**2. The freeze-drying process**

In freeze-drying process, the material must be frozen in the first step. Then, it is followed up with creating vacuum and injecting energy by microwaves in the chamber or storage compartment which contains the frozen food material [2] (**Figure 1**).

**Figure 1.** Steps must be passed in microwave-assisted freeze-drying process.

Drying is the most common way to increase the life of food products to make them easier to maintain [2]. Meanwhile, microwave technology has achieved a significant position among other methods in food industry. Not only is this method used in food industry but also in pharmaceutical industry and medical sciences, for removing water from aqueous solutions

In conventional method for drying foodstuff, it is heated, usually by flowing hot air, to evaporate its moisture. Also, the heating can be done by other methods from direct solar radiation to using microwave energy [1, 6]. In freeze-drying method, removing the moisture content of material is done by sublimation of water molecules with internal heating after freezing the material and creating a vacuum [7]. Compared with conventional methods, it causes small irreversible changes in food and thus keeps the quality of product at an excellent level [1, 2, 7]. Rehydration, color (browning), and volume (volume reduction and consequently shrinkage) are key parameters in determining the quality of foodstuff and are considered in [1]. Low temperature in this method helps to stop most bivological reactions, and hence it is suitable for dehydrating heatsensitive material like biological products [1–3]. However, this method is expensive [1, 7]. It is suitable for valuable foodstuffs like coffee [1]. Accordingly, researchers are trying to find the

Ref. [1] is a valuable review on the studies, which are done about the quality of foodstuff from different drying methods, and collects and presents different graphs about these parameters. Author in [1] presents a chart which determines the contribution of energy consumed in different operations of freeze-drying process. Also, the cost breakdown for drying two samples

Drying (or dehydrating) is removing moisture content from a material. This phenomenon,

In the traditional method, the needed energy must be transferred from dried layer (into frozen bulk), which has the low thermal conductivity. This means that it takes long time [6]. Microwave technology helps to transfer the needed energy in a form of electromagnetic wave into the frozen region, independent of thermal characteristics of dried layer. Then, the electromagnetic field is dissipated in frozen region and increases its temperature. Since the field is distributed in the frozen region, the dissipation occurs throughout frozen bulk. In fact, it

In [8], it is mentioned that the volume reductions (shrinkage) for strawberry dried by freeze-

Ref. [3] considered the conventional and microwave-assisted freeze-drying methods. It showed that the drying time is less than 20% for microwave-assisted freeze-drying method

In freeze-drying process, the material must be frozen in the first step. Then, it is followed up with creating vacuum and injecting energy by microwaves in the chamber or storage com-

drying and air-drying methods are around 6.6 and 80%, respectively [1, 8].

which required phase change in water content of material, requires a lot of energy [6].

and preserving the blood, bone, and skin [3–5].

144 Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing

optimal method by a combination of different methods.

(high- and low-value foods) is determined in [1].

creates internally volumetrically heating [2, 6, 7].

because of volumetrically heating in this method.

partment which contains the frozen food material [2] (**Figure 1**).

**2. The freeze-drying process**

**Figure 2.** Profile of different layers with typical variations of temperature in them for an infinitely long slab of material with thickness L (reproduced from [2]).

What happens during these stages? The heating of the frozen food by microwave energy causes the frozen bulk temperature to increase. With increasing bulk temperature, frozen molecules of water receive enough energy and transit from solid phase to gas phase (sublimation of frozen molecule of water). These molecules migrate (from frozen bulk) into vacuum region of chamber. In other words, the moisture is removed from frozen region, and food material is dried. This sublimation starts from the outer layer. Now, a new region forms in frozen bulk from interface of food material and vacuum and dried region (**Figure 2**). As the time proceeds, the interface between dried and frozen regions will retreat. Therefore, the frozen bulk of material is thinned, and the volume of dried section increases [2].

According to the above discussion, we are faced with three physical phenomena: producing thermal energy by dissipation of microwave energy (in frozen bulk), heat transfer (in frozen and dried regions of food material), and mass transfer which is related to the movement (flow) of water vapor in the system (in the dried region). The heat transfer in the freeze zone is done by conduction, while the heat is transferred in the dried region in conduction and convention.

