHz (room temperature), and the magnitude is
much smaller than free water as well (Ryynanen, 1995). Maxwell-Wagner’s effect is also called an
“interfacial loss mechanism”, which is the result of alternative accumulation of charged ions at the interface
of heterogeneous dielectrics. That is, when a conductive phase is attached to a non-conductive phase, the
ionic charges gather at the interface and migrate between two adjacent interfaces in an alternating field.
The Maxwell-Wagner’s effect usually occurs at a frequency of 0.1 MHz (Meakins, 1961; Metaxas and
Meredith, 1983). It could be found that both the bound water effect and Maxwell-Wagner’s effect contribute
to the dielectric properties at a very low range comparing with free water and ionic effect. This explains the
low values of dielectric properties in low moisture foods.
Food composition also affects the value of dielectric properties. Low moisture foods possess a low
dielectric property because of the lack of water. Review articles showed all other nutrition facts including
carbohydrates, protein, ash and fat have very low dielectric properties without being dissolved in water
(Calay et al., 1994; Venkatesh and Raghavan, 2004). Several studies have been conducted on the dielectric
properties of low water and high fat content paste-like food materials, such as butter and butter oil (Ahmed
et al., 2007a) and rice slurry (Ahmed et al., 2007b). Results show that fat content negatively affected the
dielectric loss factor of foods.
2.2. Radio frequency heating
Radio frequency (RF) occupies a section of the electromagnetic wave frequency band of 3 kHz to
300 MHz. Three particular frequencies (13.56, 27.12 and 40.68 MHz) were selected by Federal
Communications Commission (FCC) for industrial, science and medical (ISM) use to prevent disturbance
in telecommunications. RF has a comparatively long wavelength (7~22 m in vacuum), which is able to
penetrate relatively thick food materials and result in a good heating uniformity.
17
The amount of power conversion from electromagnetic energy to thermal energy depends on the
dielectric properties of the food, working frequency, and the electric field strength in the foods (Metaxas,
1996):
P  2f 0 " E
2
(3)
where P is the power conversion in foods per unit volume (W m-3), f is the working frequency of the RF
equipment (Hz), ε0 is the permittivity of electromagnetic wave in free space (8.854 × 10 -12 F m-1), and E
is the electric field intensity in the food material (V m-1).
The electric field intensity was obtained from Maxwell’s equations.
  E  
H
t
(4)

  H   c E   0  '  j ''
 Et
(5)
  D  v
(6)
 H  0
(7)
where E is the electric field (V m-1), H is the magnetic field (A m-2), D is the electric flux density (C m-2),
ε’ and ε” are the dielectric constant and loss factor, μ is the magnetic permeability (H m-1), ρv is the free
volume charge density (C m-3), and σc is the electrical conductivity of food material (S m-1).
Maxwell equations can be simplified to the Laplace equation with a quasi-static field approximation
in order to simplify the solving procedure. The quasi-static field approximation is assuming the heat
generation in food is much slower than the electric field variation in a time step, so the system can be seen
as at equilibrium at all times. The RF field can be seen as a time harmonic field, and the electric field
strength can be expressed in Eq. (8)
E  E0 e jt
(8)
18
where ω =2πf is the angular velocity (rad s-1) and t is the period (s).
Under time harmonic condition, put Eq (8) into Eq (5), we can obtain


 

  H   c  j 0  '  j '' E   c   0 ''  j ' E  J
(9)
where J is the current density (A m-2).
Since   J  0 and E  V , Eq. (9) can also be written as
     j 20' V   0
(10)
where    c   0 '' is the overall electrical conductivity of food. Eq. (10) is the Laplace equation,
which can be solved to obtain the electric field distribution. The Laplace equation is a solution of Maxwell’s
equations under time harmonic conditions.
2.3. RF equipment
RF heating equipment can be generally divided into two types: open circuit (also called freerunning oscillator) and 50 ohm technology based on their wave generation mechanisms, compositions and
properties.
An open circuit RF system consists of a high voltage transformer, a rectifier, an oscillator tube, a
tuned circuit, an impedance coupling and matching circuit, and an applicator (Fig. 2.2). The line power
from the wall is transformed to a high voltage, and converted into DC power by a rectifier. The oscillator
tube excited high frequency alternating electromagnetic waves and transports them to the tank circuit in
order to be tuned to a specific working frequency and to match the load. The applicator receives the high
frequency electromagnetic wave, and the load in it converts the electromagnetic wave into heat.
A 50 ohm RF system consists of a fixed-frequency crystal driven oscillator, a solid state amplifier,
a dynamic automatic impedance matching network and an applicator (Fig. 2.3). The oscillator, amplifier
and matching network are connected with 50 ohm cables. The fixed-frequency crystal driven oscillator (e.g.
19
quartz) can precisely control the frequency of the RF generator of fixed output impedance (50 ohm). The
load has to match 50 ohm in order to achieve a maximum power transfer. The power consumption and
voltage of the electrode can be displayed on the control panel.
The open circuit RF system is the most common design of RF heater, 98% of all industrial size RF
heaters are based on this technique. The most popular use of this type of RF system is for drying textiles,
paper, lumber, glass fiber etc. It is simple, less costly, and flexible because of the distinct selective heating
characteristic. However, the frequency stability and harmonic output is not as good as 50 ohm technology,
and may cause RF interference with other frequency bands. A 50 ohm system, on the other hand, is a
recently developed design of RF system. It has a more stable frequency output since the matching system
in the RF heater is automatically adjusted to maintain the load impedance at 50 ohm. The maximum power
transfer to the load can be guaranteed in this design. The 50 ohm systems are more expensive than open
circuit systems, and have not been popularly used by industries (Koral, 2013). Table 2.1 summarized the
advantages and disadvantages of open circuit and 50 ohm RF heating systems. To conclude, the 50 ohm
system is more suitable for food pasteurization/sterilization because of the accurate control in frequency
and power, and the open circuit system is a better choice for drying purposes.
3. RF heating in low moisture foods pasteurization/sterilization
Nelson et al. (1984) utilized RF heating (39 MHz) on alfalfa seeds (3.2–8.5% w.b. moisture content,
25 gram, and 1.59 cm height per batch) for reducing Salmonella, E. Coli O157:H7 and Listeria
monocytogenes populations. Slight bacteria reductions (1.81, 1.40, 1.10 log cfu/g) were achieved for
Salmonella, E. Coli O157:H7 and Listeria monocytogenes with an exposure time of 69, 20, 18 sec without
significantly damaging the germination rate. However, 5 log cfu/g reduction was not achieved without
severe reduction in germination.
Lagunas-Solar et al. (2005) investigated the effectiveness of RF pasteurization (6-14 MHz, 0.171.2 kW) in both inoculated (50 g) and packaged (1 kg) fishmeal pasteurization. The fishmeal is a
20
heterogeneous mixture of particles with a moisture content of 7–10 % (w.b.). The research showed that RF
resulted in uniform and rapid heating with a ¼ energy (comparing with traditional surface heating) and
provided a >5 log10 reduction for Salmonella spp. and E. coli O157:H7. Protein losses, lipid oxidation and
decreased digestibility were found in fish meal treated with traditional surface heating methods, but not in
RF treated one.
Gao et al. (2011) used a hot air assisted RF system (27.12 MHz, 6 kW) to inactivate the S. enteritidis
PT 30 in in-shell almonds (aw = 0.4–0.5) for a 5 log reduction. Since the bacteria only existed at the surface
of the almond shell and was more resistant in dry environment than moist conditions, a pre-soaking method
was developed to make the almond shells be heated faster than the kernels so that the bacteria were
inactivated without damaging the quality of the almond kernels. The shell was dried to the original moisture
content by both RF energy and hot air after processing. The results showed a 5 log reduction of S. enteritidis
PT 30 after being held at 73 ºC for 1.5 min, dried with 55 ºC air for 13 min, and cooled by a fan to 30 ºC.
An accelerated storage test showed the quality of almond treated by RF energy did not change significantly
even after 2 years of storage at 4 ºC.
Kim et al. (2012) explored the efficacy of RF heating (27 MHz, 9 kW, 50 ohm system) to inactivate
Salmonella and E. Coli O157:H7 in black and red pepper powder. The bacteria was inoculated in three
different particle sizes of black and red peppers and treated by RF energy for 50 s and 40 s, respectively.
Results showed Salmonella population was reduced 2.80 and 4.29 log10 cfu g-1 in black pepper, and 3.38
and > 5 log10 cfu g-1in red pepper for 50 and 40 s RF heating, respectively. Jeong and Kang (2014) studied
the influence of moisture content of powdered red and black pepper spices (red pepper 12.6–23.3% and
black pepper 10.1–30.5%, w.b.) inoculated with E Coli O:157 H:7 and Salmonella. The results showed the
inactivation rate was dependent on moisture content since it influenced the dielectric properties. The
treatment time also varied with moisture content to reach > 7 log10 cfu g-1.
The results above were listed in Table 2.2.
21
4. Mathematical modeling approaches in determining RF heating pattern of foods
Yang et al. (2003) used a computer program package TLM-FOOD-HEATING to simulate the RF
heating process (1 kW, 35 MHz) on radish and alfalfa seeds. The electromagnetic problem was solved by
TLM (transmission line method) and heat diffusion was solved by FDTD (finite difference time domain)
method. The differences between experiment and simulation results in both radish and alfalfa seeds were
1.8, 1.1, 8.9, 13.6 and 0.9, 2.4, 7.8 and 14.3 ºC at the center, top, edge, and bottom locations, respectively,
when being heated from 25 to 80 ºC . From which it can be seen that the simulation result had a larger error
at the edge and bottom locations. The author claimed this difference was due to the insufficient description
of the boundary conditions.
Chan et al. (2004) used a FEM based commercial package named HFSS for solving the coupled
equations in a RF heating process (6 kW, 27 MHz) of 1% CMC solution. By comparing the S11 parameter,
phase, and heating patterns for load with different shape, size and positions, a good agreement from the
experiment and the simulation was found. However, the heating pattern of the CMC solution with
temperature distribution was only compared with the electric field pattern from the simulation. Thus, they
only drew a general conclusion describing the discrepancy between experiment and simulation results.
Jumah (2005) developed a mathematical model for RF-assisted fluidized bed drying of grains, and
solved the partial differential equations. Various frequencies and electric field strengths were tested for
temperature and moisture content change during drying. However, the simulation considered the food load
as a uniform temperature point, so no heating uniformity tests were conducted.
Within this decade, comprehensive studies were conducted by researchers with an FEM based
software, COMSOL Multiphysics® (FEMLAB). In these works, a quasi-static assumption was made since
the alternation of E-field and power conversion from electromagnetic energy to heat is much faster than
that of heat transfer in a time step.
22
Marra et al. (2007) developed a computer simulation model to simulate the meat batter being
subjected to RF treatment. The simulation results were validated by experiments with a 50 Ω system (600
W, 27.12 MHz). The results showed that an uneven temperature distribution existed in the cylinder meat
batter. The bottom had a higher heating rate than the upper part, and a higher applied power may result in
a more uneven temperature distribution.
Romano et al. (2008) did a numerical analysis with FEMLAB 3.1 on radio frequency heating (27.12
MHz) of regular shaped meat batters. Sample shape (cube, cylinder and sphere), orientation (horizontal and
vertical), electrode distance, sample/oven volume ratio and sample surface exposed in the electrode were
chosen as the influencing factors to test the effect on heating rate and uniformity. The results showed that
the sample shape had a great influence on heating rate and uniformity, and for a cylinder product, the
vertically oriented position may achieve a better heating uniformity. It was also found that the absorbed
power in foods were relatively stable when treated under 100 and 200 W, which was 40-60%, but varied
from 20-60% at 300 and 400 W. The sample with a sphere shape had the lowest power absorption among
all the shapes, followed by that in a horizontally placed cylinder.
Wang et al. (2008) developed and solved a mathematical model by COMSOL Multiphysics® for
studying the influence of dielectric properties on mashed potatoes and circulating water subjected into RF
heating (6 kW, 27.12 MHz). Several representative spots were chosen for comparison between the
experiment and simulation results, the differences between the highest and lowest temperature were < 12 °C
while the center temperature rose from room temperature to 55 ºC. The authors also found the relationship
between loss factor and heating rate was not positively linear from both experiments and simulations.
Tiwari et al. (2011b) developed and validated a model with COMSOL Multiphysics package for
flour in RF heating (12 kW, 27.12 MHz). The temperature distribution of flour in a rectangular box from
both simulation and experiment showed a good agreement. Tiwari et al. (2011a) conducted another research
on RF power distribution analysis that was based on a computer simulation. The influences of various
23
factors including shape, size, vertical position, and dielectric properties of food load were studied. The
results showed a smaller size, smaller dielectric properties, larger gap and ellipsoid shape food sample had
better heating uniformity. This might be due to the lower absorbed power in foods. A power uniformity
index was developed to describe the heating uniformity quantitatively.
Dev et al. (2012) conducted computer simulations with FEMLAB 3.4 for in-shell eggs with
different orientation and electric field strength in a 600 W 27.12 MHz 50 Ω RF system. Maxwell’s equations
and Fourier’s equation were solved for obtaining the temperature distribution in eggs. Experiments were
conducted with a mock egg with a transparent shell to validate the heating process and observe the nonuniform heating by finding coagulation of the egg white. Simulation and experiment results agreed well,
and they showed that rotation improved the heating uniformity greatly.
It can be seen from literatures that the heating pattern of food in RF could be predicted by computer
modeling if parameters and conditions were properly set. In order to develop heating uniformity
improvement methods, computer modeling can be used as an efficient tool to understand the mechanisms,
test new strategies, optimize parameters and design appropriate RF treatment conditions for specific food
products.
24
References
Ahmed, J., Ramaswamy, H.S. and Raghavan, V.G.S., 2007a. Dielectric properties of butter in the MW
frequency range as affected by salt and temperature. Journal of Food Engineering, 82(3): 351-358.
Ahmed, J., Ramaswamy, H.S. and Raghavan, V.G.S., 2007b. Dielectric properties of Indian Basmati rice
flour slurry. Journal of Food Engineering, 80(4): 1125-1133.
Boldor, D., Sanders, T.H. and Simunovic, J., 2004. Dielectric properties of in-shell and shelled peanuts at
microwave frequencies. Transactions of the ASAE, 47(4): 1159-1169.
Chan, T.V., Tang, J. , Younce, F. , 2004. 3-dimensional numerical modelling of an industrial radio
frequency heating system using finite elements. Journal of Microwave Powers and Electromagnetic
Energy, 39(2): 87-105.
Dev, S.K., Y. Gariepy, and V. G. S. Raghavan, 2012. Optimization of radiofrequency heating of in-shell
eggs through finite element modeling and experimental trials. Progress In Electromagnetics
Research, Vol. 45: 203-222.
Gao, M., Tang, J., Johnson, J.A. and Wang, S., 2012. Dielectric properties of ground almond shells in the
development of radio frequency and microwave pasteurization. Journal of Food Engineering,
112(4): 282-287.
Gao, M., Tang, J., Villa-Rojas, R., Wang, Y. and Wang, S., 2011. Pasteurization process development for
controlling Salmonella in in-shell almonds using radio frequency energy. Journal of Food
Engineering, 104(2): 299-306.
Guo, W.C., Wu, X.L., Zhu, X.H. and Wang, S.J., 2011. Temperature-dependent dielectric properties of
chestnut and chestnut weevil from 10 to 4500 MHz. Biosystems Engineering, 110(3): 340-347.
Hasted, J.B., 1973. Aqueous dielectrics. Studies in chemical physics. Chapman and Hall, Distributed in the
U.S.A. by Halsted Press, a division of J. Wiley & Sons, New York, London,, xiii, 302 p. pp.
25
Jeong, S.G. and Kang, D.H., 2014. Influence of moisture content on inactivation of Escherichia coli
O157:H7 and Salmonella enterica serovar Typhimurium in powdered red and black pepper spices
by radio-frequency heating. International Journal of Food Microbiology, 176: 15-22.
Jumah, R., 2005. Modelling and simulation of continuous and intermittent radio frequency-assisted
fluidized bed drying of grains. Food and Bioproducts Processing, 83(C3): 203-210.
Kim, S.Y., Sagong, H.G., Choi, S.H., Ryu, S. and Kang, D.H., 2012. Radio-frequency heating to inactivate
Salmonella Typhimurium and Escherichia coli O157:H7 on black and red pepper spice.
International Journal of Food Microbiology, 153(1-2): 171-175.
Lagunas-Solar, M.C. et al., 2005. Disinfection of fishmeal with radiofrequency heating for improved quality
and energy efficiency. Journal of the Science of Food and Agriculture, 85(13): 2273-2280.
Lawrence, K.C., Nelson, S.O. and Kraszewski, A.W., 1992. Temperature-Dependence of the DielectricProperties of Pecans. Transactions of the ASAE, 35(1): 251-255.
Marra, F., Lyng, J., Romano, V. and McKenna, B., 2007. Radio-frequency heating of foodstuff: Solution
and validation of a mathematical model. Journal of Food Engineering, 79(3): 998-1006.
Meakins, R.J., 1961. Mechanisms of dielectric absorption in solids. Prog. Dielectrics, 3: 151.
Metaxas, A.C. and Meredith, R.J., 1983. Industrial microwave heating. P. Peregrinus on behalf of the
Institution of Electrical Engineers.
Nelson, S.O., 1981. Review of factors influncing the dielectric properties of cereal grains. Cereal
Chemistry, 58(6): 487-492.
Nelson, S.O., Stetson, L.E. and Wolf, W.W., 1984. Long-Term Effects of Rf Dielectric Heating on
Germination of Alfalfa Seed. Transactions of the Asae, 27(1): 255-258.
Romano, V. and Marra, F., 2008. A numerical analysis of radio frequency heating of regular shaped
foodstuff. Journal of Food Engineering, 84(3): 449-457.
Ryynanen, S., 1995. The Electromagnetic Properties of Food Materials - a Review of the Basic Principles.
Journal of Food Engineering, 26(4): 409-429.
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Sacilik, K., Tarimci, C. and Colak, A., 2006. Dielectric properties of flaxseeds as affected by moisture
content and bulk density in the radio frequency range. Biosystems Engineering, 93(2): 153-160.
Tiwari, G., Wang, S., Tang, J. and Birla, S.L., 2011a. Analysis of radio frequency (RF) power distribution
in dry food materials. Journal of Food Engineering, 104(4): 548-556.
Tiwari, G., Wang, S., Tang, J. and Birla, S.L., 2011b. Computer simulation model development and
validation for radio frequency (RF) heating of dry food materials. Journal of Food Engineering,
105(1): 48-55.
Von Hippel, A.R., 1954. Dielectrics and waves. Wiley; Chapman & Hall, New York; London.
Wang, J., Olsen, R.G., Tang, J. and Tang, Z., 2008. Influence of mashed potato dielectric properties and
circulating water electric conductivity on radio frequency heating at 27 MHz. Journal of Microwave
Power and Electromagnetic Energy, 42(2): 31-46.
Wang, S., Tang, J., Cavalieri, R.P. and Davies, D.C., 2003. Differential heating of insects in dried nuts and
fruits associated with radio frequency and microwave treatments. Transactions of the ASAE, 46(4):
1175-1182.
Yang, J., Zhao, Y. and Wells, J.H., 2003. Computer simulation of capacitive radio frequency (RF) dielectric
heating on vegetable sprout seeds. Journal of Food Process Engineering, 26(3): 239-263.
Zhao, Y.Y., Flugstad, B., Kolbe, E., Park, J.W. and Wells, J.H., 2000. Using capacitive (radio frequency)
dielectric heating in food processing and preservation - A review. Journal of Food Process
Engineering, 23(1): 25-55.
Zhu, X.H., Guo, W.C., Wu, X.L. and Wang, S.J., 2012. Dielectric properties of chestnut flour relevant to
drying with radio-frequency and microwave energy. Journal of Food Engineering, 113(1): 143150.
27
Table 2.1 Comparison of open circuit and 50 ohm RF systems
Open circuit (Free running oscillator)
Application
Cost
50 ohm technology
Most commonly used; more mature,
New technology, few applications in
established knowledge.
market.
Low cost.
High cost (the tetrode tube is much
more expensive than triode, and also a
load impedance matching circuit is
also costly; variable vacuum capacitors
are required but reliability is poor);
Expensive spare parts.
Complicity
Simple to setup, operate and maintain.
The installation and maintenance
requires specialist RF knowledge,
particularly in matching the generator
to the load.
Flexibility
Can be used on various load
Load impedance will be matched to 50
dimensions and properties, more
ohms to maintain a fixed RF power
adaptable; dynamically match the load,
level (accomplished by analyzing the
power is automatically controlled
phase and the magnitude at the co-axial
(unique for moisture control).
feed into the matching network).
Tuning range is wider.
Does not have the ability to change
power according to the moisture
content.
Power stability
Varying power, has the advantage of
Constant power.
selective heating, especially for drying.
Frequency
Lack of frequency stability and
Frequency is precisely controlled by
stability
harmonic output: will result in RF
the quartz crystal; harmonic free.
interference with communications or
other machinery. Shielding is more
important, requires a properly designed
harmonic filter to meet standards.
28
Table 2.2 Literature review of RF sterilization/pastuerization effect on pathogens in low moisture
food products
Food product
Frequency /
power
39 MHz /
aw / MC
Target
microorganism
Salmonella,
Temperature/time
113, 89, 86 ºC /
Log
reduction
3 kW
3.2, 6.5,
7.6% w.b.
Fish mealb
6-14 MHz /
0.17–1.2 kW
7-10%
w.b.
Salmonella
Almondc
27.12 MHz /
6 kW
aw = 0.40.5
S. enteritidis PT
30
73 ºC/ 1.5 min
5
27 MHz /
Salmonella
62, 67 ºC /
2.80, 4.29
9 kW
E. coli
50, 40 s
3.38, >5
27 MHz /
Salmonella
35-80 s (red pepper)
>7
9 kW
E. coli
40-60 s (black pepper)
>7
Alfalfa seeds
Pepperd
Peppere
a
E. coli,
L. monocytogenes
E. coli
69, 20, 18 sec
90 ºC / 5 min
1.81, 1.40,
1.10
>6.2
5.3
References: a (Nelson et al. 1984) b (Lagunas-Solar et al. 2005) c (Gao et al. 2011) d (Kim et al.
2012) e (Jeong and Kang, 2014)
29
Figure 2.1 Contribution of various mechanisms to the loss factor of food materials as functions of
frequency and temperature (Tang, Feng, & Lau, 2002, Chapter 1, based on Harvey & Hoekstra, 1972;
Kuang & Nelson, 1998; Metaxas & Meredith, 1993; Roebuck & Goldblith, 1972)
30
Figure 2.2 Scheme of a typical open circuit RF system (adapted from Zhao et al., 2000)
31
Crystal
controlled
Oscillator
50 W
Amplifier
50 ohm Cables
Figure 2.3 Composition of a 50 ohm RF system
32
Automatic
Matching
Network
Dielectric
applicator
CHAPTER THREE:
DIELECTRIC, PHYSICAL AND THERMAL PROPERTIES OF PEANUT BUTTER WITH
DIFFERENT WATER CONTENT
Abstract
Commercial peanut butter was used as a model food and conditioned to 5 different water contents
for representing semi-solid types of food products. The water activity, density, dielectric properties, specific
heat and thermal conductivity of samples were either determined or predicted at temperatures from 20 to
90 °C and 5 water contents: 1.3, 4, 10, 16 and 22 g water /100 g sample. The results showed that density,
specific heat and thermal conductivity increased with water content increase. Both dielectric constant and
loss factor showed an evident increasing trend with increasing water content and temperature, and
decreasing frequency except 1.3 and 4 g water /100 g samples which had increasing loss factors with
increasing frequency. Wave penetration depths calculated based on dielectric properties decreased with
increasing water content, frequency, and temperature. The results in this study will used in radio frequency
heating computer simulations as input parameters and Salmonella inactivation rate study in peanut butter
in the future.
Keywords: Peanut butter; radio frequency; dielectric properties; thermal properties; water activity.
33
1. Introduction
Peanut butter, a popular snack with an aromatic flavor and smooth mouth-feel, is often used as a
sandwich spread and baking ingredient. In the United States, 1 billion pounds of peanut butter has been
consumed per year since 2009, and the amount keeps increasing (NASS, 2012). However, a series of
multistate salmonella outbreaks related to peanut butter and paste recently happened in the United States
and other parts of the world, thus making peanut butter face serious food safety issues (Burnett et al., 2000;
Shachar and Yaron, 2006). The most recent outbreak in 2009 in the U.S. resulted in 9 deaths and more than
714 illnesses in consumers, along with the bankruptcy of reputation and huge economic loss from
companies who recalled products and suffered the resulting legal cases (Wittenberger, 2010). To prevent
the spread of illness and the resulting economic loss, the peanut butter industry is seeking a post packaged
pasteurization technology to ensure food safety.
Due to the low heat conduction rate in low moisture foods, traditional pasteurization methods, like
hot water, hot air, steam etc. may not work efficiently on peanut butter pasteurization. The slow heat transfer
could also cause the generation of heat shock protein in the bacteria, which will increase the heat resistance
of bacteria in the food material and make pasteurization even harder to accomplish (Chung et al, 2007).
Dielectric heating, including microwave and radio frequency heating, applies high energy electromagnetic
waves to food products, initiates ionic conductance and dipole rotation of water molecules, and results in a
volumetric heat generation in food materials (Nelson, 1996; Piyasena et al., 2003). Dielectric heating
methods have been recently applied to sterilization and pasteurization in agricultural and food products
(Luechapattanaporn et al., 2005; Byrne et al., 2010; Gao et al., 2011). With its advantages of relatively fast
and uniform, dielectric heating could be potentially applied to peanut butter pasteurization. Physical,
thermal and dielectric properties are thus needed to understand the interaction between the peanut butter
and the electromagnetic energy and predict the heating behavior during RF treatment.
34
Dielectric properties are the intrinsic properties of a material and can be described as     j ,
*
'
''
where the real part  ' is called the dielectric constant, and the imaginary part  '' is called the loss factor.
These two components are used to describe the ability of energy storage and conversion from
electromagnetic energy to heat. Thermal and physical properties also play important roles in RF heating
since the heat transfer inside food material and between food and environment happens throughout
processing.
Generally, all the physical, thermal and dielectric properties of a food product are dependent on the
temperature, structure and composition of food material, e.g., porosity, water content, salt content of foods.
In addition, dielectric properties are also a function of frequencies (Calay et al., 1994; Ryynanen, 1995). A
thorough understanding of the changes in properties of water content, temperature, and frequency could
benefit in selecting the optimum processing condition in RF heating. The dielectric properties of pecans,
walnuts, almonds, peanuts and chestnuts with varied water contents, frequency and temperature were
reported (Wang et al. 2003a; 2003b, Boldor et al. 2004, Sacilic et al. 2006, and Guo et al. 2011) Several
studies have been conducted on dielectric properties of low water and high fat content paste-like food
materials, like butter and butter oil (Ahmed et al, 2007a) and rice slurry (Ahmed et. al, 2007b) showed a
significant fat content effect on dielectric properties. However, no systematic data have been reported in
the literature for the properties of peanut butter as a function of water content and temperature for dielectric
heating purposes.
The objectives of the present study were: 1) to determine the properties of peanut butter samples
related to dielectric heating, which include: density, specific heat, heat conductivity, and dielectric
properties at frequencies of 10–1800 MHz, temperatures of 20–90 °C and 5 different water content levels;
and 2) to calculate the wave penetration depths of electromagnetic waves in peanut butter samples at various
combined conditions for obtaining the optimum thickness of peanut butter in processing; The results of the
35
study would provide sound information for developing an electromagnetic heating pasteurization protocol,
and realizing computer simulation optimization.
2. Materials and Methods
2.1. Samples preparation
Commercial creamy peanut butter (IGA creamy peanut butter, IGA Inc, Chicago, IL, USA) was
purchased from a local grocery store and stored at room temperature until use. Commercial peanut butter
was made from peanut by 40–60 minutes of roasting and grinding with very little addition of flavoring and
emulsifiers (<5 g/100g), so it can be considered as a homogeneous product with a stable structure and
quality. According to the label, the peanut butter contains 50 g/100g fat, 25 g/100g protein, 1.19 g/100g
salt, and 21.9 g/100g carbohydrate (including 6.3 g/100g fiber and 9.4 g/100g sugar) by weight.
2.2. Water content and water activity
The initial water content of peanut butter was determined by the vacuum oven method AOAC
926.12 (Horwitz et al., 2005). Around 10–12 g of peanut butter samples were weighed, transferred to
aluminum dishes and heated in a vacuum oven (ADP-31, Yamato Scientific America Inc., Santa Clara, CA,
USA) overnight at 110 °C and 10 kPa. Samples were taken out and weighed every 2 hrs as drying continued
until the final weight change was less than 0.05 g/100g. The samples were then cooled down in a desiccator
for 30 min until reaching room temperature, and then the final weights of the samples were measured by an
analytical balance (Ohaus Analytical Plus, Ohaus Corporation, Florham Park, NJ, USA). The experiment
was conducted twice with 3 samples per batch, and water contents were calculated in wet base.
To prepare samples of higher moisture contents, pre-weighted deionized water was added into the
commercial peanut butter sample and mixed with a hand mixer (Durabrand 5-speed hand mixer, Funai
Electric Co., Ltd., Osaka, Japan) in a beaker (1 L) for 1 min to bring the water content of the peanut butter
to 4, 10, 16 and 22 g/100g, respectively. The minimal strength and time for blending were chosen for not
generating heat inside samples. The processed peanut butter samples were stored at 4 °C for 24 h for water
36
to equilibrate, and mixed again at room temperature before measurements. The water content of the
conditioned samples was determined again by sampling from three random locations in the sample
container. The standard deviation of tested water content was less than 0.5 g/100g. Water activity of samples
equilibrated at different water contents were measured using a water activity meter (Aqualab serious 3TE,
Decagon Devices Inc., Pullman, WA, USA) at room temperature (22 °C), and the measurements were
repeated three times.
2.3. Density
The density of the original peanut butter sample was measured by the gravimetric method. An
open-end metal cylinder tube with a known mass and volume (d = 5 cm, h = 1 cm) was used as a container
for the volume measurement. Because of the high viscosity of the peanut butter, samples were heated up to
60 °C in a water bath (above melting point), and then filled into the metal cylinder tube. Precaution was
taken to avoid air bubbles in the material during transfer. After the sample was cooled down to room
temperature, both ends of the tube were scratched flat carefully. The total weight of the tube and sample
were measured. The average density was calculated by dividing sample mass by sample volume.
Measurement was made in three replicates.
Because of the difficulty in sample loading caused by the high viscosity of samples with higher
water contents, the density of the peanut butter samples with water content 4, 10, 16 and 22 g/100g and
temperature 20–90 °C were all obtained from Costherm® software (Aberdeen, UK). The prediction method
in Costherm® is based on properties of composition of food materials and their change with temperature.
It can be used for accurate prediction of most physical properties of food including initial freezing point,
thermal conductivity, and specific heat and enthalpy models to fat-containing foods with good accuracy
and over an extended temperature range (Allen et al., 1997). The basic composition of food materials and
the original density of peanut butter were also input as a reference for obtaining sample porosity, which is
related to the determination of density and thermal conductivity.
37
2.4. Specific heat
Specific heat cp (kJ/kg·K) of peanut butter samples at different water contents was determined using
a differential scanning calorimeter (DSC Q2000, TA Instruments, New Castle, DE, USA). An empty sealed
aluminum pan was used as a reference and a 10–20 mg peanut butter sample was sealed in another
aluminum pan (30 µL). The procedure included cooling the sample from room temperature to 0 °C at a
ramping rate of 10 °C/min, equilibrating for 5 min, and then heating up to 90 °C. The measurements were
made in three replicates. The DSC produced heat flow (W/g) and specific heat (kJ/kg·K) versus temperature
thermograms, and the melting point of peanut butter was obtained from the concave.
2.5. Thermal conductivity
To evaluate the heat conduction inside food materials, the thermal conductivity of samples at 5
water contents was also obtained from Costherm® in the temperature range from 20 °C to 90 °C in three
replicates.
2.6. Dielectric Properties
2.6.1.
Dielectric properties measurement
Dielectric properties of the peanut butter samples were determined using an open-ended coaxial-
line probe connected to an impedance analyzer (Agilent 4291B, Agilent Technologies, Inc., Santa Clara,
CA, USA). Prior to the measurement, the impedance analyzer was warmed up for 30 min before calibration
to minimize system errors. Then the system was calibrated with open/short/low lossy capacitance/50Ω load
in sequence, and the measuring probe was calibrated using air/short block/25 °C deionized water, as
recommended by the manufacturer. Software 85070D (Agilent Technologies, Inc., Santa Clara, CA, USA)
was used to trigger the measurement and record dielectric property data. After calibration, the dielectric
properties of creamy peanut butter samples with 5 levels of water content were measured over a temperature
range of 20–90 °C and frequency range of 10–1800 MHz. Between two measurements, both the probe and
sample holder were cleaned with deionized water, dried and cooled down to room temperature. The detailed
38
procedure and demonstrating scheme for dielectric property measurement can be found elsewhere (Wang
et al., 2003a,c). The cylinder sample holder (20 mm in inner diameter and 94 mm in height) was designed
to make sure the sample size satisfies the assumption of a semi-infinite body, which guarantees an accurate
measurement (Feng et al., 2002). Measurements were repeated twice for each sample, and the mean value
and standard deviation were calculated.
2.6.2.
Penetration depth
Penetration depth (dp, m) is defined as the distance into the material where the power is reduced to
1/e (e = 2.718) of the power at the surface when electromagnetic waves penetrate a certain lossy material.
Penetration depth was calculated using the following equation (Von Hippel, 1954):
dp 
c
2
 

