**1. Introduction**

18 Will-be-set-by-IN-TECH

[10] Zhuravlev, V. A. &Suslyaev V. I. (2006b). Analysis of the microwave magnetic permeability spectra of ferrites with hexagonal structure, *Russian Physics Journal* Vol.

49: No. 9.

Microwaves are electromagnetic radiation with wavelength ranging from 1 mm to 1 m in free space with a frequency from 300 GHz to 300 MHz, respectively. International agreements regulate the use of the different parts of the spectrum; the frequencies 915 MHz and 2.45 GHz are the most common among those dedicated to power applications for industrial, scientific and medical purposes (Metaxas & Meredith, 1983).

Although microwaves have been firstly adopted for communications scope, an increasing attention to microwave heating applications has been gained since World War II (Meredith, 1998; Chan & Reader, 2002). Reasons for this growing interest can be found in the peculiar mechanism for energy transfer: during microwave heating, energy is delivered directly to materials through molecular interactions with electromagnetic field via conversion of electrical field energy into thermal energy. This can allow unique benefits, such as high efficiency of energy conversion and shorter processing times, thus reductions in manufacturing costs thanks to energy saving. Moreover, other effects have been pointed out, such as the possibility to induce new structural properties to irradiated materials (development of new materials) and to apply novel strategies in chemical syntheses (green techniques).

Crucial parameters in microwave heating are the dielectric properties of matter; they express the energy coupling of a material with electromagnetic microwave field and, thus, the heating feasibility (Metaxas & Meredith, 1983; Schubert & Regier 1995; Tang et al., 2002). On the basis of dielectric properties, microwave devices (applicators) can be adopted in heating operations and optimized working protocols can be used.

This chapter is divided into four sections dealing with:

i. fundamentals of microwave heating and relevance of dielectric properties of materials;

© Barba and d'Amore , licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © Barba and d'Amore, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


### **2. Microwave heating fundamentals**

Peculiarity of microwave heating is the energy transfer. In conventional heating processes, energy is transferred to material by convection, conduction and radiation phenomena promoted by thermal gradients and through the materials external surface. Differently microwave energy is delivered directly to materials through molecular interactions (loss mechanisms) with electromagnetic field via conversion of electromagnetic energy into thermal energy. Whereas loss mechanisms occur, a high rate of heating and a high efficiency of energy conversion are expected. The high heating rate represents the key-feature of microwaves heating, because this makes possible to accomplish in short times (seconds or minutes) what would take minutes, or even hours, to be done with conventional heating. This depends upon slowness of heat delivery rate from the material surface to the core as determined by the differential in temperature from a hot outside to a cool inside. In contrast, use of microwave energy can produce, under some conditions, a bulk heating with the electromagnetic field interacting with the material as a whole. With reference to energy saving, thermal treatments performed by microwave heating can be seen as intensified operations1.

The ability of a material to interact with electromagnetic energy is related to the material's complex permittivity (dielectric properties or susceptibility). This property, in any homogenous, isotropic, and linear dielectric material is characterized by a frequencydepending absolute complex permittivity usually indicated with the Greek symbol :

$$
\varepsilon\_{\rm abs}(oo) = \varepsilon\_0 \cdot \varepsilon(oo) = \varepsilon\_0 \left[ \varepsilon'(oo) - i \varepsilon'(oo) \right] \tag{1}
$$

where *0 is* the vacuum permittivity (*<sup>0</sup>*= 8.85 10-12 F/m) and is the angular frequency (*2f*, *f* frequency, Hz). In scientific literature, complex permittivity is diffusely reported as a relative complex number 0 / ' *'' abs ε iε* in which the real part, ', is named dielectric constant and the imaginary part, ", is known as loss factor. The dielectric constant is a measure of how much energy from an external electric field is stored in the material; the loss

<sup>1</sup> Process intensification is a current approach in the development of equipment and methods to achieve process miniaturization, reduction in capital cost, improved energy efficiency, and, often, product quality. Additional benefits of process intensification include improved intrinsic safety, simpler scale-up procedures. The philosophy of process intensification has been traditionally characterized by four words: smaller, cheaper, safer, slicker (Coulson & Richardson's, 2002; Stankiewicz, A. & Moulijn J. 2004).