#### **3. Heat and mass transfer equations**

As mentioned previously, with increasing the temperature of bulk, two heat transfers are carried out in the bulk. The heat transfer in the frozen region is conductive, while the heat transfer in dried region is a combination of conductive and convective. The heat transfer in frozen region obeys the following relation:

$$\rho\_{\rm{p}} \mathbf{C}\_{\rm{p}\overline{t}} \frac{\partial T\_{\rm{r}}}{\partial t} + \overrightarrow{\nabla} \ . \left( -\vec{k}\_{\rm{p}} . \quad \overrightarrow{\nabla} \ \,^{\rm{T}} T\_{\rm{p}} \right) = \,^{\rm{p}} p\_{d} \tag{1}$$

For beef meat, cut into a slab, the temperature distribution is demonstrated for different times

Microwave Technology in Freeze-Drying Process http://dx.doi.org/10.5772/intechopen.74064 147

From **Figure 3**, the concentration of water vapor in dried region is decreased by getting away from the interface (between frozen and dried layers). The necessary energy for this system is provided by electromagnetic waves at 2450 MHz. In [2], it is assumed that the electric field is approximately uniform throughout the material and its intensity equals to 12.5 KV/m. The total pressure and partial pressure of water vapor in the vacuum region are 0.29 and 0.075 mmHg, respectively. The drying time for this meat is measured 6 hours when applied electric field is nearly 10 KV/m [9]. Generally, the higher the electric field intensity, the smaller

In [2], it has been shown that the optimum operation of freeze-drying process is obtained near the corona and melting point. For a slice of meat in a rectangular cross section, the variation of temperature and concentration happened in two dimensions. **Figures 5** and **6** are shown in

**Figure 3.** The temperature (left) and concentration (right) profiles for a slab of beef meat in different times (reproduced

by [2] (**Figure 3**). Its thickness is 1 inch and is in the middle of chamber.

the drying time (**Figure 4**).

from [2]).

simulation and experimental results [7].

where *TF* , *ρ<sup>F</sup>* , *CPF*, *<sup>k</sup>* → *F* , and *pd* are temperatures of frozen region, density of frozen material, heat capacity of the frozen material, the vector of thermal conductivity of frozen material, and density of dissipated microwave power, respectively. All of them are for frozen zone. The convective transfer in dried region is due to the flow of water vapor through this region. Hence, in dried region, the heat transfer obeys the following relation:

$$\rho\_{\rm D} \mathbf{C}\_{\rm pD} \frac{\partial T\_{\rm D}}{\partial t} + \stackrel{\rightharpoonup}{\nabla} \cdot \left( -\stackrel{\rightharpoonup}{\vec{\mathbf{k}}\_{\rm D}} \cdot \stackrel{\rightharpoonup}{\nabla} T\_{\rm D} \right) = p\_{\rm d} - \text{C} \vec{\mathbf{W}} \cdot \stackrel{\rightharpoonup}{\nabla} T\_{\rm D} \tag{2}$$

where *C* and *W* → are concentration and the vector of mass flux, respectively. These two parameters are related to water vapor. All other parameters are the same ones in the previous formula but for dried zone. This relation shows our need to know the concentration of water vapor. The water vapor concentration obeys the mass transfer relation. Relation (3) specifies the variation of concentration (*C*) of water vapor in dried layer:

 ∇ <sup>→</sup> . (*<sup>D</sup>* <sup>→</sup> . ∇ → *<sup>C</sup>*) <sup>=</sup> *<sup>σ</sup>* \_\_\_ <sup>∂</sup>*<sup>C</sup>* <sup>∂</sup>*<sup>t</sup>* (3)

where *D* → and *σ* are the vector of effective diffusivity and porosity of the dried material, respectively. It is possible to find the distribution of temperature by simultaneously solving these equations. Initial and boundary conditions must be considered to solve these equations. Also, the thermodynamic equilibrium, governed at the interface of frozen and dried region, determines the relationship between the concentration of water vapor and the temperature of frozen region [2, 3].

It is evident that density and porosity of food material, along with moisture and fat content, are the key factors in the determining the process.