   
2 2 f    1     1 

 
  

 
(1)
1
2
where c is the speed of light in free space (3×108 m/s) and f is the frequency (Hz). In this study, the
penetration depths of the electromagnetic wave in peanut butter samples at representative frequencies and
temperatures were calculated from the dielectric properties data.
2.7. Statistical analysis
ANOVA analysis was conducted by using Statistical Analysis System software (SAS, version 9.2,
SAS Institute Inc., Cary, NC). The least significant difference (LSD) test was used to determine the
difference between the means of data at P < 0.05.
3. Results and discussion
3.1. Physical properties
3.1.1.
Water content and water activity
39
The water content of commercial peanut butter samples ranged between 1.09–1.42 g/100g with an
average of 1.28 g/100g and standard deviation of 0.14 g/100g. This low water content in the original peanut
butter was because the roasting procedure had removed most of the water inside the peanut kernel during
processing, so the corresponding low water activity (aw = 0.23) made the peanut butter shelf-stable. Water
activities corresponding to the 5 different water contents at 22 °C have been listed in Table 3.1. Water
activity increased proportionally from 0.229 to 0.943 with a relative error of less than 0.02 with increasing
water content in peanut butter samples from 1.3 g/100g to 22 g/100g (Fig. 3.1). The increment was gradually
decreasing when water activity was above 0.8, which indicated that water activity is not so sensitive to
water content when water content increased to a certain level. Many isotherm adsorption curves validated
this trend. Burnett et al. (2000) showed the water content to be 0.5–2 g/100g and the water activity to be
0.20–0.33 in a commercial peanut butter product. He et al. (2011) mentioned that the water content of
peanut butter is less than 1 g/100g with a water activity of 0.3. The measured water content and water
activity in this study were in good agreement with the observed values reported in the literature.
3.1.2.
Density
The density of the peanut butter decreased slightly with the moisture contents but the average
density was 1115.1 kg/m3 with a standard deviation of 5.9 kg/m3 (Table 3.1). Aydin et al. (2007) studied
the true density of peanut fruit with water contents from 4.85 to 32.2 g/100g, and found the density varied
from 989 to 1088 kg/m3 with porosity from 6 to 32%. It is reasonable that the density of peanut butter
increases after crushing and grinding because of the porosity decrease.
Temperature variation (20–80 °C) had very little effect on the density of the conditioned peanut
butter samples since the density of the main components in peanut butter, such as fat, protein and
carbohydrates do not vary with temperature. The temperature effect on density was thus not presented in
this study. The porosity estimated by Costherm® software was between 1–1.3%, and the density equation
regressed from component percentage in peanut butter samples is shown below (R2 = 0.999):
40
  1116.6  118.48 X
(2)
where ρ is the density of sample (kg/m3), and X is the water content (g water/100 g sample).
3.2. Thermal properties
3.2.1. Specific heat with melting point
The specific heat (cp) of peanut butter samples increased with moisture content (1.3 to 22 g/100g)
from 1.7 to 2.8 kJ/kg·K at 20 °C, and also increased slightly as the temperature increased from 20 to 90 °C
at each water content (Fig. 3.2a). For peanut kernels with water content varying from 5.0 g/100g to 30.6
g/100g, cp was reported as 1.9–2.8 kJ/kg·K by Bitra et al. (2010), which are similar to those observed in
this study. Costherm® prediction also shows a similar result from 1.8 to 2.3 kJ/kg·K at room temperature.
Fig. 3.2a also shows that samples of all water contents had the same melting point on the DSC heat
flow chart. A concave at 44.5 °C showing in this endothermic process (Fig. 3.2b) demonstrated that peanut
fats in the food sample were experiencing a phase change during that temperature period. It also can be
seen that as the water content increases, the heat absorption peak at the melting point is reduced gradually,
which is because of the decrease in overall fat percentage. Norton et al. (2009) reported that cocoa butter
emulsions with 30 g/100g water content had a melting point of around 31.2–33.2 °C. The high fat content
and long chain structure of fatty acid increased its melting point (Rao et al., 2005).
3.2.2. Thermal conductivity
According to the predicted thermal conductivity of peanut butter samples, the thermal conductivity
of peanut butter did not change significantly with increasing temperature from 20 to 80 °C (P > 0.05), but
increased from 0.20 to 0.29 W/m·K with increasing water content from 1.3 g/100g to 22 g/100g (Table 3.1).
Bitra et al. (2010) measured peanut kernels at different water contents and ambient temperatures, and
showed the thermal conductivity at water content of 5.0 g/100g was 0.15 W/m·K. This low thermal
conductivity in raw peanut kernels is due to the porous structure of the fresh peanut kernel, which was
41
avoided by the fine grinding process for peanut butter production. The regression equation derived from
data in Table 3.3 was as follows with a coefficient of determination of R2=0.996:
K  0.194  0.00431X
(3)
where K is the thermal conductivity of sample (W/m·K) and X is the water content (g water/100 g sample).
3.3. Dielectric properties
Dielectric properties data at frequencies of 27, 40, 915 and 1800 MHz were reported in Table 3.2.
3.3.1. Frequency dependence
Figs 3.3 and 3.4 show the log-log plot of dielectric properties of peanut butter against frequency
(10–1800 MHz) at four temperatures (20–90 °C) and five water contents. When the water content of the
peanut butter samples was quite low, both the dielectric constant and loss factor were expected to be low,
especially at room temperature. For low water content samples (1.3 and 4 g/100g), their dielectric constants
were relatively independent of frequency, on the other hand, the loss factor increased with cumulative
frequency at water content of 1.3 and 4 g/100g and all available temperature (Table 3.2). However, as the
water content of the sample increased to 10 g/100g and above, both the dielectric constant and loss factor
decreased linearly with increasing frequency. The loss factor decrease is due to the dominant effects of
ionic conduction as frequency increased. As the frequency increases, ionic effect reduced and dipole
rotation of water molecules becomes dominant. This usually shows a peak at around 20 GHz at room
temperature (Ryynanen, 1995). As the peak of free water dipole rotation moved to higher frequencies when
the temperature increased (Mudgett, 1986), the flat tail accordingly appeared at a higher frequency and
gradually disappeared at a frequency of 1800 MHz. The decreasing trend of ε’ and ε” with increasing
frequency has also been reported in many other studies of low moisture foods (Nelson, 1991; Guo et al.,
2008; 2010b; Liu et al., 2009; Jiao et al., 2011). The large variation shown in the loss factor data of the low
42
water content samples, which was also found in the literature (Ahmed, 2007), may be due to the insufficient
accuracy of the equipment for low lossy food materials (Ryynanen, 1995).
3.3.2. Moisture content dependence
Generally, both ε’ and ε” increased with increasing water content (Figs. 3.3 and 3.4). For example
at 27 MHz, ε’ and ε” increased from 3.3 to 18.3 and 0.05 to 27.5 at 20 °C as water content increased from
1.3 to 22 g/100g (Fig. 3.5). Accordingly, at 915 MHz, ε’ and ε” increased from 2.9 to 8.3 and 0.3 to 3.0
(Fig. 3.6). This increment was greater at lower frequency (< 400 MHz) and minimized gradually as the
frequency increased since the ionic effect was reduced to the lowest point and dipole rotation of water
molecules has not started until frequency reached around 1 GHz (Mudgett, 1986).
It has been reported that for high water content food products (usually water content >85 g/100g),
the logarithmic value of dielectric loss factor had a linear relationship with logarithmic frequency (Schubert
and Regier, 2005; Liu et al., 2009).
 
