Microwave Heating

 

CHAPTER I

MICROWAVE  HEATING  IN  FOOD  PROCESSING  Juming Tang, Feng Hao*  and Ming Lau† Department of Biological Systems Engineering  Washington State University Pullman, WA 99164-6120, USA

INTRODUCTION Microwave heating takes place due to the polarization effect of electromagnetic radiation at frequencies between 300 MHz and 300 GHz (Decareau, 1985). Started as a by-product of the radar technology developed during World War II, microwave heating is now used in about 92% of homes in the US (Giese, 1992). Microwave heating has also found applications in the food industry, including tempering of frozen foods for further processing, pre-cooking of bacon for institutional use, and final drying of pasta products. In those applications, microwave heating demonstrates significant advantages over conventional methods in reducing process time and improving food quality. But in general, applications of microwave heating in industrial food processing are much less common than home applications. Reasons for this difference include a lack of  basic information on the dielectric properties of foods and their relationship to microwave heating characteristics and the historically high cost of equipment and electricity. The food processing industry has been reluctant to make expensive investments in a technology that has not been proven thoroughly reliable in large-scale or long-term use (Mudgett, 1989). Now, with the development of more reliable magnetrons and the invention of ferrite circulators to protect generating tubes, microwave equipment has a longer operating life. The cost for microwave equipment has been steadily reduced over the years

*Current address: Department of Food Science and Human Nutrition, University of Illinois at Urbana-

Champaign, USA. †Current

address: Technical Center of Kraft Foods, Glenview Il., USA. 1

 

2  J. Tang, F. Hao & M. Lau

and is now comparable to that for conventional heating methods. The future of microwave heating in food processing applications is promising, but successful exploration of microwave heating applications relies on a thorough understanding of the interaction between microwaves and foods, and on the ability to predict and provide a desired heating pattern in foods for specific applications. Microwave heating in foods is a complicated physical process which depends upon the propagation of microwaves governed by Maxwell’s equations for electromagnetic waves, on the interactions between microwaves and foods determined by dielectric properties, and on heat dissipation governed by basic heat and mass transfer theories. This chapter will provide a general review and discussion on the interactions between microwaves and food materials and give a brief introduction of the current commercial applications of microwave heating in food processing. It will also describe some recent research results on microwave drying, pasteurization, and sterilization at Washington State University.

MECHANISMS OF MICROWAVE HEATING Food materials are, in general, poor electric insulators. They have the ability to store and dissipate electric energy when subjected to an electromagnetic field. Dielectric properties play a critical role in determining the interaction between the electric field and the foods (Buffler, 1993). The dielectric properties of a material are given by: ε  = ε ' −   jε  " = |  ε  | e − jδ 

(1)

 =  the complex relative dielectric constant where ε  = ε '  =  the relative dielectric constant ε "  =  the relative dielectric loss factor δ  =  =  dielectric loss angle (tan δ  =  = ε "  / ε ')  j =

−1

ε ' is related to the material’s ability to store electric energy (for vacuum ε '  = 1), while ε " indicates dissipation of electric energy due to various mechanisms.

The magnetic permeability for most biological materials is the same as that  × 10−7 W/Am). Therefore, those materials do not interact of free space (µ o = 4π  × with the magnetic field component of electromagnetic waves. Magnetic materials such as ferrite, often used in susceptors and browning dishes, however, interact with the magnetic field, which results in substantial heating (Buffler, 1993). Conversion of the electric component of microwaves into thermal energy in a lossy material (Goldblith, 1967) can be calculated by: Pv = 5.56  × 10 −  11 × f ε " E2

(2)

 

Microwave Heating in Food Processing  3

where Pv =  the power conversion per unit volume (W/m3)  =  frequency (Hz)  f  = ε "  =  relative dielectric loss factor E =  electric field (V/m) In theory, electric conduction and various polarization mechanisms (including dipole, electronic, atomic and Maxwell-Wagner) all contribute to theBut dielectric loss factor (Metaxas and Meredith, 1993; Kuang and Nelson, 1998). in the microwave frequency range of practical importance to food applications (e.g. 2450 MHz and 915 MHz in North America), conduction and dipole rotation are the dominant loss mechanisms (Fig. 1). That is: "   = ε d" + ε " = ε  d" + ε σ 

σ  ε oω 

(3)

where subscribes “d ” and “σ ” stand for contribution due to dipole rotation and due to ionic conduction, respectively; ω   represents angular frequency of the microwaves, and ε o  is the permittivity of free space (8.85 × 10 −12  F/m). In the frequency range between 1 kHz to 100 MHz, Maxwell-Wagner 1  polarization plays a very important role, but it is usually not considered in microwave heating.