factor accounts for the loss energy dissipative mechanisms in the material2. Therefore, a material with a high loss factor is easily heated by microwave. On the other hand, if a material has a very low *ε"* is transparent to microwave effect. Power dissipation ( *Qg* ) is given by the common form of the average power loss density (power dissipation per unit volume, W/m3) drawn from the Poynting's theorem (Metaxas & Meredith, 1983):

92 Microwave Materials Characterization

safety limits of exposition;

operations1.

where 

**2. Microwave heating fundamentals**

ii. different techniques used in dielectric properties measurements of materials (test fixtures characteristics, technique applicability, advantages and disadvantages); iii. application of the open-ended coaxial-probe method in dielectric properties measurements of food, pharmaceutical ingredients, living materials, to understand specific heating phenomenology and, thus, to optimize thermal treatments / to define

Peculiarity of microwave heating is the energy transfer. In conventional heating processes, energy is transferred to material by convection, conduction and radiation phenomena promoted by thermal gradients and through the materials external surface. Differently microwave energy is delivered directly to materials through molecular interactions (loss mechanisms) with electromagnetic field via conversion of electromagnetic energy into thermal energy. Whereas loss mechanisms occur, a high rate of heating and a high efficiency of energy conversion are expected. The high heating rate represents the key-feature of microwaves heating, because this makes possible to accomplish in short times (seconds or minutes) what would take minutes, or even hours, to be done with conventional heating. This depends upon slowness of heat delivery rate from the material surface to the core as determined by the differential in temperature from a hot outside to a cool inside. In contrast, use of microwave energy can produce, under some conditions, a bulk heating with the electromagnetic field interacting with the material as a whole. With reference to energy saving, thermal treatments performed by microwave heating can be seen as intensified

The ability of a material to interact with electromagnetic energy is related to the material's complex permittivity (dielectric properties or susceptibility). This property, in any homogenous, isotropic, and linear dielectric material is characterized by a frequencydepending absolute complex permittivity usually indicated with the Greek symbol :

0 0 ( ) ( ) '( ) ( ) *''*

*<sup>0</sup>*= 8.85 10-12 F/m) and

 

 *<sup>ε</sup> <sup>i</sup><sup>ε</sup>* (1)

*ε iε* in which the real part, ', is named dielectric

is the angular frequency (*2*

*f*, *f*

 

frequency, Hz). In scientific literature, complex permittivity is diffusely reported as a

constant and the imaginary part, ", is known as loss factor. The dielectric constant is a measure of how much energy from an external electric field is stored in the material; the loss

1 Process intensification is a current approach in the development of equipment and methods to achieve process miniaturization, reduction in capital cost, improved energy efficiency, and, often, product quality. Additional benefits of process intensification include improved intrinsic safety, simpler scale-up procedures. The philosophy of process intensification has been traditionally characterized by four words: smaller, cheaper, safer, slicker (Coulson &

*abs* 

*0 is* the vacuum permittivity (

relative complex number 0 / ' *''*

Richardson's, 2002; Stankiewicz, A. & Moulijn J. 2004).

 

*abs* 

  iv. basics of heat and mass transfer modeling in microwave assisted processes.

$$\dot{Q}\_g = \frac{1}{2} \left. \omega \varepsilon\_0 \varepsilon^{\prime\prime} \right| \mathbf{E} \Big|^2 \tag{2}$$

where *E* is the electrical field strength [V/m]. Bulk heating is achieved when penetration depth (*Dp*), defined as the distance from the material surface at which the power drops to e-1 of its initial value, is of the same order of magnitude of materials dimensions. Assuming electromagnetic field as a plane wave that travels along one axis, penetration depth is calculated as following:

$$D\_p = \frac{c}{2\sqrt{2}\pi f \sqrt{\varepsilon \cdot \left[\sqrt{1 + \tan^2 \delta} - 1\right]}} \Big|\_{\varepsilon=0}^{\varepsilon=2} \tag{3}$$

where *c* is the light velocity in free space (3 108 m/s) and tan δ is the loss tangent. Under some conditions ((*"*/*'*) << 1, i.e. small tan δ) the penetration depth can be calculated by:

$$D\_p = \frac{c}{2\pi f} \frac{\sqrt{\varepsilon'}}{\varepsilon''} \tag{4}$$

When bulk heating is not achievable, a temperature levelling effect can occur in thick layer depending on materials thermal diffusivity that can drive the heat distribution within the whole bulk.