log  ''  log
 2 0

  log f

(4)
where σ is the electric conductivity of sample (S/m). However, for low-water food materials, a much lower
slope trend with a lag tail was obtained at higher frequencies. When there is limited water content in food
material, the salt may not be able to dissolve and provide a more effective ionic conduction. Then the bound
salt may perform as large molecules vibrating with frequency, and therefore contribute to the loss factor to
a much lower extent. Guo et al. (2010a) explained the same trend of loss factor versus frequency for flour
product with water content 7.9–10.8 (g water/100 g sample) and stated that the slope of the curve was due
to the water molecule dipole rotation effect because of the reduced mobility of the charged ions. This effect
can be summarized as: when the bound water amount is dominant in the total water content in a food
material, the slope of log ε” versus log f is no longer “-1” but slightly higher (between -1 and 0) (Liu et al.
2009).
43
For samples in the low water content range (1.3–4 g/100g), loss factors increased slightly as
frequency increased with a small peak at around 100–300 MHz. The peak moved to 400–500 MHz as
temperature increased from 20 to 80 °C (Fig. 3.3). This increasing trend and peak could be explained by
the effect of bound water, which usually shows at 100 MHz (Harvey and Hoekstra, 1972; Miura et al.,
2003). The peak only appear when the value of the loss factor is quite small, and disappears gradually as
distilled water is added and the effect of free water dominates the dielectric properties. Thus, it can be
concluded that the bound water effect does exist in low moisture products and plays an important role in
dielectric properties (Wang et al., 2003b).
In a multiphase system, each single component has a different relaxation time (shown as peaks in
the loss factor) according to Debye’s polarization theory. Furthermore, in a solid or a highly viscous
material, activation energy should also be introduced to consider the hindered motion among molecules
(Debye, 1929). Maxwell-Wagner’s interfacial polarization also exists in a multiphase system at the interface
of layers to describe the charge’s vibration. It usually shows a peak in the kHz range but may also extend
its effect to the MHz range and contribute to the dielectric loss factor when the ionic effect is not as strong
and the volume fraction of non-polar impurities is quite low (Meakins, 1961). Since the sample in this case
had both low water content and low salt content, and was composed of a large amount of protein,
carbohydrate and oil, a combination effect mentioned above formed the trend of a curve, which is still not
able to be quantitatively described. Hence, due to the complexity of the composition and the various
interactions among molecules in food systems, it is still difficult to explain and predict the dielectric
properties in non-aqueous materials.
3.3.3. Temperature dependent
Table 3.2 shows that at lower water content range (1.3–10 g/100g), the dielectric properties
increased correspondingly with temperature increase. Taking the sample with water content of 1.3 g/100g
as an example, ε’ increased from 3.3 to 3.6 at 27 MHz, but the values for ε” varied from 0.01 to 0.05 in a
44
nonlinear trend at 20–80 °C. However, as the water content exceeded 16 g/100g, both ε’ and ε” appeared
to show an increasing trend with increasing temperature (Fig. 3.4). This trend became sharp when the
temperature went beyond 60 °C. Calay et al. (1994) also showed an insignificant decrease of ε” and an
increase of ε’ for oil and fat along with the frequency increase. This result verified that fat content is
dominant when the water content is low in a food product.
3.3.4. Predictive equations for the dielectric properties
Predictive equations for the dielectric properties as functions of temperature and water contents at
three selected frequencies were derived based on the experiment results (Table 3.3). Third degree
polynomial regression equations were obtained by the least squares method using Microsoft Excel with a
coefficient of determination ≥ 0.95. Including both temperature (T, °C) and water content (M, g/100g) as
independent variables make the equations easy to use in future computer simulations for electromagnetic
heating.
3.4. Penetration depth
Penetration depths of electromagnetic energy at four frequencies in peanut butter samples with
different water contents over the measured temperature range were summarized in Table 3.4. The
penetration depth of samples with higher water content (above 4 g/100g) also showed a manifest decrease
with increasing frequency and temperature, which agrees with other studies (Boldor et al., 2004; Guo et al.,
2010b; Jiao et al., 2011). The penetration depth of sample with water content of 1.3 g/100g did not show a
regular monotonic change, which was due to the variation of measurement in small loss factor value.
4. Conclusion
Representative physical, thermal and dielectric properties of peanut butter samples with five water
activity levels (0.23–0.95) were measured and predicted at different temperatures (20–90 °C) to provide
data for processing protocol design and mathematical simulation in electromagnetic heating. The specific
45
heat and thermal conductivity increased with increasing temperature and water content. The dielectric
constant and loss factor of peanut butter decreased with increasing frequency but increased with increasing
water content and temperature. Temperature affected the dielectric properties of high water content samples
much more than lower ones. Penetration depths decreased with increasing frequency and water content.
The regression equations of the dielectric properties were obtained as a function of temperature and water
content, which could be used as input parameters in a computer simulation.
46
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50
Table 3.1 Water activity, density and thermal conductivity of peanut butter with 5 different water
contents at 22 °C
Water content (g/100g)
Water activity (-)
Density (kg/m3)
1.3
4
10
16
22
0.229±0.019 0.364±0.018 0.661±0.018 0.844±0.017 0.943±0.003
1115.11
1111.90
1104.79
1097.69
1090.58
0.20
0.21
0.24
0.26
0.29
Thermal conductivity
(W/m·K)
51
Table 3.2 Dielectric constant and loss factor of peanut butter samples with five water contents at
eight temperature and four frequencies
MC
1.3%
4%
10%
16%
T
(°C)
Dielectric constant
Dielectric loss factor
Frequency (MHz)
Frequency (MHz)
27
40
915
1800
27
40
915
1800
20
3.3±0.1
3.3±0.1
2.9±0.1
2.9±0.01
0.05±0.01
0.09±0.01
0.3±0.1
0.2±0.1
30
3.3±0.1
3.3±0.1
3.0±0.1
2.8±0.01
0.04±0.01
0.08±0.01
0.3±0.1
0.1±0.1
40
3.4±0.1
3.4±0.1
3.0±0.1
2.9±0.04
0.03±0.01
0.07±0.01
0.3±0.1
0.2±0.1
50
3.4±0.1
3.4±0.1
3.1±0.1
2.9±0.03
0.01±0.00
0.07±0.01
0.3±0.1
0.2±0.1
60
3.5±0.1
3.5±0.1
3.1±0.1
2.9±0.01
0.01±0.01
0.05±0.01
0.3±0.1
0.2±0.1
70
3.5±0.1
3.5±0.1
3.1±0.1
3.0±0.04
0.02±0.01
0.04±0.01
0.3±0.1
0.2±0.0
80
3.6±0.1
3.6±0.1
3.1±0.1
3.0±0.03
0.01±0.01
0.03±0.01
0.2±0.1
0.2±0.1
90
3.6±0.1
3.7±0.1
3.2±0.1
3.1±0.02
0.04±0.01
0.01±0.01
0.2±0.1
0.1±0.1
20
3.4±0.3
3.4±0.3
3.1±0.2
2.8±0.3
0.1±0.1
0.1±0.1
0.2±0.1
0.2±0.3
30
3.5±0.3
3.5±0.3
3.1±0.3
2.7±0.7
0.1±0.0
0.1±0.0
0.2±0.1
0.6±0.6
40
3.6±0.3
3.6±0.3
3.2±0.3
2.6±0.6
0.1±0.0
0.2±0.0
0.2±0.1
0.6±0.5
50
3.7±0.4
3.7±0.4
3.3±0.3
2.7±0.7
0.1±0.0
0.2±0.0
0.2±0.2
0.6±0.5
60
3.8±0.5
3.8±0.5
3.3±0.5
2.6±0.8
0.1±0.0
0.2±0.1
0.1±0.2
0.6±0.4
70
3.9±0.7
3.8±0.7
3.3±0.6
2.6±0.9
0.2±0.1
0.2±0.1
0.1±0.2
0.7±0.5
80
4.0±1.9
3.9±0.9
3.4±0.7
2.6±1.1
0.2±0.1
0.2±0.1
0.1±0.3
0.7±0.4
90
4.0±1.0
4.0±1.0
3.4±0.8
2.6±1.1
0.2±0.1
0.2±0.1
0.1±0.3
0.8±0.3
20
6.8±0.2
6.4±0.2
4.5±0.1
4.3±0.2
1.7±0.2
1.5±0.1
0.8±0.1
0.8±0.4
30
6.9±0.1
6.5±0.1
4.5±0.1
4.3±0.3
1.9±0.1
1.7±0.1
0.8±0.1
1.0±0.4
40
7.3±0.2
6.8±0.2
4.6±0.1
4.2±0.3
2.2±0.1
1.9±0.0
0.8±0.1
1.0±0.3
50
7.5±0.6
7.0±0.6
4.6±0.4
4.2±0.1
2.4±0.4
2.1±0.3
0.8±0.1
1.0±0.4
60
8.0±1.1
7.4±1.1
4.6±0.8
4.1±0.2
3.0±0.5
2.6±0.4
0.8±0.2
1.1±0.5
70
8.1±2.4
7.4±2.2
4.4±1.4
4.0±0.8
3.5±1.1
3.0±0.9
0.9±0.4
1.2±0.5
80
8.9±2.0
8.0±1.9
4.5±1.2
4.1±0.9
4.1±0.5
3.6±0.5
0.9±0.3
1.3±0.4
90
10.3±2.2
9.2±2.0
4.8±1.4
4.2±1.0
5.7±0.5
4.8±0.4
1.1±0.3
1.5±0.5
20
13.1±1.8
11.6±1.5
6.5±0.6
6.1±0.5
8.3±2.6
6.8±2.0
1.7±0.3
1.0±0.3
30
14.1±1.1
12.5±0.9
6.7±0.3
6.3±0.1
9.3±1.5
7.6±1.1
1.8±0.2
1.1±0.4
40
15.0±0.8
13.2±0.7
6.8±0.3
6.3±0.0
10.5±1.3
8.6±0.9
1.9±0.1
1.1±0.4
50
16.7±1.9
14.6±1.7
7.3±0.7
6.5±0.0
12.0±0.8
9.8±0.7
2.1±0.3
1.5±0.1
60
20.9±0.5
17.7±0.1
8.0±0.2
7.1±0.3
20.4±4.7
16.0±3.2
2.7±0.1
2.0±0.5
70
25.0±2.1
20.9±1.3
8.6±0.1
7.7±0.3
29.8±10.8
23.0±7.7
3.4±0.4
2.5±0.6
80
29.3±3.7
24.3±2.6
9.1±0.2
8.2±0.4
40.0±17.4
30.6±12.3
4.1±0.8
3.0±0.7
90
34.8±6.1
28.7±4.4
9.8±0.4
8.7±0.5
54.0±25.0
40.9±17.8
5.1±1.3
3.7±1.1
52
22%
20
18.3±1.2
16.1±1.1
8.3±0.2
8.0±0.3
27.5±1.8
20.3±1.4
3.0±0.3
2.4±0.1
30
20.0±0.8
17.7±0.8
8.9±0.0
8.6±0.6
36.4±4.2
26.4±2.9
3.4±0.4
3.0±0.7
40
23.7±0.5
20.6±0.1
9.9±0.1
9.4±0.6
65.8±0.1
46.5±0.1
4.6±0.2
3.9±0.7
50
26.2±0.9
22.4±0.5
10.2±0.4
9.5±1.1
83.2±4.9
58.6±3.0
5.3±0.2
4.5±0.8
60
30.9±3.5
26.1±2.4
11.1±1.1
10.2±1.7
114.7±9.9
80.3±7.1
6.7±0.5
5.3±0.4
70
39.5±1.7
32.4±0.7
13.0±0.7
11.5±0.8
172.1±42.6
119.8±28.6
9.3±1.3
6.9±1.6
80
54.2±3.6
43.8±1.2
15.9±0.3
14.0±0.4
278.7±63.7
193.3±42.4
14.1±2.2
9.8±2.2
90
83.7±15.2
65.8±9.5
20.9±2.0
18.2±1.7
473.3±28.3
328.2±17.2
22.6±0.3
15.0±1.1
53
Table 3.3 Binary statistical regression equations of dielectric properties with temperature (T, °C)
and water content (M, g water/g sample) at three interested frequencies (valid in T = 20–90 °C, M = 1.3–22
g/100g sample)
Frequency
Regression equations
R2
(MHz)
27.12
ε' = 29.1288*T*M2+0.0805*T2*M-762.0730*M20.98
11.8745*T*M+335.1172*T2+0.4849*M-9.1519
ε" = 55947.12*M3+0.00055*T3+0.5156*M*T2+275.2705*M2*T-27521*M20.95
2
97.1019*T*M-0.1173*T +4280.8270*M+8.2767*T-187.1640
40.68
ε' = -1384.45*M3+6.4900-5*T3+0.0602*M*T2+21.8632*T*M2-55.0055*M20.98
8.8556*T*M-0.0136*T2+207.0913*M+0.8898*T-12.7167
ε" = 36972.48*M3+0.000378*T3+0.3578*M*T2+187.9769*T*M20.95
18349.9*M2-66.7055*T*M-0.08133*T2+2895.626*M+5.7204*T-128.279
915
ε' = 111.7235*M3+1.55-5*T3+0.0137*M*T2+6.7082*M2*T-194.8*M20.99
2
2.3698*T -0.00326*M*T+79.4664*M+0.2252*T-1.5412
ε" = -7.4806*M3+0.3663*T3+155.0551*M*T2-0.00532*T*M2-4.1012*M20.97
821.761*T*M+11.1093*T2+0.02359M+2.48-5*T+1486.421
54
Table 3.4 Penetration depth of peanut butter with five water contents at eight temperatures and four
frequencies
Penetration depth (m)
Water content
1.3%
4%
10%
16%
Temp.
Frequency (MHz)
(°C)
27
40
20
61.93±2.88
25.35±2.43
0.34±0.01 0.28±0.04
30
75.49±20.76
25.69±1.16
0.31±0.01 0.35±0.11
40
107.06±4.99
32.06±0.84
0.32±0.02 0.33±0.15
50
239.48±35.23
30.84±0.15
0.34±0.02 0.29±0.10
60
271.77±28.82
41.77±1.79
0.36±0.01 0.30±0.13
70
264.31±15.77
56.89±4.06
0.35±0.01 0.26±0.02
80
306.05±23.92 95.43±32.72 0.39±0.02 0.32±0.17
90
92.06±11.44
170.6±76.04 0.41±0.02 0.44±0.31
20
23.32±8.72
13.36±3.25
0.42±0.07 0.24±0.08
30
21.12±8.68
12.62±2.84
0.38±0.03 0.29±0.03
40
19.98±6.96
11.8±2.09
0.36±0.04 0.17±0.11
50
18.4±6.63
11.45±1.52
0.35±0.03 0.17±0.08
60
18.20±6.24
10.72±1.13
0.34±0.01 0.11±0.08
70
16.63±3.46
10.59±1.04
0.34±0.01 0.10±0.08
80
13.98±1.45
9.43±0.48
0.33±0.02 0.09±0.05
90
12.21±1.69
8.27±0.21
0.39±0.11 0.06±0.03
20
2.70±0.21
1.97±0.12
0.15±0.01 0.07±0.03
30
2.49±0.15
1.86±0.1
0.14±0.01 0.06±0.03
40
2.24±0.03
1.67±0.01
0.14±0.01 0.06±0.02
50
2.09±0.24
1.55±0.16
0.14±0.02 0.06±0.02
60
1.73±0.19
1.29±0.12
0.14±0.03 0.05±0.02
70
1.50±0.24
1.12±0.16
0.14±0.04 0.05±0.01
80
1.30±0.02
0.97±0.01
0.12±0.02 0.04±0.01
90
1.03±0.02
0.77±0.01
0.10±0.01 0.04±0.01
20
0.84±0.20
0.64±0.14
0.08±0.01 0.07±0.02
30
0.76±0.09
0.58±0.06
0.08±0.01 0.06±0.02
40
0.69±0.06
0.53±0.04
0.07±0.01 0.06±0.02
55
915
1800
22%
50
0.64±0.01
0.49±0.01
0.07±0.01 0.05±0.01
60
0.44±0.08
0.35±0.06
0.06±0.01 0.04±0.01
70
0.35±0.10
0.28±0.07
0.05±0.01 0.03±0.01
80
0.30±0.09
0.23±0.07
0.04±0.01 0.03±0.01
90
0.25±0.08
0.20±0.06
0.03±0.01 0.02±0.01
20
0.33±0.01
0.27±0.01
0.05±0.00 0.03±0.01
30
0.27±0.02
0.23±0.02
0.05±0.01 0.03±0.01
40
0.18±0.01
0.15±0.01
0.04±0.01 0.02±0.01
50
0.16±0.01
0.13±0.01
0.03±0.01 0.02±0.01
60
0.13±0.01
0.11±0.00
0.03±0.01 0.02±0.01
70
0.11±0.02
0.09±0.01
0.02±0.01 0.01±0.01
80
0.08±0.01
0.07±0.01
0.02±0.01 0.01±0.01
90
0.06±0.01
0.05±0.01
0.01±0.01 0.01±0.01
56
Figure 3.1 Water activity of peanut butter samples as a function of water contents at room
temperature (22°C)
57
Figure 3.2 Specific heat of peanut butter samples measured by DSC as a function of water content
(a) and temperature with heat flow chart at 1.3 g/100g water (b)
58
Figure 3.3 Dielectric constant of peanut butter with water content levels of 1.3 (a), 4 (b), 10 (c), 16
(d), and 22 (e) g/100g at four selected temperatures
59
Figure 3.4 Loss factor of peanut butter with water content levels of 1.3 (a), 4 (b), 10 (c), 16 (d), and
22 (e) g/100g at four selected temperatures
60
120
100
1.3%
4%
10%
16%
22%
Dielectric constant
80
60
40
20
0
0
20
40
60
80
100
80
100
Temperature (oC)
600
500
1.3%
4%
10%
16%
22%
Dielectric loss factor
400
300
200
100
0
0
20
40
60
Temperature (oC)
Figure 3.5 Dielectric properties of peanut butter with five water contents and eight temperatures at
27 MHz
61
25
Dielectric constant
20
1.3%
4%
10%
16%
22%
15
10
5
0
0
20
40
60
80
100
80
100
Temperature (oC)
25
Dielectric loss factor
20
1.3%
4%
10%
16%
22%
15
10
5
0
-5
0
20
40
60
Temperature (oC)
Figure 3.6 Dielectric properties of peanut butter with five water contents and eight temperatures at
915 MHz
62
CHAPTER FOUR:
INFLUENCE OF DIELECTRIC PROPERTIES ON THE HEATING RATE IN FREE-RUNNING
OSCILLATOR RADIO FREQUENCY SYSTEMS
Abstract
The heating behavior of a food product in a radio frequency (RF) heater with a free-running
oscillator largely depends on the dielectric properties of the food materials in processing. In this study,
heating rate was mathematically derived as a function of its influencing factors in a RF system. This
relationship was validated by experiments using conditioned salt solutions and peanut butter samples in a
27.12 MHz, 6 kW RF system. The dielectric properties of the materials used to validate the model ranges
from 3.3 to 91.6 for dielectric constant and from 0.1 to 1577.0 for dielectric loss factor. The comparison
between theoretical and experimental results showed a good agreement for tested samples. Both dielectric
constant and loss factor influenced the heating rate under a fixed electrode gap and frequency. When the
values of dielectric constant and loss factor were close to one another, the maximum heating rate can be
reached.
Keywords: Dielectric properties; radio frequency; heating rate; mathematical modeling.
63
1. Introduction
Radio frequency (RF) is an electromagnetic wave with a frequency range of 3 kHz to 300 MHz.
The US Federal Communications Commission (FCC) allocates 13.56, 27.12 and 40.68 MHz in the RF
range for industrial, scientific and medical (ISM) application (Wang and Tang, 2001). RF heating has been
applied in the food industry as an efficient dielectric heating method for years. Because of its volumetric
heating, adjustable heating rate and high energy efficiency, RF heating is already showing its advantages
in thawing and in conditioning of biscuits post-baking (Farag et al., 2011; Palazoglu et al., 2012). Wide
applications have also been explored in disinfestation, enzyme inactivation, pasteurization and sterilization
(Rice, 1993; Wang et al., 2003b, 2010; Luechapattanaporn et al., 2005; Guo et al., 2006; Manzocco et al.,
2008; Gao et al., 2011). The 50 ohm technology and free-running oscillators are two different designs of
RF heating systems. Although 50 ohm systems use modern methods to control the frequency and power,
the free-running oscillator design is still the most commonly used in the food industry because of its low
cost, simple structure and flexibility. In a free-running oscillator RF heater, the portion of power converted
to useful heat depends mainly on the properties of the material (Rowley, 2001).
For a free-running oscillator RF system, “parallel plates” are the most commonly used electrode
configuration for bulk material heating (Jones and Rowley, 1996). The food material is placed in-between
the two parallel plate electrodes of the applicator, which act as a capacitor. When energized, the generator
provides high voltage, high frequency power to the electrodes in the applicator, and the food material with
certain dielectric properties is heated up in the high density alternating electric field. In dielectric heating,
the dielectric properties of food products are important intrinsic properties that directly influence the energy
conversion rate. The complex dielectric property ε* is the sum of the real part – dielectric constant ε’, and
the imaginary part – loss factor ε˝. Due to the nature of the free-running oscillator RF system, the dissipated
power could not be measured directly because of the varying voltage and electric field. Therefore, the only
64
way to estimate the dissipated power in food is to calculate from theoretical equations. The power
conversion in the material is described as (Choi and Konrad, 1991):
P  2f 0“ Em
2
(1)
where P is the power dissipation in food material from electromagnetic to thermal energy, (W/m3); f is the
frequency of the RF generator, (Hz); ε0 is the permittivity of vacuum (8.854 × 10
-12
F/m); ε˝ is the loss
factor of the material; E m is the electric field intensity in the food sample (V/m) (Fig. 4.1).
The dielectric properties of various food materials over the RF frequency band have been reported
over the past 40 years (To et al., 1974; Nelson, 1981; Calay et al., 1994; Sosa-Morales et al., 2010). The
dielectric properties are usually functions of temperature, frequency, density, moisture content, and other
compositions of the food. Thus, for a given material, the dielectric properties may vary during heating, and
the heating behavior may also change accordingly. Therefore, knowing the dielectric properties as a
function of temperature, moisture content and other properties before running experiments may help to
predict possible thermal run away and temperature distribution in the bulk food.
It has been a general belief that the power absorption in food is positively related to the loss factor
of a food material (Piyasena et al., 2003). However, Birla et al. (2008a) found that in a free-running
oscillator RF system, the maximum heating rate was reached when the loss factor of a load was 180 in the
studied range between 80 and 350. But the conclusion was derived through theoretical analysis without
experimental validation. Wang et al. (2008) reported a reverse relationship between ε˝ and heating rate in
mashed potato samples of different salt contents based on both experimental and simulation results. A
theoretical equation was developed to explain the phenomena, but the simple assumptions in this study
limited its application only to a narrow range of dielectric properties, i.e.: ε’: 83.3–84.7; ε˝: 78.7–173.2.
Tiwari et al. (2011a) conducted a computer simulation on RF heating of dry food with COMSOL
65
Multiphysics® software to analyze the influence of dielectric properties on power distribution. In their
results, the maximum power distribution and better heating uniformity were reached when the values of
dielectric constant and loss factor were small and comparable; but no adequate explanation was given for
this phenomenon. So far, there is no systematic research showing in details how the dielectric properties
influence heating behavior in free-running oscillator RF systems.
The general goal of this study was to better understand the influence of dielectric properties on RF
heating, and further assist experiment design to guide the development of industrial RF heating processes.
The specific objectives of this study were to: (1) theoretically analyze the influencing factors of RF heating
rate, and use a mathematical model to estimate the heating rate as a function of material properties for a
given condition of a RF heater; (2) validate the mathematical model with salty water when only dielectric
loss factor changes as a function of salt concentration; and (3) validate the model with conditioned peanut
butter samples when both dielectric constant and loss factor change as a function of moisture content and
temperature.
2. Materials and methods
2.1.
Theoretical model
The power conversion in a food material during RF heating depends on the working frequency,
loss factor and the electric field density inside the material (Birla et al., 2008b). When heat loss to the
ambient is negligible, the heating rate in a food after absorbing RF power can be described as:
P  c p
T
 2f 0 " Em
t
2
(2)
where ρ is the density of the load, (kg/m3); cp is the heat capacity of the load, (J/kg K); ∂T/∂t is the transient
heating rate of the load during RF heating (ºC/s).
66
When air is the only surrounding media between the electrodes other than the food sample, the
continuity boundary condition of the electric flux density can be applied at the interface of the load and air
for a simplified case shown in Fig. 4.1 (Metaxas, 1996; Birla et al., 2008a, b). The continuity equation can
be written as:
Dn   0 E0   0 * Em
(3)
where Dn is the normal electric flux density, (C/m2); E0 is the electric field intensity in the air gap, (V/m);
ε* is the relevant (to air) complex permittivity of the load, ε* = ε’ – jε˝, which leads to:


E0   '  j " Em
(4)
Since the bottom electrode is normally grounded, the voltage on the upper electrode is the total
electric potential between the two electrodes (V), which can be divided into voltage falls in the air gap (V0)
and the voltage falls in food material (Vm):
V  V0  Vm  E0 d0  Em d m
(5)
Substitute Eqs. (4) into (5), it becomes:
Em 
 d
'
V
(6)
  
2
"
0  d m   d0
2
Then substitute Eqs. (6) back into (2) yields:
Pd  c p
2
T
"
 2f 0 " Em  2f 0V 2
2
t
 ' d0  d m   " d0

67
 

2
(7)
or:
T
"
 2f 0V 2
t
c p   ' d0  d m


   d  
2
2
"
(8)
0
Accordingly, for linear temperature increases, the final temperature after processing can be described as:
T f  Ti  t  2f 0V 2

"
  
2
2
c p   ' d0  d m   " d0 


(9)
where Tf is the final temperature of load (ºC), Ti is the initial temperature of load (ºC), and t is the total
processing time (s).
Metaxas (1996) studied the voltage across the load of a free-running oscillator RF system and found a
7% variation between empty and full loads in a typical industrial scale system. Therefore, it is appropriate
to assume a constant voltage at the upper electrode for a certain product during RF heating. The assumption
has been used in many previous researches (Marra et al., 2007; Birla et al., 2008a; Tiwari et al., 2011a,b).
Since 2πfε0V2 can be seen as a constant when the electrode gap is fixed, the heating rate only depends on
2
2
the value of  " c p  ' d0  d m    " d0    .

 


It can be seen from Eq. (8) that as the d0 is reduced to zero, the value of ε’ does not influence heating
rate any more, which means that ε˝ is the dominating factor in heat production. In this case, the heating
mechanism changes from dielectric heating to resistive heating, in which the energy conversion is
dominated by the electric conductivity of the food (Metaxas, 1996):
P  2f 0 " Em
2
  Em
68
2
(10)
where σ = 2πfε0ε˝, σ is the effective electric conductivity of the food load, (S/m).
However, d0 is necessary in dielectric heating for in-package food heating in a continuous system.
It can be found from Eq. (8) that as d0 increases, the effect of ε’ becomes more significant. If all other
parameters are considered as constant except for ε’ and ε˝, Eq. (8) can be seen as a binary function with ε’
and ε˝ as independent variables. But for a fixed ε˝ value, the function becomes a monotonic decreasing
function, which decreases as ε’ increases. Accordingly, for a fixed ε’, the maximum result that can be
 

2
'
obtained is 2f 0V c p  d m/ d0 when ε˝ = ε’ + dm/d0. Therefore, it can be concluded that when ε˝ < ε’
+ dm/d0, an increase in ε˝ will result in thermal runaway; but when ε˝ > ε’+ dm/d0, an increase in ε˝ will
reduce the heating rate. For most moist food, the ε’ and ε˝ are much larger than dm/d0 when d0 and dm are
comparable. So the conclusion can be also written as: the maximum heating rate can be reached when ε’ ≈
ε˝. This can be an approximate method for determining the heating rate trend by simply looking at dielectric
properties of materials.
To validate the theoretical analysis over a wide range of dielectric properties, two representative
foods were chosen for RF heating experiments: salty water and peanut butter. For salt water, the dielectric
constant is relatively constant but loss factor changes largely with salt concentration; for peanut butter, both
dielectric constant and loss factor change with varying moisture content and temperature. The dielectric
properties and RF heating behaviors of the two materials would be adequate to validate the mathematical
model. Furthermore, the two model foods were fed into different containers and treated with different
electrode gaps in RF equipment to validate the high adaptability of the mathematical model.
2.2.
Experiment validation I – salt solution
2.2.1.
Sample preparation
A salt solution was prepared with table salt and double-deionized water by controlling the weight
percentage at 17 g/l (Sartorius BP 3100s, Data Weighing Systems Inc, IL, USA) and mixed evenly at room
69
temperature. After an overnight stabilization, the solution was diluted to 9 different concentrations. The
electric conductivity of each solution was measured by a bench conductivity meter (Con500, Cole Parmer,
IL, USA). A standard curve of NaCl solution with different salt concentrations and electric conductivities
was made (Fig. 4.2). Then solutions with electric conductivity of 0.03, 0.05, 0.1, 0.15, 0.2, 0.3, 0.5, 1, 2
and 3 S/m were selected and prepared to validate the model.
2.2.2.
Properties of salt solution
Dielectric properties of the salt solutions with selected electrical conductivity were measured by an
open-ended coaxial probe connected with an impedance analyzer (4291B, Agilent technologies Inc, Santa
Clara CA, USA) at 22 ºC in the frequency range of 10–1800 MHz. Prior to the measurement, the impedance
analyzer was warmed up for 30 min before calibration to minimize system errors. Then the system was
calibrated with open/short/low loss capacitance/50 Ω load in sequence, and the measuring probe was
calibrated using air/short block/25 °C deionized water, as recommended by the manufacturer. Software
85070D (Agilent Technologies, Inc., Santa Clara, CA, USA) was used to trigger the measurement and
calculate the dielectric properties. A cylinder sample holder (d = 20 mm, h = 94 mm) was designed to make
sure the sample size satisfied the assumption of a semi-infinite body, which guarantees an accurate
measurement (Feng et al., 2002). The sample holder was connected to an oil bath, which was used to bring
the sample temperature up to 80 °C. After calibration, the salt solutions were poured into the sample holder
one at a time, and the dielectric properties were measured. Between each measurement, both the probe and
sample holder were cleaned with deionized water, dried and cooled down to room temperature. The detailed
procedure and demonstrating scheme for dielectric property measurement can be found elsewhere (Wang
et al., 2003a,c). Measurements were repeated twice for each sample.
2.2.3.
RF heating test
The heating rate tests were conducted with a 6 kW, 27.12 MHz free-running oscillator RF system
(COMBI 6-S, Strayfield International, Wokingham, UK). A detailed description of the RF heating system
70
can be found elsewhere (Wang et al., 2010). A volume of 45 ml of each of the solutions with different
concentrations was put into a 50 ml centrifuge tube (inner diameter d = 2.5 cm, h = 11.0 cm). The sample
height was 9.5 cm (dm) in the tube. The tube was placed vertically at the center of the bottom electrode. The
gap between the electrode plates was fixed at 11 cm (air gap d0 = 1.5 cm) for all tests so as to provide a
reasonable comparison. A pre-calibrated fiber optical sensor (FOT-L, FISO, Quebec, Canada) was placed
at the center of the sample for tracking temperature changes versus time (Fig. 4.3). The heating time was
set for 3 min for all tests. Convective heat loss can be neglected because the sample containers were closed
during treatment and there is no forced air flow during treatment.
2.3.
Experiment validation II – peanut butter samples
2.3.1.
Sample preparation
Commercial creamy peanut butter (IGA creamy peanut butter, IGA Inc, Chicago, IL, USA) was
purchased from a local grocery store and stored at room temperature until use. The initial water content of
the peanut butter was determined by the vacuum oven method (AOAC 925.40, 2010). Specifically, 2 g
samples of peanut butter were weighed, transferred to aluminum dishes, spread evenly and heated in a
vacuum oven (ADP-31, Yamato Scientific America Inc., Santa Clara, CA, USA) at 100 °C and 10 kPa.
Samples were taken out and weighed every 1 h as drying continued, until the final weight change between
the two consecutive measurements was less than 0.05 g/100 g. The samples were then cooled down in a
desiccator for 30 min to room temperature, and then the final weights of the samples were measured by an
analytical balance (Ohaus Analytical Plus, Ohaus Corporation, Florham Park, NJ, USA). The experiment
was conducted twice with 3 samples per batch, and water contents (wet basis) were calculated.
To prepare samples of higher moisture contents, pre-determined weights of deionized water were
added into the commercial peanut butter samples and mixed by a hand mixer (Durabrand 5-speed hand
mixer, Funai Electric Co., Ltd., Osaka, Japan) in a beaker (1 L) for 1 min to bring the moisture content of
the peanut butter to 4%, 10%, 16% and 22% (w.b.), respectively. The minimal strength and time for
71
blending were chosen to avoid generating heat and introducing air into the samples. The processed peanut
butter samples were stored in air-tight glass containers at 4 °C for 24 h to allow the moisture to equilibrate,
and mixed again at room temperature before taking measurements (AOAC 935.52, 2010). The moisture
content of the conditioned samples was determined again by sampling from three random locations in the
sample container to guarantee sample uniformity. The standard deviation of the tested moisture content was
less than 0.5 %.
2.3.2.
Physical properties
The density of the original peanut butter sample was measured by the gravimetric method. An
open-end metal cylinder tube with a known mass and volume (d = 5.0 cm, h = 1.0 cm) was used as a
container for the volume measurement. Because of the high viscosity of the peanut butter, samples were
heated up to 60 °C in a water bath (above melting point), and then filled into the metal cylinder tube.
Precaution was taken to avoid air bubbles in the material during transfer. After the sample was cooled down
to room temperature, both ends of the tube were scratched flat carefully. The total weight of the tube and
sample were measured. The average density was calculated by dividing sample mass by sample volume.
Measurements were made in three replicates.
Because of the difficulty in sample loading caused by the high viscosity of samples with higher
water contents, the density of the peanut butter samples with water content 4%, 10%, 16% and 22% (w.b.)
and temperature 20–90 °C were all obtained from Costherm® software (Aberdeen, UK). The prediction
method in Costherm® is based on properties of composition of food materials and their change with
temperature. It can be used for accurate predictions of most physical properties of food including initial
freezing point, thermal conductivity, and heat capacity and enthalpy models to fat-containing foods with
good accuracy and over an extended temperature range (Allen et al., 1997). The basic composition of food
materials and the original density of peanut butter were also input as a reference for obtaining sample
porosity for the determination of density with other moisture contents.
72
Heat capacity cp (kJ/kg K) of peanut butter samples at different water contents was determined
using a differential scanning calorimeter (DSC Q2000, TA Instruments, New Castle, DE, USA). An empty
sealed aluminum pan was used as a reference and a 10–20 mg peanut butter sample was sealed in another
aluminum pan (30 µl). The procedure included cooling the sample from room temperature to 0 °C at a
ramping rate of 10 °C/min, equilibrating for 5 min, and then heating up to 80 °C. The measurements were
made in three replicates.
Dielectric properties were measured using the same equipment and procedure as for the salt
solution at 10–1800 MHz and 20–80 ºC.
2.3.3.
RF heating tests
The RF heater, temperature sensor and data logger used in this test were the same as for the salt
solution test (Section 2.2.3). Rectangular polymeric trays (14.2  10.0  3.0 cm3) were selected as the
containers for peanut butter samples. Each individual peanut butter sample at different moisture contents
was loaded into a polymeric tray with a thickness of 2 cm. The gap between the two electrodes was fixed
at 10 cm to allow comparison for all samples, and the temperature sensor was kept in the center of the
peanut butter tray to satisfy the one dimensional model. Each peanut butter sample was subjected to RF
heating for 4 min for comparison.
To determine the temperature dependence, a peanut butter sample with 22% (w.b.) moisture content
was placed into the same rectangular tray as mentioned and tested in the RF unit with an electrode gap of
13 cm and heating time of 48 min. The heating profile for each test was recorded by a data logger connected
to the fiber optical temperature sensor (FOT-L, FISO, Quebec, Canada). This experiment was replicated
twice.
73
3. Results and discussions
Salt solution – salt concentration dependence
3.1.
The mean values of salt solution dielectric properties are summarized in Table 4.1. The thermal
properties and density of all solutions were assumed to be the same as water since they were relatively
stable with concentration change (cp = 4.2 kJ/kg K, ρ = 1,000 kg/m3). The anode current showing on the RF
operating panel was constant for every solution at I = 0.42 A. The temperature‒time profiles of the salt
solutions during RF heating are shown in Fig. 4.4. It can be seen for all the tested solutions that the heating
rate of the one with electric conductivity of 0.1 S/m was the highest (displayed by the dashed line). The
heating rate of the solutions increased when the electric conductivity of the solution increased from 0.03 to
0.1 S/m. But then the heating rate decreased as the concentration increased from 0.1 to 3 S/m. Also, the
temperature curves for the 0.03 and 0.05 S/m solutions are slightly non-linear, which is perhaps due to the
temperature dependence of the dielectric properties. The heating rates of solutions with electrical
conductivity higher than 0.1 S/m are relatively constant (not temperature sensitive).
By putting various properties into Eq. (8) and (9), the heating rate and final temperature for 27.12
MHz were calculated. The top electrode voltage used in the prediction was 17,000 V according to the
estimating equation (Birla et al., 2008a). The final temperature obtained from both Eq. (9) and experiment
was shown in Fig. 4.5, in which the two curves correlated well. The discrepancy may come from the error
of voltage estimation and the linear temperature increase assumption in Eq. (9). The error may also be
caused by the limitation of the one dimensional assumption in the theoretical model since the actual sample
surface area was not as big as the electrodes. Although the tube had a relatively small diameter, the predicted
trend still agreed well with experiment. This is because the discrepancy from the one-dimensional
assumption only caused the fringe field at the corners but would not influence the center temperature much.
3.2.
Peanut butter
3.2.1.
Moisture dependence
74
All the measured properties of peanut butter with various moisture contents are summarized in
Table 4.2. The loss factor increased with increasing moisture content. This is possibly due to the
fact that the salt dissolved more in the water as moisture content increased and formed more freely
conductive ions. The electric current indicated on the RF machine operating panel varied from 0.52 to 0.60
A. Referring to the dielectric properties of peanut butter samples in Table 4.2, the loss factor ε˝ was much
smaller than the dielectric constant ε’ at moisture content 1.3 and 4 %, and ε˝ was larger than ε’ when
moisture content was 22 %. Thus, based on our earlier discussion, an approximate conclusion can be made
that the maximum heating rate may happen in either 10 % or 16 % samples because the value of ε’ and ε˝
for those samples are more comparable.
The heating profile of peanut butter samples at various moisture contents is shown in Fig. 4.6.
Within the 4 min heating period, all five heating curves were relatively linear, and the 10 % sample had the
highest heating rate (7.3 ºC/min). Assuming the voltage at the upper electrode was 8500 V (Birla et al.,
2008a; Tiwari et al., 2011b), the final temperatures obtained by both experimental and predicted methods
are presented in Fig. 4.7. The estimated and experimental results agreed well, and the variation between the
calculated and experimental values was less than 5 ºC.
3.2.2.
Temperature dependence
From the dielectric properties for the 22 % (w.b.) moisture content peanut butter sample in Table
4.2, it can be observed that ε˝ > ε’ at room temperature, and ε˝ increased faster than ε’ as the temperature
increased. This trend may lead to a decreasing heating rate as discussed previously in the calculation in
Section 2.1. The temperature‒time curve for the peanut butter sample with 22 % (w.b.) moisture content
over a 48 min heating period in RF system is shown in Fig. 4.8. As the temperature increased with time,
the heating rate decreased, which supported the theoretical prediction.
75
To further analyze the trend, the heating rate versus temperature is plotted in Fig. 4.9 (a). The