Log (ε )

Contribution by Contribution by ionic conduction conductio



Effect of increasing temperature

Free water  relaxation Maxwell-Wagner effect

0.1

Bound water  relaxation

100

Effect of increasing temperature

20,000 MHz

Log (  f  )  )

 Fig. 1 Contributions of various mechanisms to the loss factor of moisture materials as a function of frequency and temperature (based on Roebuck and Goldblith, 1972; Harvey and Hoekstra, 1972; Metaxas and Meredith, 1993; Kuang and Nelson, 1998).

1

Maxwell-Wagner polarization arises from charge build-up in interface between components in heterogeneous systems (Metaxas and Meredith, 1993). It peaks at about 100 kHz at room temperature heterogeneous of 20°C.

 

4  J. Tang, F. Hao & M. Lau

 FACTORS AFFECTING DIELECTRIC PROPERTIES OF FOODS Dielectric properties of food materials are affected by many factors, including frequency of the microwaves, food temperature, moisture content, salt content, and other constituents. Effects of Frequency and Temperature

In a food system, the change of dielectric properties with respect to temperature depends upon frequency, bound water to free water ratio, ionic conductivity, and composition of the material. For example, at microwave frequencies used by the food industry, both the dielectric constants and the loss factor due to polarization of bound water in foods would increase with temperature. On the other hand, these two properties of free water would decrease when temperature increases (Calay e t a l ., 1995). An important concept in understanding how frequency and affecttime dielectric properties dipole rotation,  τ . It is defined as thedue timetorequired (3),temperature is the relaxation ε d"  in Eq. for preferentially oriented molecules, under a static external electric field, to relax back to 1/e (or 36.8%) of the original condition on sudden removal of  the external field. In general, the larger the molecules, the longer the relaxation time. For a pure liquid, such as water, the dielectric loss factor ε d"   reaches the 1 ) maximum at the relaxation frequency ( f c = 2πτ  . The relaxation time τ   of free water at 20°C was measured to be between 0.0071 to 0.00148 ns, which corresponds to a peak in ε d" at around 16 GHz (Mashimo et al., 1997). Water molecules are polar and are the most important constituent that contributes to the dielectric properties of moist foods. Water molecules bound to the surface of food solids in mono- or multi-layers have much longer relaxation times than free water molecules. For example, the relaxation time of bound water in different food materials at 20°C was determined to be between 0.98 ns to 2.00 ns, which corresponds to a peak in ε d" at about 100 MHz. Harvey and Hoekstra (1972) found that ε d" of monolayer bound water in lysozyme peaked at 200 MHz (2 ×  10 8  Hz) and ε d" for the second layer bound water peaked at about 10 GHz (1010  Hz) (Figs. 2 and 3). Debye related the relaxation time for the spherical molecule to viscosity and temperature as a result of randomized agitation of the Brownian movement (von Hippel, 1954):  3v τ  = V  kT 

(4)

 

Microwave Heating in Food Processing  5

 Fig. 2 Dielectric constant ( ε ') and loss factor ( ε ") as a function of frequency for packed lysozyme samples containing slightly more than one monolayer of bound water at 25°C (Harvey and Hoekstra, 1972).

 Fig. 3 Dielectric constant ( ε ') and loss factor ( ε ") as a function of frequency for packed lysozyme samples containing nearly two layers of bound water at 25°C (Harvey and Hoekstra, 1972). The two dispersions correspond to the first and second layers of bound water, respectively.

where v is viscosity, T   is absolute temperature, V   is volume of the sphere, and k is a constant. For non-spherical water molecules, we may have the following relation: τ  ∝

v T 

(5)

 

6  J. Tang, F. Hao & M. Lau





 = 2π  f ,  f   is frequency in Hz)  Fig. 4 Effect of temperature on dielectric behavior of free water ( ω  = (from Mudgett, 1985).

while the viscosity of all fluid decreases with increasing temperature (Macosko, 1994): Ea

(6)

 = voe RT 

v

where Ea  is activation energy and R  is the universal gas constant. Therefore, as temperature rises, relaxation time for water decreases. The shifting of  the relaxation time toward a smaller value (thus the frequency at the maximum ε d"   shifts toward a larger value as temperature increases) reduces the value of  ε d"   for water at a fixed microwave frequency (Fig. 4). For example, as the relaxation time τ  decreases   decreases with increasing temperature, the dispersion peak moves to higher frequencies, and the loss factor of pure water at 2450 MHz (2.45 ×  109  Hz) decreases with increasing temperature. The dielectric constant ε ' of free water also decreases with increasing temperature as the result of increased Brownian movement. " due to ionic conduction decreases with The dielectric loss factor ε σ  "

of  ε σ 

increasing frequency as shown in Eq.MHz (3). (2.45 The contribution the overall loss factors is smaller at 2450 ×  109  Hz) than atto 915 MHz (0.915 ×  109  Hz) (Fig. 5).