Under a physical point of view, interactions between materials and electromagnetic energy are inherent in the ability of the electric field to polarize the material charges and in the impossibility of this polarization to follow the rapid changes of the oscillating electric field (dielectric dissipative mechanisms). In presence of an external electric field, different kinds of polarization mechanisms are possible: the electronic polarization, caused by modification of electrons position around the nucleus; the atomic polarization, related to positional shifts of nucleus due to the non-uniform distribution of charges within the molecule; the orientation polarization (dipoles rotation) due to the reorientation of the permanent dipoles under the influence of the electric field; the spatial charge polarization observed in materials containing free electrons confined on surface (Maxwell-Wagner effect) (Metaxas and Meredith, 1983). Depending on frequency, one or two mechanisms dominate over the others. In particular, among the dielectric mechanisms of energy dissipation above outlined,

<sup>2</sup> The loss tangent (tan δ = "/') is frequently used in dielectric heating literature providing indications of how the material can be penetrated by an electric field and how it dissipates the energy in heat.

the dipoles rotation is the dominant polarization mechanism in irradiating materials rich in water (such as biological tissues, foods, mixtures based on water or polar solvents) in the microwave electromagnetic spectrum region (industrial high frequency heating 107<f[Hz]<109). In the same region also ionic dissipative phenomena (Joule's loss effect) may occur if ionic species are present, and can be lossy. The atomic and the electronic polarization mechanisms are relatively weak, and usually constant over the microwave region (Fig. 1.).

Being in dielectric measurements difficult to separate conduction losses from those due polarization, the overall dissipative feature (loss factor) of a material can be expressed by the following equation:

$$
\stackrel{\circ}{\varepsilon}\_{\text{measured}}^{\circ}(oo) = \stackrel{\circ}{\varepsilon}\_{cp}^{\circ}(oo) + \stackrel{\circ}{\varepsilon}\_{ap}^{\circ}(oo) + \stackrel{\circ}{\varepsilon}\_{dp}^{\circ}(oo) + \stackrel{\circ}{\varepsilon}\_{\text{interf}\%}^{\circ}(oo) + \frac{\sigma}{\varepsilon\_0 \cdot oo} = \stackrel{\circ}{\varepsilon}^{\circ}(oo) + \frac{\sigma}{\varepsilon\_0 \cdot oo} \tag{5}
$$

where the subscript *ep*, *ap, dp* and *intefp* refer to electronic, atomization dipolar and interfacial polarization mechanisms, respectively; and σ is the conductivity of the medium.

**Figure 1.** Typical frequency-regions of the loss mechanisms.

Microwave heating processes are currently applied in many fields: from food industry, including packaging (Tang et al., 2002; Schubert & Regier, 2005) to materials processing (polymers, wood, ceramics and composites) (Zhou et al., 2003); from minerals treatments (Al-Harahsheh & Kingman, 2004) and environmental remediation processes (soil remediation, toxic waste inertization) (Kulkarni et al., 2008; Remya & Lin, 2011; Barba et al., 2012) to pharmaceutical emerging technologies (McMinn et al., 2005; Auriemma et al., 2011). Key of all processes above is the energy transfer that, as first discussed, is based on the ability of a material to store and to dissipate electromagnetic energy. Knowledge of the dielectric properties appears fundamental for heating treatments because they have a crucial role in designing (or choosing) of microwave devices (applicators) and on setting operative parameters (time of exposure, power). Moreover, as dielectric properties can be affected by many factors including frequency of microwaves, temperature, chemical composition of the materials (abundance of water, salt content and other constituents) (Kraszewski, 1996; Chan & Reader, 2002; Tang et al., 2002), microwave heating requires to be appropriately addressed on the basis of dielectric behaviour studies.