coefficient " c p [( ' d0  d m )2  ( " d0 )2 ] is calculated and plotted versus temperature in Fig. 4.9 (b).
Comparing (a) and (b), the trends correlate well. Similar trends can also be found in Wang et al. (2003a)
for the heating rate of codling moth slurry and gellan gel, which has a loss factor larger than the dielectric
constant, and increases much faster than dielectric constant.
3.3.
Determination of heating rate from dielectric properties plot
According to the calculation discussed above (Section 2.1), a method to estimate the heating rate
of samples in this study is to plot the dielectric constant versus loss factor (Fig. 4.10). A y = x is also plotted
as a reference for the comparison of dielectric constant and loss factor. The closer the data points
approached y = x, the higher heating rate that can be achieved based on the theoretical calculations.
For peanut butter samples except the one with 22% (w.b.) moisture content, it is difficult to tell
which one may have a higher heating rate from the graph since they are all close to the y = x curve. In this
situation, a specific analysis needs to be conducted as mentioned in the results section. The temperature
dependent dielectric properties of the 22 % (w.b.) sample showed that the data point was leaving the y = x
as temperature increased. This trend agreed with the experiment results in Fig. 4.9. For salt solution samples,
the data points showed the highest heating rate occurred between 0.1 and 0.15 S/m, which approximately
agreed with Fig. 4.4. The specific heating rate comparison can be found through the mathematical model.
4. Conclusions
A mathematical equation was deduced to better understand the heating behavior of food products
in RF heating. Dielectric properties were found as the major factor affecting the heating rate in RF systems
with a fixed electrode gap. The properties of salt solutions and peanut butter samples were obtained as the
input parameters for the mathematical model to predict the RF heating behavior. It was found from the
model that with a certain air gap and material thickness, the closer ε˝ approaches ε’, the higher heating rate
76
that can be obtained. The experimental results showed that dielectric properties influenced the heating
behavior in a free-running oscillator RF system in a predictable manner. The results from two food samples,
salt solution and peanut butter with adjusted moisture contents, indicated that the heating rate can be
predicted by the mathematical model with a large range of dielectric properties and various RF heating
conditions. That is, when the value of ε’ was closer to ε˝, the heating rate was the highest. This conclusion
may contribute to a better understanding as to how heating rate is influenced by food properties in a RF
system with a free-running oscillator.
77
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80
Table 4.1 Dielectric properties (mean ± SD of two replicates) of NaCl solutions with 10 electric
conductivities at 22 ºC and 27.12 MHz
Electrical conductivity (S/m)
Dielectric properties (-)
ε’
ε”
0.03
77.33±0.12
18.12±0.62
0.05
78.21±0.93
30.47±1.32
0.10
78.95±0.57
36.18±3.58
0.15
80.17±0.81
64.93±7.53
0.2
79.29±0.13
119.24±9.31
0.3
80.65±1.03
155.99±10.06
0.5
80.63±0.27
277.99±19.28
1
83.08±0.84
573.45±17.73
2
87.03±0.43
1080.15±23.41
3
91.56±2.59
1577.03±36.52
81
Table 4.2 Properties of peanut butter with 5 selected moisture content levels at temperature 20–80
ºC and 27.12 MHz (dielectric properties presented in mean ±SD of two replicates)
Moisture content (w.b.)
1.3
4
10
16
22
Density (kg/m3)
1115.1
1111.9
1104.8
1097.7
1090.6
Heat capacity (kJ/kg·K)
2.03
2.17
2.45
2.67
2.91
20 ºC 3.26±0.01 3.40±0.28 6.77±0.17
13.12±1.79
18.25±1.24
30 ºC 3.32±0.03 3.51±0.32 6.92±0.08
14.12±1.06
20.01±0.78
40 ºC 3.39±0.02 3.62±0.32 7.26±0.18
15.02±0.81
23.66±0.46
50 ºC 3.43±0.01 3.74±0.35 7.52±0.64
16.74±1.89
26.20±0.93
60 ºC 3.48±0.01 3.81±0.54 8.01±1.11
20.86±0.45
30.89±3.54
70 ºC 3.52±0.01 3.87±0.69 8.12±2.36
24.95±2.11
39.52±1.70
80 ºC 3.58±0.01 3.95±0.87 8.85±2.01
29.26±3.74
54.22±3.60
20 ºC 0.09±0.03 0.10±0.02 1.72±0.16
8.30±2.62
27.51±1.82
30 ºC 0.08±0.02 0.10±0.02 1.89±0.12
9.25±1.50
36.35±4.20
40 ºC 0.07±0.01 0.12±0.02 2.15±0.05
10.51±1.27
65.77±0.08
50 ºC 0.07±0.02 0.14±0.02 2.37±0.38
11.96±0.78
83.23±4.87
60 ºC 0.06±0.02 0.14±0.01 2.97±0.54
20.40±4.65
114.68±9.88
70 ºC 0.05±0.01 0.15±0.04 3.51±1.08
29.81±10.82
172.10±42.63
80 ºC 0.04±0.01 0.18±0.06 4.14±0.52
40.03±17.35
278.67±63.73
(%)
Dielectric constant (ε’)
Loss factor (ε”)
82
Upper electrode
V
E
d
Air
V
E
d
Food
V
Bottom electrode
Figure 4.1 Scheme of RF heating system with parallel plate electrodes
83
Electric conductivity (S/m)
4
3.5
3
2.5
y = 0.1762x
R²= 0.9972
2
1.5
1
0.5
0
0
5
10
15
Concentration (g/l)
20
25
Figure 4.2 Electrical conductivity regression curve for NaCl solutions with various salt
concentrations
84
Fiber optical sensor
Food
Data logger
Computer
Figure 4.3 Experimental setup for foods with a temperature measurement system in radio frequency
heating
85
80
Temperature (deg C)
70
300
500
60
1,000
50
1,500
2,000
40
3,000
30
5,000
10,000
20
20,000
30,000
10
0
0.5
1
1.5
Time (min)
2
2.5
3
Figure 4.4 Temperature-time histories for NaCl solutions with different electrical conductivity
levels of 0.03 (◊), 0.05 (□), 0.1 (Δ), 0.15 (×), 0.2 (♦), 0.3 (○), 0.5 (●), 1 (▲), 2 (+) and 3 (■) S/m (dash for
0.03–0.1and bold for 0.15–3) subjected to RF heating at 27.12 MHz for 3 min (mean of 2 replicates)
86
80
Temperature (ºC)
70
60
50
40
30
20
10
0
0.03
0.3
Electric conductivity (S/m)
3
Figure 4.5 Final temperatures after 3 min RF treatment of salt solutions with 10 different electric
conductivities at 27.12 MHz obtained by experiments (○) and theoretical prediction (Δ).
87
60
Temperature (ºC)
50
40
30
20
10
0
0.5
1
1.5
2
Time (min)
2.5
3
3.5
4
Figure 4.6 Temperature-time histories for peanut butter with 5 moisture contents, 1.3% (×), 4% (○),
10% (□), 16% (Δ) and 22% (◊) w.b. during 4 min RF heating at 27.12 MHz
88
60
Temperature (ºC)
50
40
30
20
10
0
0
5
10
15
Moisture content (w.b.) (%)
20
25
Figure 4.7 Final temperature comparison of peanut butter samples with five water contents after 4
min RF heating at 27.12 MHz between experiments (○) and prediction (Δ)
89
Temperature (ºC)
80
70
60
50
40
30
20
10
0
0
10
20
30
Time (min)
40
50
Figure 4.8 Time-temperature curve for peanut butter with 22% (w.b.) moisture content with 48 min
27.12 MHz RF heating (mean of 2 replicates)
90
Heating coefficient
(mºC/kJ)
Heating rate dT/dt
(ºC/min)
3
2.5
2
1.5
1
0.5
0
20
30
40
50
Temperature (ºC)
0.0024
0.0020
0.0016
0.0012
0.0008
0.0004
0.0000
60
20
30
40
50
60
Temperature (ºC)
(a)
(b)
Figure 4.9 Tendency comparison between heating rate for a 48 min RF heating at 27.12 MHz (a)
and heating rate coefficient
𝜀 " / 𝜌𝑐𝑝 𝜀 ′ 𝑑0 + 𝑑𝑚
2
+ 𝜀 ′′ 𝑑0
2
peanut butter with 22% (w.b.) moisture content
91
(b) calculated from the dielectric properties of
200
15
y=x
10
Dielectric constant (-)
160
5
0
0
120
5
10
15
0.03 S/m 0.05 S/m 0.1 S/m
0.15 S/m
0.2 S/m
80
Effect of temperature increase
40
0
0
40
80
120
Dielectric loss factor (-)
160
200
Figure 4.10 Dielectric properties of peanut butter samples (pb 1.3% (◊), 4% (□), 10% (Δ), 16% (×)
at room temperature, 22% (●) at 20–70 °C) and salt water (electric conductivity 0.03–0.2 S/m (○) at room
temperature) with a function curve of y = x at 27.12 MHz for estimating the maximum heating rate
92
CHAPTER FIVE:
A NEW STRATEGY TO IMPROVE HEATING UNIFORMITY OF LOW MOISTURE FOODS
IN RADIO FREQUENCY TREATMENT FOR PATHOGEN CONTROL
Abstract
Multistate Salmonella outbreaks in low moisture foods have created food safety concerns in recent
years. Radio frequency (RF) heating could be applied to eliminate pathogens and reduce the damage to
food quality. However, non-uniform heating in RF treatment is still a major problem for developing a food
pasteurization process. In this study, commercial peanut butter in a cylindrical jar was used as a model of
low moisture food for studying the RF heating uniformity. Polyetherimide (PEI) was placed around peanut
butter samples to provide better heating uniformity. A computer simulation model was established with
COMSOL Multiphysics®, and experiments with a RF machine (27.12 MHz, 6 kW) were performed to
validate the effectiveness of the PEI assisting method. Top surface and vertical cross-sectional temperature
distributions of peanut butter in a cylindrical container were obtained with an infrared camera, and
temperatures at 18 locations inside the container were measured with T type thermocouples. The results
showed that PEI assistance reduced the difference between the maximum and minimum temperature of the
top surface from 13 to 7 ºC and the cross-sectional surface temperatures from 28 to 18 ºC. The same strategy
was used on wheat flour and heating uniformity was improved. The computer model was then used with a
group of 9 jars of peanut butter for RF processing, and PEI assistance was also found to be effective in
improving heating uniformity. Thus, PEI assisted RF heating has potential as a pasteurization intervention
for low moisture foods after optimization of this process by the food industry.
Keywords: Radio frequency heating; low moisture foods; heating uniformity; dielectric properties;
computer simulation.
93
1. Introduction
Low moisture food is a large category of foodstuffs, including tree nuts, dried spices, wheat flour,
legumes, grains, and butter among others. Peanut butter is a popular food due to its appealing taste, smooth
mouth feel, high protein content and a moisture content below 2% (aw < 0.3 at room temperature). It is
normally considered a shelf stable food since its low moisture environment usually prevents bacterial
growth and multiplication (Beuchat, 1981). Salmonella, however, was found to survive in a low moisture
environment for several months, and even 1 cfu/ml can result in human illness or even death (Gelosa, 1984;
Kapperud et al., 1990; Burnett et al., 2000). Several cases of peanut butter contamination with Salmonella
have been reported by the Centers for Disease Control and Prevention in recent years (CDC, 2012). The
main source of Salmonella implicated in the reported outbreaks was found to be the cross contamination
occurring during the multiple steps involved in processing peanut butter. To ensure sufficient elimination
of Salmonella in peanut butter products, a pasteurization step could be added after packaging. However,
peanut butter has a relatively low thermal diffusivity, which makes traditional heating technologies
insufficient for inactivating Salmonella without causing severe food quality degradation (Shachar and
Yaron, 2006; Ma et al., 2009). Therefore, novel heating technologies need to be developed in order to
explore their effectiveness in pathogen control for peanut butter.
Radio frequency (RF) heating involves utilizing electromagnetic energy at a frequency range of 3
kHz–300 MHz. This electromagnetic energy can be converted into heat in foods. The volumetric heating
usually provides a much faster heating rate than traditional hot air or hot water heating, which saves
processing time and potentially improves product quality. A parallel plate RF heater with a free-running
oscillator is a popular design, which has been widely used in the food industry, e.g. drying (Jumah, 2005),
thawing (Farag et al., 2011), and post-baking (Palazoglu et al., 2012). The thermal effect of RF was also
found to be effective in food pasteurization (Geveke and Brunkhorst, 2004; Gao et al., 2011) and
sterilization (Luechapattanaporn et al., 2005; Kim et al., 2012; Wang et al., 2012).
94
Although the relatively longer wavelength of RF (compare to microwave) usually results in more
predictable temperature distributions in foods, edge over-heating is still a problem for foods heated inside
of containers (Tiwari et al., 2011a,b). This is caused by the different dielectric properties of food and the
surrounding medium (usually air), which results in an unevenly distributed electric field (Birla et al., 2004).
Severe non-uniform heating may result in a loss of quality at high temperatures, e.g., oil rancidity in nuts
(Wang et al., 2005; Wang et al., 2007) or thermal damage in fruits (Birla et al., 2004). Several methods
have been reported to improve uniformity in RF heating of fruits and nuts. These methods include: rotation
and water immersion for apples (Birla et al., 2004), intermittent stirring for walnuts (Wang et al., 2005),
hot water preheating for apples (Wang et al., 2006) and persimmons (Tiwari et al., 2008), and hot air
assistance for almonds and white bread (Gao et al., 2011; Liu et al., 2011). Tiwari et al. (2011b) used
computer simulation to comprehensively study the effect of shape, size, position, dielectric properties of
low moisture foods, and the shape of a bent upper electrode in RF cavities on heating uniformity. Their
results showed that when the dielectric constant and loss factor of the load are relatively close, the shape of
the load is spherical and the food sample is placed in the middle of the electrodes, the sample may achieve
good heating uniformity. The upper electrode bent to a certain angle also helped improve heating uniformity.
However, these methods all have some limitations when applied to peanut butter processing. Firstly, the
water immersion method is only effective for high moisture foods. Secondly, intermittent stirring and hot
air assisting methods work well for porous materials or particles, such as grains or nuts, but would not be
practical and effective for pre-packaged paste foods, such as peanut butter. Moreover, not many food
containers can be made in a spherical shape. Also, bending the electrode to suit the geometry of a specific
food cannot be performed in all cases.
To reduce the edge over-heating and obtain a relatively uniform temperature distribution in foods,
a uniform electric field needs to be generated throughout the treated food sample. Theoretically, the
dielectric constant determines the electric field distribution when the loss factor is far smaller than the
dielectric constant (Metaxas, 1996; Jiao et al., 2014). The uniformity of the electric field in the food could
95
be improved by minimizing the difference between the dielectric constant of the food and the surrounding
material.
The objectives of this study were to (1) conduct computer simulation studies on the effectiveness
of using a plastic material – polyetherimide (PEI) – to assist improvement of RF heating uniformity in
peanut butter in cylindrical plastic jars; (2) conduct experiments in a pilot scale RF unit to validate
simulation results; (3) use the validated model to further analyze the heating uniformity of different spatial
arrangements of multiple peanut butter jars with and without PEI sheets for potential high-throughput
industrial processes; and (4) conduct further experiments with wheat flour to assess possibilities of
extending the method to other food products.
2. Materials and methods
2.1. Sample preparation
Commercial creamy peanut butter was purchased from a local grocery store (IGA Inc., Pullman,
WA). The compositions of peanut butter as reported by the manufacturer were: 50 g/ 100 g fat, 25 g/ 100 g
protein, 1.19 g/ 100 g salt, and 21.9 g/ 100 g carbohydrates (including 6.3 g/ 100 g fiber and 9.4/ 100 g
sugar). Moisture content of the peanut butter sample was 1.3 g/ 100 g sample. Peanut butter was filled into
a plastic cylindrical container (made of polypropylene, inner-diameter d = 10 cm, height h = 5 cm, wall
thickness l = 1 mm) and covered with a lid for all treatments.
Wheat flour (Gold Medal, General Mills, Minneapolis, MN, USA) with a moisture content of 11.0%
(w.b.) was purchased from a local grocery store (IGA Inc., Pullman, WA). The same plastic cylindrical
container and lid used for the peanut butter samples was used for the wheat flour samples in RF heating
experiments.
96
2.2. Physical properties of food material
Dielectric properties of peanut butter were determined with an open ended coaxial probe connected
to a network analyzer (Agilent E5071C, Agilent Technologies, Inc., Santa Clara, USA). Before
measurement, the network analyzer was warmed up for 30 min and calibrated with open/short/low lossy
capacitance/50 Ω load in sequence. The probe was then calibrated with air/short block/25 ºC deionized
water following standard procedures. Agilent software 85070D (Agilent Technologies, Inc., Santa Clara,
CA, USA) was used to trigger measurement and record data. The peanut butter sample was placed into a
cylinder sample holder (d = 20 mm, h = 94 mm), with oil circulating through the jacket of the sample holder.
The sample temperature was then raised up to the target temperature by the heated oil. The detailed design
of the measurement system and procedure can be found elsewhere (Wang et al., 2003). Triplicate
measurements were performed at 20–80 ºC with10 ºC intervals at frequencies of 1–1800 MHz. The density
and thermal properties of peanut butter were from Jiao et al. (2014).
2.3. Surrounding material selection
Plastic materials were chosen based on their similarity in dielectric properties to peanut butter.
Dielectric properties of common plastic materials at a frequency of 1 MHz, which is close to the RF heating
frequency, were taken from the literature (Table 5.1). Comparing all the listed materials, Polyetherimide
(PEI) has the closest dielectric constant to that of peanut butter (Table 5.2) and a lower dielectric loss factor.
PEI is an amorphous plastic material with high heat resistance, high mechanical strength, high electric
strength and known dielectric properties, which meets all the requirements of this study (Karasz, 1972).
Therefore, PEI was chosen as the surrounding material for heating uniformity improvement of peanut butter
in RF heating.
2.4. Temperature profiles of peanut butter in hot water and RF heating
A 6 kW 27.12 MHz free-running oscillator RF machine with parallel-plate electrodes (COMBI 6S, Strayfield International, Wokingham, U.K.) was used for RF treatments. The scheme and dimensions of
97
the RF machine can be found in Fig. 5.1. Peanut butter (460 g) was fed into a plastic container (d = 10 cm,
h = 5 cm). Two PEI sheets (l = 45 cm, w = 25 cm, h = 2.5 cm) were stacked together as one piece, and a
hole with a slightly larger diameter (d = 10.4 cm) than that of the peanut butter container was cut in the
center of the PEI sheets. The sample container was inserted into the PEI sheets which were in turn placed
between the two electrodes of the RF system. Only the side surface of the food sample was covered by PEI
sheets, with the top and bottom left uncovered and exposed to air (Fig. 5.1a). The peanut butter sample
underwent RF heating with an electrode gap of 9 cm. The gap was selected based on preliminary
experiments to obtain an appropriate heating rate. RF treatments were conducted individually for peanut
butter with and without PEI assistance.
For hot water treatments, another peanut butter sample in an equally sized container was prepared
and placed in a preheated water bath (Humboldt deluxe water baths H-1390, Humboldt Mfg. Co., Schiller
Park, IL, USA). The water temperature of the water bath was set as 72 ºC.
In all treatments, a fiber optical sensor (UMI, FISO Technologies, Inc., Saint-Foy, Quebec, Canada)
with an accuracy of ± 1 ºC was calibrated and placed in the center of the sample to monitor temperature
change versus time. The time-temperature history was recorded by the connected data logger (FOT-L, FISO,
Quebec, Canada). The initial sample temperature for both RF and hot water treatments was 23 ±1 ºC.
2.5. Computer simulation
2.5.1.
Physical model
The RF system with a free-running oscillator included a generator and an applicator. The generator
provided electromagnetic energy to the applicator. The applicator had two parallel metal plate electrodes
and the space between the two electrodes formed a cavity filled with an electromagnetic field when the
system was in operation. The food material in the cavity was heated through conversion from
electromagnetic energy to thermal energy.
98
The amount of power conversion from electromagnetic energy to thermal energy is related to the
dielectric properties of the food, the working frequency, and the electric field intensity in the food (Metaxas,
1996):
P  2f 0" E
2
(1)
where P is the power conversion in foods per unit volume (W m-3), f is the working frequency of the RF
equipment (Hz), ε0 is the permittivity of electromagnetic waves in free space (8.854 ×10 -12 F m-1), ε″ is the
loss factor of food material, and E is the electric field intensity in the food material (V m-1).
2.5.2.
Governing equations
The electric field intensity in the electromagnetic field can be obtained by solving the Maxwell’s
equations. The RF field is a time-harmonic field so the Maxwell’s equation can be simplified to the Laplace
equation with a quasi-static assumption (Choi and Konrad, 1991; Birla et al., 2008):
     j 20' V   0
(2)
where σ is the electrical conductivity of the food material (S m-1), j   1 , ε′ is the dielectric constant of
food material, and V is the electric potential across the electrode gap (V).
The heat transfer inside the food material is described by Fourier’s equation:
T
P
  2T 
t
c p
(3)
where T t is the instant heating rate in food material, (ºC s-1); α is the thermal diffusivity (m2 s-1); ρ is
the density (kg m-3); and cp is the specific heat (J kg-1K-1).
99
By simultaneously solving Eqs. (1)‒(3), the temperature profile in a peanut butter jar within a
certain time period can be obtained.
2.5.3.
Initial and boundary conditions
The initial temperature was set at room temperature (23 ºC). In the case of peanut butter surrounded
by PEI, the outer surface of the peanut butter container was in direct contact with the vertical, cylindrical
surface of the PEI sheets (Fig. 5.1b). The other surfaces of the PEI sheets were exposed to still air and the
convective heat transfer coefficient (h) was assumed to be 15 W m-2 ºC-1 for natural convection (Romano
and Marra, 2008). In the case of peanut butter without PEI surrounding it, a convective heat transfer
boundary condition (h = 15 W m-2 ºC-1) was used at the outer surface of the peanut butter container. The
metal enclosure boundary of the RF machine was considered as thermal insulation, T  0 . The top
electrode was set as the electromagnetic source since it introduced high frequency electromagnetic energy
from the generator to the heating cavity. It was difficult to measure the actual voltage during processing
without disturbing the electric field (Marshall and Metaxas, 1998), thus, the voltage of the top electrode
was estimated by the following equation (Birla et al., 2008):
V   d air