 

Microwave Heating in Food Processing  7

εd

εσ

 Fig. 5 Effect of temperature on dielectric properties of 0.5 N aqueous sodium chloride at three temperatures (from Roebuck and Goldblith, 1972).

   t 80   n   a    t   s   n 60   o   c   c    i   r 40    t   c   e    l   e 20    i    D

915 MHz 2450 MHz

0

0

20

40

60

Temperature, C

80   r   o    t   c   a    f   s   s   o    L

915 MHz

60

2450 Mhz

40 20 0 0

20

40

60

Temperature, C

 Fig. 6 Effect of temperature and frequency on dielectric properties of cottage cheese (11% protein, 4% lactose, 2% fat and 0.5% NaCl) (Herve et al., 1998).

 

8  J. Tang, F. Hao & M. Lau Tabl Ta blee 1 Dielectric properties of water and ice at 2450 MHz (Schiffmann, 1986)

State of water

Relative dielectric constant ( ε ')

Loss factor ( ε " )

Loss tangent (tan  δ)

Water (25°C)

78

12.5

0.16

Ice

3.2

0.0029

0.0009

The electric conductivity σ  in   in ionic solutions solutions increases increases with temperature due to decreased viscosity and hence increased mobility of the ions (Trump, 1954). "   also increases with temperature (Fig. 5). For Therefore, based on Eq. (3), ε σ  example, at 915 MHz the dielectric constant of ionic solutions generally increases with temperature. Figure 6 shows the effect of frequency and temperature on the dielectric constant, ε ', and loss factor, ε " , of cottage cheese with about 0.5% NaCl. Ice is almost transparent to microwaves (Table 1). When a food is frozen, both dielectric constant and loss factor are significantly reduced, the degree of  reduction depends, to a large extent, upon the amount of water in the unfrozen state and the ionic conductivity of the free water. Figures 7 and 8 show the effect of temperature on the dielectric properties of different foods at 2450 MHz (Bengtsson and Risman, 1971). The high salt content in cooked ham makes the dielectric properties of this product quite different from those of the rest of the materials in the graphs. Due to ionic polarization, both dielectric constant and loss factors of cooked ham increase with temperature above the freezing point, which is contrary to the trend of  dielectric properties of other foods in which loss mechanisms are mostly determined by the dipole polarization of free water. One advantage of the decreased loss factor with increasing temperature in low salt foods at microwave frequencies is the so-called temperature leveling effect. That is, when a certain portion of a food is overheated, the loss factor of that part is reduced, which results in less conversion of microwave energy to heat at that part of the food and helps to reduce non-uniform spatial temperature distribution. On the other hand, if the dielectric loss factor increases with increasing temperature, the foods would experience a phenomenon called thermal runaway. For example, when thawing frozen foods at relatively high microwave power levels, certain areas of the food are overheated while the other areas are still frozen. This is because faster thawing of a portion of food due to uneven heating dramatically increases the loss factor of that part of the food due to the high loss factor of free water (Figs. 7 and 8), which in turn increases microwave absorption, causing more uneven heating. In practice, a low microwave power level is often used in micro-wave thawing so that heat conduction can reduce

 

Microwave Heating in Food Processing  9

 Fig. 7 Dielectric constant of selected foods as affected by temperature (from Bengtsson and Risman,

1971).

 Fig. 8 Dielectric loss factor of selected foods as affected by temperature (from Bengtsson and Risman, R isman, 1971).

non-uniform temperature distribution. In industrial tempering of large blocks of meat or fish (a process that brings deep frozen products from −30°C to a few degrees below freezing point for further processing), convective surface cooling at below freezing temperature is often used to prevent possible thermal runaway.

 

10  J. Tang, F. Hao & M. Lau

Effect of Moisture Content

Due to the dipole nature of water molecules, food moisture content is an important determinant of the dielectric properties. In general, the higher the moisture content, the larger the dielectric constant and loss factor of the material. At temperatures above freezing, moisture exists in foods in one of the   —

two forms free water and bound water. The free water components have dielectric properties similar to those of liquid water, while the bound water exhibits ice-like dielectric properties. Dielectric properties of foods, in general, decrease rapidly with decreasing moisture content to a critical moisture level. Below this moisture level, the reduction in loss factor is less significant due to the bound water (Fig. 9). During microwave drying, the wetter parts of foods absorb more microwave energy and tend to level off the uneven moisture distribution. The moisture leveling effect is less pronounced when the moisture content is below the critical moisture, as the reduction of loss factor with reducing moisture content is not as significant.