#### **4. The transient variation of temperature during freeze-drying**

When an infinitely long slab of the proposed material is available, it can be assumed that all variations happen in direction orthogonal to the surface of slab (one-dimensional variation). The typical distribution of temperature in different layers (frozen, dried, and vacuum) and the concentration of water vapor in dried layer are shown in **Figure 2**. It is sufficient to show the variation only in just half of the structure because of symmetry.

where *Tc* , *Ti* , *TS* , *Ci* , and *CR* are the temperatures in the middle of frozen bulk, the temperature of interface (between frozen and dried regions), the temperature of vacuum, the concentration of water vapor in interface (between frozen and dried regions), and the concentration of water vapor in interface of vacuum and dried regions [2]. The sublimation will continue until the temperature of dried zone (in the interface) is kept under the melting point of frozen region [2]. The variation of temperature in dried region is a part of the parabolic. It is valid for frozen region, too.

For beef meat, cut into a slab, the temperature distribution is demonstrated for different times by [2] (**Figure 3**). Its thickness is 1 inch and is in the middle of chamber.

*ρ<sup>F</sup> CPF*

where *TF*

, *ρ<sup>F</sup>* , *CPF*, *<sup>k</sup>* → *F* , and *pd*

*ρ<sup>D</sup> CPD*

→

∇

are the key factors in the determining the process.

where *C* and *W*

where *D* →

where *Tc*

, *Ti* , *TS* , *Ci* <sup>∂</sup>*T*\_\_\_*<sup>F</sup>* <sup>∂</sup>*<sup>t</sup>* <sup>+</sup> <sup>∇</sup>

146 Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing

<sup>→</sup> . (<sup>−</sup> → kD . ∇ →

<sup>→</sup> . (*<sup>D</sup>*

**4. The transient variation of temperature during freeze-drying**

variation only in just half of the structure because of symmetry.

<sup>→</sup> . ∇ →

dried region, the heat transfer obeys the following relation:

∂*T*\_\_\_\_*<sup>D</sup>* <sup>∂</sup>*<sup>t</sup>* <sup>+</sup> <sup>∇</sup>

the variation of concentration (*C*) of water vapor in dried layer:

<sup>→</sup> . (−*<sup>k</sup>* → *<sup>F</sup>* . ∇ →

capacity of the frozen material, the vector of thermal conductivity of frozen material, and density of dissipated microwave power, respectively. All of them are for frozen zone. The convective transfer in dried region is due to the flow of water vapor through this region. Hence, in

eters are related to water vapor. All other parameters are the same ones in the previous formula but for dried zone. This relation shows our need to know the concentration of water vapor. The water vapor concentration obeys the mass transfer relation. Relation (3) specifies

*TF*) = *pd* (1)

<sup>∂</sup>*<sup>t</sup>* (3)

*TD* (2)

are temperatures of frozen region, density of frozen material, heat

*TD*) = *pd* − *CW*

are concentration and the vector of mass flux, respectively. These two param-

*<sup>C</sup>*) <sup>=</sup> *<sup>σ</sup>* \_\_\_ <sup>∂</sup>*<sup>C</sup>*

and *σ* are the vector of effective diffusivity and porosity of the dried material, respec-

tively. It is possible to find the distribution of temperature by simultaneously solving these equations. Initial and boundary conditions must be considered to solve these equations. Also, the thermodynamic equilibrium, governed at the interface of frozen and dried region, determines the relationship between the concentration of water vapor and the temperature of frozen region [2, 3]. It is evident that density and porosity of food material, along with moisture and fat content,

When an infinitely long slab of the proposed material is available, it can be assumed that all variations happen in direction orthogonal to the surface of slab (one-dimensional variation). The typical distribution of temperature in different layers (frozen, dried, and vacuum) and the concentration of water vapor in dried layer are shown in **Figure 2**. It is sufficient to show the

of interface (between frozen and dried regions), the temperature of vacuum, the concentration of water vapor in interface (between frozen and dried regions), and the concentration of water vapor in interface of vacuum and dried regions [2]. The sublimation will continue until the temperature of dried zone (in the interface) is kept under the melting point of frozen region [2]. The variation of temperature in dried region is a part of the parabolic. It is valid for frozen region, too.