' 2  " 2
 c p dT 

 d mat 
 f 0 ' dt 


(4)
where dair is the air gap between the electrodes and food sample (m), dmat is the thickness of the food material
(m), and ε′ and ε″ are the dielectric constant and loss factor of food materials, respectively.
Because of the different heating rates, the estimated voltages are 6,350 and 11,000 V for simulation
without and with PEI sheets, respectively. All the metal shielding parts except the top electrode were
grounded, and considered as electrical insulation,   E  0 .
2.5.4.
Simulation procedure
100
A commercial finite element method (FEM) based software COMSOL Multiphysics (V4.2a
COMSOL Multiphysics, Burlington, MA, USA) was used to simulate the RF heating process. The joule
heating module used in this study was a conjugation module of electromagnetic heating and heat transfer,
which can solve the electromagnetic equations and heat transfer equations simultaneously. In the food
sample and on the top electrode, extremely fine tetrahedral mesh was incorporated in to guarantee the
accuracy of temperature distribution predictions. Other parts of the system were meshed with normal size
tetrahedral mesh. The mesh size was chosen based on the convergence study of when the difference of the
maximum temperature between successive calculations was less than 0.1%. The final meshes contained
115,231 domain elements, 20,104 boundary elements, 997 edge elements and 64 vertex elements. The time
step used in this study was 0.1 s. The computer simulation was conducted on a Dell workstation with two
Dual Core 2.80 GHz Xeon processors, 12 GB RAM on a Windows 7 64 bit operating system. Each
simulation case took around 20 minutes to complete.
2.6. Model validation - RF experiments
The 6 kW free-running oscillator RF heating machine with a working frequency of 27.12 MHz was
used in experiments to validate the computer simulation model. The cold spot location in the container was
determined by both experimental and computer simulation methods. In a cylinder container, the temperature
distribution at every vertical cross-sectional surface across the central axis of the container should ideally
be the same. Therefore, the temperature distribution of the top surface and one such vertical cross-sectional
surface could represent the whole geometry for determining the cold spot location (Fig. 5.2). In the
experiment, thermal images of the top and a vertical cross-sectional surface of the food were taken after RF
treatments, and the lowest temperature location of the two surfaces was identified as the cold spot of the
food sample. In the computer simulation, the cold spot location was found from the volumetric temperature
map with the software. In RF heating experiments, when the cold spot temperature of the food sample
reached 70 ºC, the sample container was removed from the heating cavity. Then the surface temperatures
of the top surface or cross-sectional surface were immediately measured with an infrared camera to an
101
accuracy of ±2 ºC (ThermaCAMTM Researcher 2001, FLIR Systems, Portland, OR, USA). The camera was
calibrated by comparing the output temperature with the actual temperature measured with a calibrated
thermocouple. The emissivity of the food, plastic film and container was 0.99.
To obtain the temperature profile at a vertical cross-sectional surface, a cylindrical container was
cut into half along the axis (Fig. 5.3), and each half was sealed with a 0.1 mm thick plastic film using super
glue. The assumption behind using a thin plastic film was that the film and the peanut butter adjacent to it
had equivalent temperatures. The two halves were reassembled forming a cylinder, and then filled with a
peanut butter sample for RF treatment. A thermal image of the cross-sectional surface after treatment was
also taken with the infrared camera. The target temperature was chosen based on normal food pasteurization
temperatures.
A board fixed with 18 thermocouple sensors (Type-T, Omega Engineering Ltd, CT, accuracy ±0.5
ºC) was used to obtain the temperature distribution in the peanut butter samples after RF heating (Fig. 5.4a).
The board was made from a plastic block (d = 10 cm, h = 2 cm) glued to the top of the container lid. Nine
holes (d = 2 mm) were drilled through the lid and glued block. Nine threaded rods (d = 2 mm, h = 9 cm)
were inserted through the block and extended beyond the base of the board by 5 cm to allow for the
attachment of thermocouples. All the rods were fastened with nuts on both sides. Another 9 holes with
diameters double those of the thermocouple wires’ (d = 1 mm) were drilled next to the rods to allow sensor
wires to pass through. Two thermocouple wires were fixed through each hole, and fastened with thread at
two different vertical positions (h1 = 3 cm, h2 = 1 cm measured from the container bottom). All together,
the board had 18 thermocouple wires labeled as shown in Fig. 5.4b. It was then used to determine the sample
temperature distribution of the two layers.
Immediately after infrared pictures of the surfaces were taken, sensors were inserted into the peanut
butter, and temperatures at all 18 spots were recorded. The entire temperature measurement procedure was
completed within 15 s. These experiments were replicated three times.
102
2.7. Heating uniformity of wheat flour
The same RF treatment used for the peanut butter samples was applied to the wheat flour samples
in a cylinder container with and without surrounding PEI. The target heating temperature was selected as
60 ºC due to product quality limitations. A thermal image was taken of the top surface of the wheat flour.
The effectiveness of the PEI surrounding method on improving the heating uniformity was evaluated by
comparing the temperature distributions at the top surface of the wheat flour.
2.8. Heating uniformity of multiple containers under RF treatment
After the computer simulation model was validated, the model was used to study heating uniformity
of multiple containers in a single RF cavity to simulate possible industrial RF heating processes. The model
considered nine containers arranged in two different spatial patterns heated in RF systems with and without
PEI assistance (Fig. 5.5). The heating uniformity of treated samples was evaluated by the uniformity index
(UI) (Alfaifi et al., 2014) below. In RF treatments, a smaller index corresponds to better heating uniformity.
UI 