 Fig. 9 Rate of evaporation and dielectric loss factor as affected by food moisture content (Metaxas and Meredith, 1983).

 

Microwave Heating in Food Processing  11

Other Factors

Salting reduces free water and depresses the dielectric constant and the dipolar loss, while increasing the conductive loss (Calay et al., 1995). Sugar molecules are relatively large and non-polar. An increase in sugar content reduces the dielectric constant. Hydration of sugar in water solutions shifts relaxation time to lower frequencies, thus increasing the dielectric loss factor at microwave frequencies (Roebuck and Goldblith, 1972). Similarly, hydration of protein and starch in solutions made up of 50% solids reduces the dielectric constant and increases the dielectric loss factor (Roebuck and Goldblith, 1972). Predictive Models

Values of dielectric constant and loss factor of dry food solids, fats and oils are small and are relatively independent of frequency and temperature. Tabl Ta blee 2 Dielectric properties of oil and solids (Kent, 1986)

F(Hz) Products

25 Soybean salad oil

49 82

25 Cotton oil 49

ε ' ε " ε ' ε " ε ' ε "

2.85 0.159 2.88 0.138 2.86 0.092

2.62 0.168 2.71 0.174 2.72 0.140

ε ' ε " ε ' ε "

2.83 0.174 2.87 0.134

2.64 0.175 2.70 0.174

2.8 0.184 3.5 0.196 4.0 0.160

2.8 0.184 2.7 0.235 3.2 0.275

0

ε ' ε "

2.1 0.038

1.9 0.040

40

ε "' ε  ε ' ε "

2.1 0.044 2.4 0.067

1.8 0.054 0.2 0.072

40 70

Skimmed milk powder

109

107

ε ' ε " ε ' ε " ε ' ε "

0 Flour (mc = 3.2%)

108

10 6

T(°C)

70

 

12  J. Tang, F. Hao & M. Lau

The dielectric properties of selected oils and low moisture solids are listed in Tabl Ta blee 2. A food material of high moisture content can be considered a mixture of  dielectrically active ionic solutions and dielectrically inert solids (Mudgett, 1985). The dielectric properties of two-phase mixtures of aqueous ions and colloid solids are related to the dielectric properties of each component and their volume fractions, shown in the following distributive model (Mudgett, 1985): ε m

= ε sV   s  + ε   c (1 −  V s)

(7)

where ε m =  relative permittivity of the mixture, ε s =  relative permittivity of the suspended solids, ε c =  relative permittivity of the continuous aqueous phase, V s =  volume fraction of the solids. According to Mudgett et al. (1977), reasonable estimation of dielectric properties for various liquid and solid foods can be obtained from the above relation. However, Eq.which (7) requires estimation of theNewer volume fractionmodels of the solid or liquid phases, is oftenan difficult to obtain. empirical have been developed in which dielectric properties are related to the mass fraction of various components. For example, based on selected groups of data in the literature, Sun et al. (1995) developed the following empirical relationships to correlate the dielectric properties of a meat product to temperature, moisture content and ash content:

× T  ε ' = m water(1.0707 − 0.0018485   ) +  mash (4.7947) + 8.5452   ε " = m water (3.4472 − 0.01868

R = 0.97

(8)

R = 0.99

(9)

× T + 0.000025 × T 2 ) 2

+ m ash (−57.093 + 0.23109 × T  ) − 3.5985

Calay et al. (1995) also developed empirical polynomial correlation to relate dielectric properties to moisture content and temperature for selected foods. Due to the influences of two different loss mechanisms, and the effect of  temperature and food composition, it is difficult to develop a general predictive equation that can accurately take into account the influence of various factors mentioned in the previous sections.

PENETRATION DEPTH OF MICROWAVES When microwaves propagate through a lossy material, a fraction of microwave energy is converted into heat and the remaining power decreases with the

 

Microwave Heating in Food Processing  13

distance from the surface (Fig. 10). Lambert’s law describes microwave power reduction as a function of the distance that microwaves travel into a semi-infinite lossy body: P(z) =  Po e −2α z

(10)

where Po is incident microwave power at the surface, P(z) is microwave power at distance z in the direction of microwave propagation within the lossy material, and α   is the attenuation constant. Attenuation factor can be calculated according to von Hippel (1954):



α  =

 

2

2π   1   ε "   ε '  1 +    λ o  2   ε '  



 

   − 1       

1 2

(11)

where λ o  is the wavelength of microwaves in free space. For 2450 MHz microwaves, λ o = 12.24 cm, and for 915 MHz MHz microwaves, microwaves, λ o = 32 32.7 .77 7 cm. cm. Lambert’s law is applicable to a large body of lossy material where microwaves are largely attenuated with little reflection within the material at the opposite interface with the air. Ayappa et al. (1991) proved that for a sufficiently thick slab, Lambert’s law applies as long as the thickness of the slab satisfies the following condition: L ≥ Lcrit = 5. 4dp − 0.08cm

(12)

where, dp is penetration depth of microwaves in food. When Eq. (12) is satisfied, the Lambert’s law results in less than 1% error as compared to more rigorous analysis with the Maxwell equations for plane waves. When the thickness of a slab is less than Lcrit, the interference between transmitted and reflected waves between the surfaces may create standing waves, causing internal hot and cold spots. As described by the Lambert’s law, microwave intensity reduces exponentially with the depth into a lossy material (Fig. 10). Penetration depth of microwave power is defined as the depth where the power is reduced to 1/ e  (e = 2.718) of  the power entering the surface. That is:  

P(dp  ) =

Po e .

 

14  J. Tang, F. Hao & M. Lau

Food material Decay of microwave power according to Lambert’s Law

Po

Microwave radiation

Po*1/e

dp Depth into the material z, m

 Fig. 10 Definition of penetration depth of microwave in a lossy material.

  4.0   m   c  ,    h    t 3.0   p   e    d   n 2.0   o    i    t   a   r    t   e 1.0   n   e    P

915 MHz 2450 MHz

0.0 0

20

40

60

Temperature, C

 Fig. 11 (11% Effectprotein, of temperature on the2% penetration depthNaCl) of 914 (Herve and 2450 microwaves in cottage cheese 4% lactose, fat and 0.5% etMHz al., 1998).

From Eq. (10), a relation can be derived for dp: dp =

1 . 2α 

(13)

In general, 915 MHz microwaves have deeper penetration depth in foods than 2450 MHz, and the penetration depth of microwaves also varies with temperature (Fig. 11 and Table 3). The limited penetration depth of microwaves in foods often causes non-uniform heating.

 

Microwave Heating in Food Processing  15 Tablee 3 Penetration depth (dp) of microwaves in selected foods (all data were measured in our Tabl laboratory, except for ham)

915 MHz

2 4 5 0 M Hz

Temp (°C)

ε '

ε "

dp (mm)

ε '

ε "

dp (mm)

20 −12 23

79.5

3.8

122.5

–

–

11620

77.2

20.8

21.5

10.3 0.003 15.6

16.8

–

78.2 3.2 75.8

Ham*

25 50

61 50

96 140

5.1 3.7

60 53

42 55

3.8 2.9

Yogurt (pre-mixed) Apple (Red Delicious) Potato (raw) Asparagus Whey protein gel (20% solid) Corn oil

22 22 25 21 22

71 60 65.1 73.6 50.9

21 9.5 19.6 20.6 17.0

21.2 42.7 21.7 22.2 22.4

68 57 53.7 71.34 40.1

17.5 12 15.7 16 12.9

9.3 12.3 9.2 10.4 10.6

25

2.6

0.18

481.1

2.5

0.14

216.7

Material

Water Deionized Ice +0.5% Salt

10.9

*From Mudgett (1986).

ENERGY COUPLING The intrinsic impedance in a material is defined as (Sadiku, 1995): µ  η = εε   o

η

=

o

ε 

(14)

where η  is a complex quality, ηo (= µ    o  / ε o )   is the intrinsic impedance of  free space, µ o( = 4 π × 10 − 7  H/m) is the permeability of free space, and ε o(= 8.854 × 10−12  F/m) is the permittivity of free space); ηo  is about 377 Ω. For example, water at 25°C has an intrinsic impedance of about 43 Ω, and ice has a value of about 210 Ω  at 2450 MHz. The difference between the intrinsic impedance of two media causes mismatch. This would lead to two consequences: 1) the microwaves will change their direction of propagation once entering a new material, and 2) a portion of microwave power will be reflected at the interface. Snell’s Law of Refraction describes the refraction for transmitted waves (Mudgett, 1985):

 

16  J. Tang, F. Hao & M. Lau

Incident waves, PPi i    

φ

φ

Reflected 1 1)  i,  waves, Prr   (= waves, (=  Γ where  0