Vvol
T  Tav dVvol
Tav  Tinitial Vvol
(5)
where T is the local temperature of the food (ºC), Tinitial is the initial temperature of the food (ºC), Tav is the
average temperature of the food volume (ºC), and Vvol is the volume of food (m3).
In this study, we compared the UI of all 9 samples and also the centrally located sample in Fig. 5.5.
The centrally located sample was selected to represent the samples in industrial large scale processing
without the influence of edge over-heating.
2.9. Statistical analysis
The mean values of three replicates of the temperature measured by the thermocouples were
analyzed by Microsoft Excel®. All the statistically significant comparisons were made at a significance
level of P = 0.05.
103
3. Results and discussion
3.1. Dielectric and thermal properties of peanut butter
The properties of peanut butter, PEI and air at room temperature were used in the computer
simulation (Table 5.2). Dielectric properties of peanut butter had a non-linear relationship with temperature,
so only average values at all temperatures were used in the simulation. The low dielectric constant and loss
factor of peanut butter were due to the high fat content (around 50%) and low moisture content (1.3% w.b.)
of the composition. The dielectric properties of peanut butter are close to those of vegetable oil (Kent, 1987).
3.2. Heating rate comparison among peanut butter in hot water in RF treatments
Fig. 5.6 (a) shows the temperature histories of the peanut butter samples during RF heating with an
electrode gap of 9 cm and hot water heating from a starting temperature of 23 ºC. In both cases, processing
times were selected to ensure that the cold spot in the food reached 70 ºC for a fair comparison. The heating
time of the hot water treatment was around 220 min. This was reduced to 6.5 min with RF heating. With a
more linear heating rate, RF heating was about 34 times faster than hot water heating. The rapid heating
rate of RF suggests that RF technology could prevent unnecessary quality degradation of food samples by
reducing excess heating time.
Typical experimental temperature–time profiles at the center of the peanut butter sample when
subjected to RF heating with an electrode gap of 9 cm with and without PEI assistance are shown in Fig.
5.6 (b). Heating rates were relatively constant under both conditions. After adding PEI sheets, the heating
rate at the center of the peanut butter sample increased from 6.8 to 20.8 ºC min -1 while the heating time
required to reach 70 ºC was reduced from 10.0 to 2.8 min. The corresponding anode current also increased
from 0.52 to 1.20 A. This is because increased dielectric material volume provided a better impedance
match between the load circuit and the tank circuit, which resulted in increased input power. The power
conversion in the food sample was automatically adjusted by the free-running oscillator RF system based
on the impedance match. During RF treatment, the temperature of the PEI plates increased from
104
approximately 23 ºC to 28 ºC, which was only about 10% of the temperature increase in the food sample
with the same treatment.
3.3. Determination of cold spot location in a sample container
The voltage used in computer simulation was 8,800 and 12,100 V for peanut butter under RF
treatment without and with PEI plates, respectively. The voltages were obtained by sweeping a voltage
range around the estimated value in computer simulation to match the heating profiles of the experiments
(Birla et al., 2008). The difference between the estimation and actual value used (around 2000–2500 V)
was due to the limitation of using only the heating rate at the center of the sample to represent the sample
geometry.
Based on both experimentation and computer simulation results, the cold spot location was found
to be at the center of top and bottom surfaces for samples with or without PEI sheets (Figs. 5.7 and 5.9).
The selection of the RF treatment period was based on confirmation that the cold spot location reached the
target pasteurizing temperature, which was 70 ºC in this study.
3.4. Model validation
Surface and contour plots of the top surface of peanut butter with and without PEI sheets assistance
after RF treatment for 2.8 and 10.0 min are shown in Fig. 5.7. The low temperatures measured at the outer
edge of the food in the experiments were attributed to the heat loss that occurred during the time when the
samples were being transferred from the RF equipment to the camera. The computer simulation result in
Fig 5.8a illustrates how the electric field pattern between two RF electrodes was distorted in the presence
of the peanut butter jar which causes severe edge heating. The electric field distortion was reduced when
placing a PEI material around the sample jar (Fig. 5.8b). Similar results were reported by Tiwari (2011a)
and Alfaifi (2014) for wheat flour and dry fruits. Judging from the heating patterns presented in Figs 5.7,
the simulation and experimental results agreed well, which validated the simulation model. The
experimental results showed that when the lowest temperature reached 70 °C, the highest temperature had
105
reached 83 °C with no PEI sheets surrounding the sample. After adding PEI, the highest temperature was
reduced to 77 °C. The computer simulation indicated that the temperature range was from 70 to 80 °C
without PEI, and 70 to 73 °C when using PEI. The reduced temperature differential between the hot and
cold spot validated the effectiveness of using PEI to surround the sample to improve RF heating uniformity.
Fig. 5.9 shows surface and contour plots of temperature distributions obtained from experiments and
the computer simulation for the central cross-sectional surface of a peanut butter container following RF
treatment with and without PEI as the surrounding medium. The low temperatures at the edge of the
temperature profile from the experiments were, again, caused by a time delay for the temperature
measurement after RF treatment was finished. The temperature pattern is symmetric both horizontally and
in parallel since the sample is located at the center of the RF cavity. The experimental contour plot shows
that the highest temperature on the cross-sectional surface was 95 °C without PEI, but was reduced to 85 °C
with PEI. This comparison indicated that the hot spot temperature was sharply reduced using the PEI
assisted method. Both computer simulation and experimentation showed similar results, which again
validated the effectiveness of the mathematical model.
3.5. Overall heating uniformity improvement evaluation
The maximum, minimum, average temperature and standard deviation of the top surface and central
cross-section of peanut butter are summarized in Table 5.3. For the top surface, the difference between
maximum and minimum temperatures with PEI assistance was reduced from 13 to 7 ºC. The standard
deviation was reduced from 4 to 2 °C, which also implies a better heating uniformity. The heating
uniformity improvement for the central cross-sectional area was also obvious. The difference between
maximum and minimum temperature was reduced from 28 to 18 °C, and the standard deviation was reduced
from 6 to 4 °C.
The internal temperature distribution in the peanut butter jar obtained from the thermocouples is
shown in Fig. 5.10. The average temperature and standard deviation of all 18 locations without and with
106
PEI assistance was 86.7 ± 1.0 and 78.6 ± 0.7 ºC, respectively. Thus, the smaller scatter range showed that
temperature uniformity improved volumetrically with PEI assistance.
3.6. Heating uniformity of wheat flour
The top surface temperature distribution of wheat flour after 8.0 min of RF treatment (electrode
gap of 9 cm) without PEI assistance and 4.3 min RF treatment with PEI assistance are shown in Fig. 5.11.
The cold spot location was the same as that of peanut butter, which was at the center of the top surface. It
is clear from Figure 5.11 that the high temperature zone (white color) vanished after adding PEI sheets.
Without PEI assistance, the edge temperature reached 80 ºC when the center temperature reached 60 ºC.
When PEI sheets were added, the edge temperature decreased to 67 ºC, which indicated that heating
uniformity improved. This demonstrates that the PEI assistance method could possibly be applied to other
low moisture food products.
3.7. Heating uniformity of multiple peanut butter samples
The simulated temperature profiles of the middle layer of 9 peanut butter samples in two different
spatial arrangements are shown in Fig. 5.12. For both arrangements, heating uniformity was largely
improved by adding PEI sheets around the samples, causing the maximum temperature to be reduced from
120 ºC to 99 ºC while minimum temperature stayed the same (70 ºC). Overheating was observed at the
outside layer of samples not surrounded with PEI, but was found to be reduced when PEI sheets were added.
Overheating problems remaining after applying PEI sheets can be explained by the difference in dielectric
properties of PEI sheets and peanut butter samples.
The uniformity indexes (UI) were calculated volumetrically for all 9 samples and for the central
sample with and without PEI (Table 5.4). For all 9 samples, the UI was clearly reduced after adding PEI
sheets. Also, edge heating was effectively reduced by utilizing PEI assistance. There was little difference
between the two designs in terms of average temperature and UI.
107
If we only consider the heating uniformity of the centrally located peanut butter container, which
represents food samples in industrial processing, design 2 was better than design 1. The average temperature
was lowered from 94.1 to 88.7 °C in design 1 and 93.0 to 89.4 °C in design 2. Also, the UI decreased from
0.0576 and 0.0499 to 0.0440 and 0.0336, respectively. This was because the spaces filled with PEI between
containers were smaller, resulting in a better heating uniformity.
4. Conclusion
A computer model was developed to explore the effectiveness of a PEI assistance method to
improve the heating uniformity of peanut butter subjected to RF heating in a 6 kW, 27.12 MHz RF system.
Results from computer simulation and experimental methods showed good agreement for the temperature
distribution of both the top and cross-sectional surfaces of peanut butter samples. For peanut butter samples
heated from room temperature to 70 ºC, the maximum temperature difference in the peanut butter was
reduced from 28 to 18 ºC after adding PEI. The same treatment was applied to wheat flour with samples
that were heated from room temperature to 60 ºC, which resulted in a reduction in the maximum temperature
difference at the top surface from 20 to 7 ºC after adding PEI. The validated computer simulation model
was then used to test the PEI addition method in 9 peanut butter jars with two different spatial arrangements.
All the results indicated that the use of the PEI addition method has the potential to improve the heating
uniformity of low moisture foods heated in RF systems. The heating uniformity of multiple jars can also be
improved by putting the jars as close together as possible. Furthermore, the model can be used to optimize
the parameters in heating uniformity improvement methods, for example, adjusting the dielectric properties
of the surrounding material to explore the best material for a specific food sample.
108
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Table 5.1 Dielectric properties of common plastic materials at 1 MHz and room temperature
Plastic material
Dielectric constant ε'
Dielectric loss factor ε"
Polytetrafluoroethylene (PTFE)
2.1
0.00063a
Polyethylene terephthalate (PET)
3.0
0.048b
Polypropylene (PP)
2.1
0.0001a
Polyvinyl chloride (PVC)
3.1
0.017b
Polyvinylidene chloride (PVDC)
3.0
0.15b
Polyetherimide (PEI)
3.2
0.003c
Polycaprolactam (Nylon)
3.0
0.108b
a
Mark (1999)
b
Modern Plastics Encyclopedia (1991)
113
c
Zhu et al. (2011)
Table 5.2 Properties of peanut butter, polyetherimide and air for mathematical modeling (dielectric
properties of peanut butter averaged at temperature 20–80 ºC at 27.12 MHz)
Polyetherimide
Airc
Peanut butter
(PEI)
a
b
Density (kg/m3)
1115a
1270
1.2
Heat capacity (J/kg·K)
2030a
2000
1000
Thermal conductivity (W/m·K)
0.209a
0.122
0.026
Dielectric constant
4.03
3.15
1
Dielectric loss factor
0.4
0.0025
0
Jiao et al. (2014) b Kelly and Zweben (2000)
c
COMSOL material library (2012)
114
Table 5.3 Infrared picture analysis of top and side surfaces of a peanut butter jar with and without
PEI assistance after RF treatment
Temperature (ºC)
Min
Top surface
Central cross-sectional
surface
Max Max-Min Average Stdev
without PEI
70
83
13
76
4
with PEI
70
77
7
73
2
without PEI
70
98
28
87
6
with PEI
70
88
18
79
4
115
Table 5.4 Uniformity index (UI) comparisons between two spatial arrangements of 9 peanut butter
samples and the centrally located sample under RF treatment with and without PEI assistance
9 samples
Average temperature (ºC)
Uniformity Index (UI)
Centrally located sample
Average temperature (ºC)
Uniformity Index (UI)
Design 1
without PEI
with PEI
98.6
89.8
0.0887
0.0541
Design 1
without PEI
with PEI
94.1
88.7
0.0576
0.0499
116
Design 2
without PEI
99.6
0.0948
Design 2
without PEI
93.0
0.0440
with PEI
90.6
0.0393
with PEI
89.4
0.0336
(a)
(b)
Figure 5.1 3-D Scheme (a) and dimensions (b) of the 6 kW 27.12 MHz RF system and a food load
(peanut butter) with PEI sheets (dimensions are in mm)
117
Figure 5.2 Cold spot location determination method: comparison of top surface and cross sectional
surface temperature distribution.
118
Plastic film
Figure 5.3 Cutting a cylindrical container in half for temperature distribution measurement at the crosssectional surface
119
(a)
(b)
Figure 5.4 Eighteen thermocouples (with labeled locations) connected to data logger for measuring
temperature distribution inside the food container after RF treatment
120
(a)
(b)
Figure 5.5 Two spatial arrangements of 9 peanut butter jars for RF treatment (top view): Arrangement
1 (a) and Arrangement 2 (b)
121
100
80
80
Temperature (ºC)
Tempearture (ºC)
100
60
40
Hotwater
RF
20
0
70 °C
60
40
RF without PEI
RF with PEI
20
0
0
100
200
300
0
Time (min)
5
Time (min)
(a)
10
(b)
Figure 5.6 A typical measured temperature-time curve of peanut butter in a cylindrical container (a)
subjected to hot water heating and RF heating and (b) subjected to RF heating with and without PEI
assistance with an electrode gap 9 cm (temperature at the center of peanut butter)
122
Without PEI
With PEI
Experiment
Top
surface
Experiment
70 80
75
80
80 75
80
70
75
75
70
75
70
75
75
70
75 75
70
75
8080
Top
contour
80
75
75
70
70
75
75
80 75
70
80
75
75
70
70
75
75
Simulation
Top
surface
Simulation
Top
Contour
Figure 5.7 Comparison of simulated and experimental results for top surface temperature
distributions of peanut butter without and with PEI assistance after 10.0 and 2.8 min RF heating with an
electrode gap of 9 cm
123
Top electrode
Air
Peanut butter
Bottom electrode
(a)
Top electrode
Air
PEI
Peanut butter
PEI
Bottom electrode
(b)
Figure 5.8 Simulated electric field (arrow) and electric potential (contour) plot for peanut butter (a) without
PEI and (b) with PEI assistance after 10.0 and 2.8 min RF treatment (electrode gap 9 cm)
124
Without PEI
With PEI
Experiment
Side
Surface
Experiment
Side
Contour
Simulation
Side
Surface
Simulation
Side
Contour
Figure 5.9 Comparison of simulated and experimental results for cross-sectional surface temperature
distributions of peanut butter without and with PEI assistance after 10.0 and 2.8 min RF heating with an
electrode gap of 9 cm
125
110
100
Temperature (ºC)
90
80
70
60
50
40
30
with PEI
20
without PEI
10
0
1
2
3
4
5
6 7 8 9 10 11 12 13 14 15 16 17 18
Thermocouple location number
Figure 5.10 Experimentally measured temperature at18 locations in peanut butter container after 10.0
min RF treatment without PEI and 2.8 min with PEI
126
Without PEI
With PEI
Figure 5.11 Thermal images of surface temperature distribution of wheat flour after 8.0 and 4.3
min RF treatment without and with PEI sheets (electrode gap = 9 cm)
127
Design 1
Design 2
Without PEI
With PEI
Figure 5.12 Simulated temperature distribution (middle layer) of two spatial arrangements of 9 peanut
butter samples with and without PEI assistance under 6 min RF treatment with an electrode gap of 9 cm
128
CHAPTER SIX:
IMPROVEMENT OF RF HEATING UNIFORMITY ON LOW MOISTURE FOODS WITH
POLYETHERIMIDE BLOCKS
Abstract
Radio frequency (RF) heating is rapid and volumetric, and is thus suited for in-packaged food
pasteurization applications. However, the non-uniform heating problem needs to be resolved. In this study,
a method of adding Polyetherimide (PEI) cylindrical blocks on top of and at the bottom of a bottle of peanut
butter samples (d = 10 cm, h = 5 cm) was evaluated to improve RF heating uniformity. A computer
simulation model built with COMSOL Multiphysics® was used for heating pattern prediction, and a new
heating uniformity index was proposed to suitably evaluate pasteurization process heating uniformity.
Results showed a pair of PEI blocks with a diameter of 8 cm among all five diameters (2, 4, 6, 8, 10 cm)
added to the cold spots of a given peanut butter sample could make the sample reach the best heating
uniformity. Using the computer model, the optimized height of PEI blocks was found to be 1.4 cm after
sweeping from 0.1 to 2.3 cm with a step of 0.1 cm. Simulation results also showed that the combination of
PEI surrounding and the addition of 8 cm diameter PEI blocks could further control the temperature
distribution range in peanut butter within 7.1 ºC when the peanut butter was heated from 23 to 70 ºC. The
newly developed heating uniformity index provided a more reasonable evaluation on heating uniformity of
pasteurization process than the traditional uniformity index.
Keywords: Radio frequency; heating uniformity; computer modeling; cold spot.
129
1. Introduction
Salmonella, a foodborne pathogen, is one of the most common causes of food poisoning in the U.S.
and Europe. According to the Centers for Disease Control (CDC), Salmonella causes 1.2 million illness
cases in the U.S. every year (CDC, 2012). The source of Salmonella is usually animal products, e.g. raw
poultry meat, egg, milk and excreta. Cross-contaminations due to unclean processing conditions or
inappropriate storage may bring the pathogen from animal products to shelf stale foods and cause serious
poisoning to people. Most of the low moisture foods, e.g. beef jerky, milk powder, chocolate, peanut butter,
and pet food, are shelf stable. However, many of those have been reported as being contaminated by
Salmonella in the last decade (Vought, 1998; Matsui et al., 2004). To eliminate the pathogen, a postpackaging pasteurization process for shelf stable foods would be important.
Thermal inactivation is the most common pasteurization method for foods. By elevating the
temperature of foods, the optimum living environment of the pathogen is disrupted, resulting in the
inactivation of pathogens. Traditional thermal inactivation utilize hot air and hot water as a heat medium.
However, low moisture food products are difficult to heat due to the low thermal conduction rate. This will
result in a longer heating period, and consequently, a lower food quality (Wang et al., 2001; 2007b; Birla
et al., 2005; Gao et al., 2010). Furthermore, the slow heating rate may increase the heat resistance of bacteria
since the generation of heat shock protein made the bacteria adapt to their environment quickly (Xavier,
1997; Chung et al., 2007).
Radio frequency (RF) technology uses electromagnetic waves with a frequency range of 3 kHz to
300 MHz to heat target foods. It has been applied to drying, thawing and pest control in the food industry
(Jumah, 2005; Lagunas-Solar et al., 2007; Gao et al., 2010; Wang et al., 2010; 2014; Alberti et al., 2011;
Farag et al., 2011; Kocadagli et al., 2012; Alfaifi et al., 2014). Studies also showed that RF has the potential
for packaged food pasteurization/sterilization (Houben, 1991; Luechapattanaporn et al., 2004; 2005). RF
over-heating at the edges and corners of food samples remains an important challenge. Non-uniform RF
130
heating is mainly caused by the difference between the dielectric properties of food and its surrounding
medium (Birla et al., 2004; Jiao et al., 2014a). Studies have been reported to improve the heating uniformity
in a food matrix in RF treatments. For high water content food, like fruits, researchers used water
surrounding combined with a moving or rotating method (Ikediala et al., 2002; Birla et al., 2004; 2005;
2008; Hansen et al., 2005; Wang et al., 2006); for intermediate/low moisture foods, scientists developed
hot air assistance, intermittent stirring, movement, electrode modification, and plastic sheets surrounding
methods to enhance the heating uniformity(Wang et al., 2005; 2007a; Gao et al., 2011; Liu et al., 2011;
2012; Pan et al., 2012; Alfaifi, 2013; Jiao et al., 2014a).
In this study, we propose a method to improve the heating uniformity by strategically increasing
the amount of energy delivered to the cold spot of a sample. In a free-running oscillator RF system, the
energy delivered into the load is auto-adjusted by the matching circuit. When a food sample with a nonuniform thickness is placed between the electrodes, the thicker portion of the sample would normally absorb
a larger amount of energy and would be heated faster eventually (Mehdizadeh, 2009). Therefore, for a
product with a uniform thickness, increasing the thickness at the cold spot location will help localize the
electric field and bring up the local temperature, which will result in a better heating uniformity. Therefore,
we chose to place cylindrical dielectric blocks at the cold spots of the peanut butter sample in a cylindrical
container during RF treatment.
The objectives of this study were to: (1) establish a computer simulation model to predict the
electric field intensity and temperature distribution with PEI blocks adjacent to the cold spots of peanut
butter in a cylindrical container; (2) conduct experiments with peanut butter and various diameters of PEI
blocks in a RF system to verify the simulation results; (3) use the validated computer model to find the
optimum height of the PEI blocks; and (4) use the computer model to predict the effectiveness of a
combination method of PEI sheets surrounding and PEI blocks addition and compare the effectiveness.
131
2. Materials and methods
2.1. Sample preparation
Peanut butter (IGA brand) was purchased from a local grocery store (IGA, Pullman, WA). It is a
homogeneous paste without peanut chunks and oil separation. Peanut butter (460 g) was fed into a
cylindrical plastic container (polypropylene, d = 10 cm, h = 5 cm) for RF treatments. The physical, thermal
and dielectric properties of the peanut butter were reported by Jiao et al. (2014a).
2.2. Block material and size selection
PEI was selected as the material for the dielectric blocks because of its high heat resistance and
electric strength. The dielectric properties of PEI material limited its heat absorbance during RF treatment,
which could make the heat focus more on foods (Jiao et al., 2014a). Since the peanut butter was in a
cylindrical container, the PEI blocks were also cut into cylinders to match the shape of the cold areas in the
experiments and simulations. The height of PEI blocks for experiments was selected to be 0.6 cm, which
was determined from preliminary experiments results to better fit in the RF cavity and provide a reasonable
heating rate to the food sample. Five diameters of PEI blocks were selected for testing: 2 cm, 4 cm, 6 cm,
8 cm, and 10 cm.
A combination method for enhancing heating uniformity was to add a pair of PEI blocks with an
optimum diameter at the cold spots and a PEI sheet (60 ×20 ×5 cm3) surrounding the peanut butter sample.
The details of the PEI surrounding method could be found in Jiao et al. (2014a).
2.3. Sequence of the study
The studies were carried out in the following sequence: firstly built up a computer simulation model
to test the effectiveness of adding PEI blocks in the RF heating uniformity improvement by plotting the
electric field of peanut butter with and without PEI blocks. Then a set of experiments were conducted to
obtain the top surface temperature distribution of the peanut butter in a cylindrical container with a different
sized the PEI block to validate the established model. Once the model was validated, the temperature
132
profiles at a cross-sectional surface of peanut butter were plotted, and the heating uniformity index of each
case was calculated. After finding the optimum diameter of the PEI blocks, computer simulations were run
to compare the sample heating uniformity index of the PEI surrounding method, PEI blocks addition
method and a combination of both, and also to find the optimized height of PEI blocks. The optimum height
of PEI blocks was also obtained by computer simulation.
2.4. Computer simulation
2.4.1.
Physical model
The physical model was built for a 6 kW, 27.12 MHz RF heating system with free-running
oscillator and a pair of parallel-plate electrodes (COMBI 6-S, Strayfield International, Wokingham, U.K.).
The waves with electromagnetic energy from the RF generator was transferred to the RF cavity and
eventually converted to heat in the food load. To simplify the modeling procedure, only the RF cavity and
food load were described as the physical model. The dimensions of the RF system can be found in Jiao et
al. (2014a), and the scheme of the peanut butter sample size and position in the RF cavity was shown in
Fig. 6.1.
2.4.2.
Governing equations
The conversion from electromagnetic energy to heat energy depends on the following equation:
P  2f 0  " E
2
(1)
where P is the power conversion in foods per unit volume (W m-3), f is the working frequency of the RF
system (Hz), ε0 is the permittivity of electromagnetic waves in free space (8.854 × 10
-12
F m-1), ε″ is the
loss factor of food material, and E is the electric field intensity in the food (V m-1).
Maxwell’s equations describe the electromagnetic field. The RF field can be seen as a time
harmonic field since the variation time of radio frequency is far smaller than the time needed for heat
133
transfer. Therefore, the Maxwell’s equations can be simplified to the Laplace’s equation (Eq. 2) based on
a quasi-static assumption. By solving the Laplace’s equation, the electric field intensity can be obtained and
the temperature distribution in the food can be found based on their thermal properties. It takes less time
and effort solving the Laplace’s equation than Maxwell’s equations.
     j 2 0 'V   0
where σ is the electrical conductivity of the food material (S m-1),
(2)
j
1 ,
ε′ is the dielectric constant of
food material, and V is the electric potential across the electrode gap (V).
The absorbed RF power raises the temperature of the food sample, so heat transfer takes place
inside the food and between the food and the outside. The heat transfer process can be described in Fourier’s
equation:
T
P
  2T 
t
c p
(3)
where T t is the instant heating rate in food material, (ºC s-1); α is the thermal diffusivity (m2 s-1); ρ is
the density (kg m-3); and cp is specific heat of the food sample (J kg-1K-1).
The temperature distribution in the food can be obtained by simultaneously solving Eqs. (1)-(3).
2.4.3.
Initial and boundary conditions
The initial temperature of all cases of simulation was set as 23 ºC. The boundary conditions at
surfaces of PEI in contact with the peanut butter container were set as heat conduction, and all other surfaces
exposed to air were set as natural convection with a heat transfer coefficient of 15 W m-2 ºC-1 (Jiao et al.,
2014a). Properties of the peanut butter, PEI blocks and air used in simulations were listed in Table 6.1.
134
The top electrode of the RF system was set as the electromagnetic source. In order to obtain the
voltage on the top electrode, an estimation equation was employed as an alternative way to calculate the
voltage (Eq. 4). This estimation equation was based on a 1-D assumption of the heating system, which
assumes the electric field distribution in the food volume is uniform (Birla et al., 2004).
V   d air

 '2   "2
 c p dT
 d mat 
 f 0 ' dt





(4)
where dair is the total air gap between the electrodes and food sample (m), dmat is the thickness of the food
material (m), and ε′ and ε″ are the dielectric constant and loss factor of food materials, respectively. The
voltage used in computer simulation was determined by trial and error until the heating rate in the food
matched with the experimental results.
The bottom electrode and the metal shield of the RF system were set as electric insulation.
2.5. Simulation procedure
The commercial finite element method (FEM) software, COMSOL Multiphysics® (V4.2a
COMSOL Multiphysics, Burlington, MA, USA), is commonly used to provide numerical solutions to the
electromagnetic heating problem. The joule heating module, which conjugates the electric current and heat
transfer models, was employed in this study to achieve a reliable and fast prediction of the heating pattern
in foods.
After drawing the geometry based on the food sample and the RF system, all domains were meshed
to obtain a numerical solution to the problem. The convergence criteria of meshing was to ensure the
difference of the maximum temperature was less than 0.1% before and after the number of mesh elements
was doubled. Based on preliminary simulation studies, default extremely fine tetrahedral meshes were
generated in the food sample and on the top electrode, and normal size meshes were generated in all other
domains. Numbers of elements in the whole geometry after meshing were shown in Table 6.2.
135
2.6. RF experiments
All RF experiments were conducted at a room temperature of 23 ºC with a fixed gap between
electrodes of 10.1 cm. Peanut butter in cylinder containers was prepared and capped with its original lid.
PEI blocks were manufactured from PEI sheets with a thickness of 0.6 cm. A hole (d = 2 mm) was drilled
at the center of all PEI blocks and the container lid along its axis to allow temperature sensors to go through.
In experiments, the food sample was sandwiched by two PEI blocks and positioned coaxially in the
center of the RF cavity. The food samples were elevated to the middle between the two electrodes to achieve
a symmetric heating pattern. For all cases with different sizes of PEI blocks, cold spot locations were
determined by finding the lowest temperature from thermal images of a top surface and a cross sectional
surface taken by an infrared camera (ThermaCAMTM Researcher 2001, FLIR Systems, Portland, OR, USA).
The detailed procedure could be found in Jiao et al., (2014a). All RF experiments in this study were
conducted based on the cold spot reached target pasteurization temperature (70 ºC). A fiber optical sensor
(UMI, FISO Technologies, Inc., Saint-Foy, Quebec, Canada) was inserted through the PEI blocks and the
container lid to the center of the food to obtain the temperature-time history and calculate the heating rate.
When the cold spot reached 70 ºC, the sample was taken out immediately in order to take a thermal image.
2.7. Heating uniformity evaluation of different uniformity improvement methods
The effectiveness of several heating uniformity improvement methods were compared by obtaining
a heating uniformity index from computer simulation results. The methods were: PEI blocks addition
method (this study), PEI surrounding method (Jiao et al., 2014a) and a combination of both.
The heating uniformity of heated samples was evaluated by two heating uniformity indices. The
first heating uniformity index (TUI) was developed by Alfaifi et al. (2014).
UI 

Vvol
T  Tave dVvol
Tave  Tinitial Vvol
136
(5)
where T is the local temperature in the food (ºC), Tinitial is the initial temperature of the food (ºC), Tave is the
average temperature of the volume (ºC), and Vvol is the volume of food (m3). In addition, a new heating
uniformity index (HUI) (Eq. 6) was developed based on Alfaifi’s UI by replacing the ‘average temperature
(Tave)’ with the ‘target temperature (Tt)’.
TUI 

Vvol
T  Tt dVvol
Tt  Tinitial Vvol
(6)
where Tt is the target heating temperature (ºC). A smaller index corresponds to better heating uniformity.
The new HUI might be more suitable for describing the heating uniformity of a
pasteurization/sterilization process which requires the cold spot location to reach a certain target
temperature. It would reflect the degree to which temperature in the volume deviated from the target
temperature. Peanut butter samples treated with three methods in RF systems were simulated under the
same electrode gap (10.1 cm) and were heated until the cold spot location reached 70 ºC for pair comparison.
The combined method used the 8 cm diameter PEI block with PEI sheets surrounding. Both UI and TUI
were calculated and compared.
2.8. Height optimization of PEI blocks
To further improve the heating uniformity, the optimum height of the PEI blocks was determined
using computer simulation. With a fixed diameter (d = 8 cm), the height of the PEI blocks was swept from
0.1 to 2.3 cm with an interval of 0.1 cm. All the simulation cases were run under an electrode gap of 10.1
cm, electrode voltage 6100 V and heating time 600 s for comparison. Uniformity indexes were calculated
and the heating pattern at cross-sectional surfaces of the peanut butter were compared.
137
3. Results and discussion
3.1. Predicted electric field distribution
Typical electric field directions, electric field intensities and electric potentials in the RF cavity and
peanut butter with and without PEI blocks are shown in Fig. 6.2. When the peanut butter sample was treated
without PEI blocks, the center of the top and bottom portraits of the sample had the lowest electric field
intensity (light blue color). However, when PEI blocks were attached to the center of the top and bottom of
the sample, the electric field intensity increased and turned to a yellow color. The electric field intensity
looked more uniform after adding PEI blocks, which indicates that increasing the thickness of a portion of
the sample did help increase the local electric intensity, and had the potential of elevating the local
temperature.
3.2. Heating rate of peanut butter with different size of PEI blocks
The temperature-time history at the center of the peanut butter with various sizes of PEI blocks
treated in RF systems is shown in Fig. 6.3. All heating curves were relatively linear, and the heating rates
were obtained by calculating the slope of the curves and prepared for estimating the voltage as the
electromagnetic source in computer simulation. The heating rate increased with increases in PEI block
diameter. The peanut butter sample with a 10 cm diameter of PEI blocks had the highest heating rate, and
the sample without PEI blocks had the lowest. This is due to the automatic adjustment of the RF matching
circuit. A larger volume of sample usually results in a higher heating rate under the same RF treatment
condition (Mehdizadeh, 2009).
3.3. Voltage estimation
The estimated and actual simulation voltage used in the computer simulation are listed in Table 6.3.
Both the estimated and simulation voltage were in a range of 4500–6200 V. The difference between the
two was because the voltage estimation was based on an assumption which neglected the fringing field and
non-uniform temperature distribution in the food load (Birla et al., 2004). The reason for the unclear trend
138
of simulation voltage is due to the shift of the cold spot after adding PEI blocks during computer simulations,
the simulation voltage was changed in order to control the lowest temperature at 70 ºC.
3.4. Computer model validation
The top surface temperature of peanut butter samples obtained from both the experiment and the
simulation, and the cross-sectional surface temperature distribution from the computer simulation are
shown in Fig. 6.4. The differences between maximum and minimum temperature and the standard deviation
of the sample’s top surface are summarized in Table 6.4. From the top surface temperature comparison,
computer simulation results had a similar heating pattern as the experiment results, showing the smallest
temperature deviation was achieved by adding a pair of 8 cm PEI blocks. From the experiment plots, when
the center reached 70 ºC, the hot spot reached around 85 ºC without PEI blocks. After adding PEI blocks,
the hot spot temperature on the surface was reduced gradually from 85 ºC to 79 ºC as the diameter of PEI
blocks increased from 2 to 8 cm. When the PEI block diameter was continually increased to 10 cm, the hot
spot temperature increased to 81 ºC.
From the cross-sectional surface plots, the highest temperature of RF treated peanut butter without
PEI blocks reached 95.7 °C. After adding PEI blocks, the highest temperature of the cross-sectional surface,
which represented the temperature of the whole volume, reduced to 92.8, 92.2, 91.0, and 89.5 ºC with PEI
blocks of diameter 2, 4, 6, and 8 cm, respectively. The maximum temperature with 10 cm PEI blocks
reached the highest value of 101.4 ºC. The 8 cm PEI block improved the heating uniformity most
significantly, reducing the difference between maximum and minimum temperature in the volume from
25.7 to 19.5 °C. Two heating uniformity indexes of peanut butter with different sizes of PEI blocks after
RF treatment were presented in Table 6.5. The uniformity index (UI) calculated from the validated computer
model decreased from 0.0839 to 0.0624 when diameter of PEI blocks increased from 0 cm to 6 cm, and
then started increasing gradually to 0.0832 when diameter of PEI blocks increased to 10 cm. But the new
temperature uniformity index (TUI) showed the smallest value was found when the diameter of PEI blocks
was 8 cm. The results from 6 cm and 8 cm blocks were relatively close. This is due to the edge heating
139
effect that usually happens within 1-2 cm near the edges in this study. The 8 cm diameter PEI blocks were
selected for further testing as indicated by the TUI because it is more reasonable for describing the
temperature distribution around 70 ºC for pasteurization purposes. When the diameter increased to 10 cm,
the HUI was even higher than that of the peanut butter without PEI blocks.
3.5. PEI blocks height optimization
The uniformity indexes of peanut butter sandwiched by a pair of PEI blocks with various heights
are shown in Fig. 6.5. The UI firstly decreased as the height of PEI blocks increased until the block height
reached 1.4 cm, and started to increase afterward. The cross-sectional surface temperature plot of peanut
butter treated with 0.1, 1.4 and 2.3 cm height of PEI blocks in RF were presented in Fig. 6.6. Although the
minimum temperature was not controlled in the geometry, it could still be found that the uniformity
increased when the height of blocks increased from 0.1 to 1.4 cm, judging from the heating pattern. During
the height increase from 0.1 to 1.4 cm (Fig 6.6 a to b), the hot spot stays at the same location, but the
temperature distribution was more uniform from the radius direction. When the height increased to 2.3 cm,
the heating pattern changed as the hot spot switched to locations between the sample center and the PEI
blocks. This is probably because a longer PEI block can aggregate more electric energy and result in a
higher temperature. Although the 2.3 cm PEI blocks did not provide the best heating uniformity among all
heights, the resulted heating pattern made it more suitable for a combination with traditional hot air or hot
water heating since the outside layer of the sample had a lower temperature.
3.6. Heating uniformity comparison of uniformity improvement methods
The cross-sectional surface temperature distribution of peanut butter that was treated by PEI
surrounding method, PEI addition method and a combination method is shown in Fig. 6.7. The highest
temperature reached 89.5, 89.4 and 77.1 ºC in PEI surrounding, PEI addition and combination method,
respectively. With the PEI surrounding method, the cold spot locations were still at the top and bottom
surfaces, which suggested that the heating uniformity could be improved by combining the PEI blocks
addition method. The computer simulation conditions and the calculated uniformity indexes for three
140
heating uniformity improvement method are shown in Table 6.6. Comparing with the UI, the PEI sheets
surrounding method is the highest, 0.0859, then comes the combination method, 0.0715, and the PEI blocks
addition method is the lowest, 0.0635. However, the HUI showed the combined method has the lowest TUI,
0.0715, and PEI surrounding method is in-between, and the PEI blocks addition method has the highest
TUI, 0.2546. The reason for UI showing the PEI blocks addition method has the best heating uniformity is
probably due to the average temperature of the food volume being higher than that of the other two methods.
The TUI comparison results is in accordance with the cross-sectional plot since the combination method
provides the lowest maximum temperature.
4. Conclusion
A method of adding cylindrical PEI blocks onto the cold spots of peanut butter in a cylindrical jar
was evaluated to improve its heating uniformity in RF treatment. Computer simulation results showed that
after adding PEI blocks, the electric field distribution was more uniform and the temperature distribution
was more even, which indicated that the heating uniformity can be effectively improved by increasing the
thickness of the blocks material in RF treatment. Among five diameters of PEI blocks, 8 cm was found to
be the optimum one which leads to the best heating uniformity. An optimized height (1.4 cm) of PEI block
further improved the uniformity. Although the computer simulation might not provide an accurate
estimation, the trend of the heating uniformity index influenced by the PEI block height indicated there was
an optimized height in-between the minimum and maximum height, which could be the direction of further
exploration. A modified heating uniformity index was evaluated by comparing it with traditional uniformity
index and was found to be more effective. In a pasteurization process or other heating process which
requires a minimum heating temperature, the modified TUI would be more suitable in evaluating the
heating uniformity. The combination of the PEI blocks addition method and the PEI surrounding method
could reach a better heating uniformity than any single method applied. The computer simulation model
141
can be used to explore the effectiveness of combining the PEI blocks addition with other methods for
heating uniformity improvement.
142
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147
Table 6.1 Properties of peanut butter, polyetherimide and air for mathematical modeling (adapted
from Jiao et al., 2014b)
Polyetherimide
Airc
Peanut butter
(PEI)
b
Density (kg/m3)
1115a
1270
1.2
Heat capacity (J/kg·K)
2030a
2000
1000
Thermal conductivity
0.209a
0.122
0.026
Dielectric constant
4.03
3.15
1
Dielectric loss factor
0.4
0.0025
0
(W/m·K)
a
Jiao et al. (2014b)
b
Kelly and Zweben (2000)
148
c
COMSOL material library (2012)
Table 6.2 Number of different type of mesh generated in all domains in computer simulation
Diameter of PEI blocks
No PEI
2 cm
4 cm
6 cm
8 cm
10 cm
Tetrahedral
14658
15779
18470
23344
26583
33743
Triangular
2113
2298
2542
3125
3314
4312
Edge
300
320
336
356
356
413
Vertex
44
60
60
60
60
60
149
Table 6.3 The heating conditions and voltages for peanut butter with various size of PEI blocks in
a 6 kW 27.12 MHz RF system
Diameter of PEI blocks
No PEI
2 cm
4 cm
6 cm
8 cm
10 cm
Heating time (min)
10'00"
10'00"
9'00''
8'26"
8'00"
7'30"
Heating rate, dT/dt (ºC/s)
0.042
0.047
0.057
0.064
0.070
0.078
Estimated voltage (V)
4510
4755
5243
5552
5815
6150
Simulation voltage (V)
6100
5950
6000
5800
5700
5700
150
Table 6.4 Temperature distribution analysis on the top surface of peanut butter from experiment
with various size of PEI blocks (T, °C)
Diameter of PEI blocks
No PEI
2 cm
4 cm
6 cm
8 cm
10 cm
Minimum temperature
70
70
70
70
70
70
Maximum temperature
87
84
81
80
79
81
Maximum-Minimum
temperature
Average temperature
17
16
11
10
9
11
78
74
74
73
72
73
Standard deviation
5
5
3
2
2
3
151
Table 6.5 Uniformity index of peanut butter with various size of PEI blocks in RF treatment in
computer simulation
No PEI
2 cm
4 cm
6 cm
8 cm
10 cm
Average temperature (ºC)
85.1
82.8
89.0
94.4
101.0
113.9
Maximum-Minimum
temperature (ºC)
UI (Alfaifi's)
25.7
22.8
22.2
19.5
19.8
31.4
0.0839
0.0706
0.0649
0.0624
0.0694
0.0832
TUI (modified)
0.3649
0.3198
0.3011
0.2572
0.2243
0.4207
152
Table 6.6 Simulation conditions and uniformity comparison of peanut butter treated with PEI
surrounding, PEI blocks addition and a combination methods
PEI surrounding +
PEI surrounding
PEI blocks addition
Voltage(V)
12100
5700
12100
Heating time (s)
165
525
140
19.5
19.8
7.1
UI (Alfaifi's)
0.0859
0.0694
0.0715
TUI (modified)
0.1634
0.2243
0.0715
Maximum – Minimum
temperature (ºC)
153
addition
Figure 6.1 Scheme of a peanut butter sample in a cylindrical container with PEI blocks in a 6 kW
27.12 MHz RF cavity
154
Figure 6.2 Electric field direction (arrow), electric field intensity (surface), and electrode potential
(streamline) of peanut butter treated by RF with and without PEI blocks
155
90
Temperature (°C)
80
70
60
50
40
30
20
No PEI
10
2cm
4cm
6cm
8cm
10cm
0
0
5
10
15
20
25
Time (min)
Figure 6.3 Temperature-time history of peanut butter at the container center with different sizes of
PEI blocks in a 6 kW 27.12 MHz RF system having an electrode gap of 10.1 cm (mean of three replicates)
156
Diameter
of
PEI blocks
Experiment
Top surface
Simulation
Top surface
No PEI
2 cm
4 cm
6 cm
8 cm
10 cm
157
Simulation
Cross-sectional surface
Figure 6.4 Temperature distribution on the top surface of peanut butter from experiment and
computer simulation and cross-sectional surface from simulation with various size of PEI blocks in RF
treatment (upper temperature scale: experiment; lower temperature scale: simulation)
158
0.14
Uniformity index
0.12
0.1
0.08
0.06
0.04
0.02
0
0
0.5
1
1.5
Height of PEI blocks (cm)
2
2.5
Figure 6.5 Uniformity index of peanut butter with various height and 8 cm diameter of PEI blocks
in RF
159
(a)
(b)
(c)
Figure 6.6 Heating pattern of peanut butter with PEI blocks (a: height 0.1 cm, b: height 1.4 cm, c:
height 2.3 cm) and diameter of 8 cm in RF treatments
160
PEI surroudning
PEI blocks addition
PEI surroudning +
addition
Figure 6.7 Cross-sectional surface temperature distribution of peanut butter treated in RF with three
different methods (electrode gap is 10.1 cm)
161
CHAPTER SEVEN:
CONCLUSIONS AND RECOMMENDATIONS
1. Conclusions
This research was conducted to investigate the possible reason of non-uniformity in RF heating and
explore new methods for RF heating uniformity improvement especially for low moisture foods. Peanut
butter was selected as a model of low moisture foods in this research. The thermal and dielectric properties
of peanut butter with various moisture contents were measured at the frequency range of 10–1800 MHz. A
mathematical model of food heated in RF systems was first established for heating rate prediction, and
validated by saline water with different concentrations and peanut butter with various moisture contents. A
computer simulation model was built up with COMSOL Multiphysics® software for a 27.12 MHz, 6 kW
RF system to investigate the heating uniformity in peanut butter in a cylindrical container. The model was
validated by experiments and then used to explore solutions for heating uniformity improvement. A
Polyetherimide (PEI) sheets surrounding method was initially evaluated to minimize the dielectric
properties difference between the food sample and air to improve the heating uniformity. Another method
that adds PEI cylindrical blocks to the cold spot locations of food sample was developed to increase the
heating uniformity. The major findings of this research are summarized as follows:
·
The heating rate cannot be simply predicted by watching the loss factor. Both the dielectric
constant and loss factor of samples influenced the RF heating rate. With a certain air gap and
material thickness, when the value of ε˝ and ε’ of the food load equals to each other, the highest
can be reached.
·
Differential heating was found between the edges and center of peanut butter in a cylindrical
plastic container (d = 10 cm, h = 5 cm). The maximum temperature difference was 28 °C from
both experiments and computer simulation results when the peanut butter sample was heated from
room temperature to 70 ºC. The dielectric properties difference between food and the surrounding
162
medium, which is air in most of the RF heating cases, was the main cause of non-uniformity in
RF heating.
·
Using PEI sheets to surround the peanut butter sample, the difference of dielectric constant
between peanut butter and the surrounding medium decreased, so the edge heating was reduced.
The temperature difference between the hot and cold spot was reduced to 18 °C when heating
peanut butter from 23 to 70 ºC. Applying this method to a group of samples to simulate industrial
processing, computer simulation results showed that the method is effective. The PEI sheets
surrounding method was also found could potentially be applied to other low moisture foods, e.g.
wheat flour.
·
Adding PEI blocks to the cold spots could increase the local electric field intensity. A pair of 8
cm diameter PEI blocks added to the cold spots of the peanut butter could significantly improve
the heating uniformity by reducing the maximum and minimum temperature difference to 19.8 ºC
when peanut butter was heated from 23 to 70 ºC.
·
Combining the PEI sheets surrounding and the PEI blocks addition method may provide a better
heating uniformity than any single method could from computer modeling results. The
temperature difference from hot and cold spot could be reduced to 7.1 ºC when peanut butter was
heated from 23 to 70 ºC.
2. Contributions to knowledge
The relationship between dielectric properties and heating rate would help people estimate the
heating behavior of a certain material in dielectric heating. By bringing out two heating uniformity
improvement methods, the results showed both methods could effectively improve the heating uniformity
either by reducing edge heating or enhancing cold spot heating. A combination of both methods may
ultimately solve the non-uniform heating problem in low moisture foods.
163
3. Recommendations
The RF pasteurization step could be applied to packaged low moisture foods processing to ensure
food safety. For example, in a peanut butter processing line, raw peanuts will normally go through hulling,
roasting, blanching, grinding, mixing and jarring. Although the high-temperature long-time roasting period
would kill all bacteria in peanuts at the beginning, there might be microbial contamination during the
following processing steps due to poor hygiene which may cause safety problems. A RF pasteurization step
could be added right after jarring to inactivate pathogens and avoid further contaminations (Fig. 7.1).
In order to scale up the RF pasteurization process for industrial use, the following research could
be conducted for further RF heating uniformity improvement:
·
The uniformity improvement methods developed in this study could also be tested for
intermediate/high moisture foods based on their particular needs in pasteurization or disinfestation.
·
The material of PEI blocks can be optimized to focus the energy more efficiently.
·
The PEI blocks addition method could be applied on containers in other shapes to compare their
effectiveness.
·
Combination methods could be developed for further heating uniformity improvement, e.g. the top
electrode bending method combined with the PEI sheets surrounding method, the PEI sheets
surrounding method combined with moving and etc. The corresponding computer modeling
strategies also need to be developed.
·
Computer simulation techniques could be improved to avoid relying on experimental values. This
could be done by providing a more accurate voltage as electromagnetic source through developing
a more accurate estimation equation or designing a direct measurement circuit.
164
Roasting
Raw peanut receiving
Cooling down
Hulling, screening, sizing
Mixing with other ingredients
Jarring, sealing, labeling
(160-240 ºC
40-60 min)
Grinding
Cooling
Blanching
Storing
RF pasteurization
Figure 7.1 An option for placement of RF pasteurization (in dash) in peanut butter industrial
processes
165