, and *CR* are the temperatures in the middle of frozen bulk, the temperature

<sup>→</sup> . ∇ → From **Figure 3**, the concentration of water vapor in dried region is decreased by getting away from the interface (between frozen and dried layers). The necessary energy for this system is provided by electromagnetic waves at 2450 MHz. In [2], it is assumed that the electric field is approximately uniform throughout the material and its intensity equals to 12.5 KV/m. The total pressure and partial pressure of water vapor in the vacuum region are 0.29 and 0.075 mmHg, respectively. The drying time for this meat is measured 6 hours when applied electric field is nearly 10 KV/m [9]. Generally, the higher the electric field intensity, the smaller the drying time (**Figure 4**).

In [2], it has been shown that the optimum operation of freeze-drying process is obtained near the corona and melting point. For a slice of meat in a rectangular cross section, the variation of temperature and concentration happened in two dimensions. **Figures 5** and **6** are shown in simulation and experimental results [7].

**Figure 3.** The temperature (left) and concentration (right) profiles for a slab of beef meat in different times (reproduced from [2]).

**Figure 6.** The time variation of moisture content for a bar of meat with square cross section (reproduced from [7]).

Microwave Technology in Freeze-Drying Process http://dx.doi.org/10.5772/intechopen.74064 149

**Figure 7.** A setup used to microwave-assisted freeze-drying process (reproduced from [2]).

**Figure 4.** Dry time for a slab of beef meat (reproduced from [9]).

**Figure 5.** The temperature profile along X and Y axes for a bar of meat with square cross section (reproduced from [7]).

**Figure 6.** The time variation of moisture content for a bar of meat with square cross section (reproduced from [7]).

**Figure 4.** Dry time for a slab of beef meat (reproduced from [9]).

148 Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing

**Figure 5.** The temperature profile along X and Y axes for a bar of meat with square cross section (reproduced from [7]).

**Figure 7.** A setup used to microwave-assisted freeze-drying process (reproduced from [2]).

**Figure 7** shows a setup used in [9] for freeze-drying process by injecting microwave power. A microwave oven supplies sufficient adjustable energy. A magnetron with the capability of delivering 1.2 KW adjustable power at 2450MHz is used in the oven (A). The proposed material (D) is located in the middle of microwave cavity (B), and they are surrounded by a vacuum chamber (C). This cavity has dimensions 39 × 39 × 51 cm, all of its walls are made of perforated aluminum sheets to supply the needed electromagnetic boundary conditions and provide a path to free flow of water vapor simultaneously. To avoid harmful reflection from the cavity, a circulator is used just after the generator. To absorb the reflected power, it is necessary to match other ports of the circulator. A twist (J) is used to change the polarization of transmitted wave. The electric field, at the output of twist, is vertical to slab of beef meat. A bidirectional coupler (H) is used to measure the forward and reflected waves. These data are used to determine lost power, including all components in addition to proposed material (D) [2].

migration of birds and insects. Also, Doppler radar is used to monitor the mass flow rate of crop [12], detecting and controlling the insects in stored grains and heating seeds with impermeable coat by microwave radiation to improve their germination and determination

Microwave energy is used to defrosting meat. It reduces the required time from hours to a few minutes. Also, it is used in sterilizing some heat-sensitive foods and cacao bean roast-

In microscopic scale, when a dielectric is subjected to the electric field, their molecules are arranged to reduce the overall electric field in the bulk of dielectric (**Figure 8**). This arrangement depends on constitutive molecules and their polarizations. In other words, the mol-

The molecules start to oscillate by applying the electric field with sinusoidal variation. Friction between molecules in the oscillation produces heat (as a thermal source) and increases the temperature of dielectric [7, 10]. Since the needed energy for oscillating molecules is provided by the electric field, the generated heat is as a result of energy conversion (from electromagnetic to thermal). Another phenomenon, which is effective in the loss factor of a dielectric, is ionic conduction. It relates to movement of dissolved ions, and the generation of heat when these ions collide with other molecules and atoms [10]. In a macroscopic view, this phenomenon is characterized by imaginary part of permittivity. Also, real part of permittivity is known

Generally, the electromagnetic properties of each material are specified by relative electric

″ \_\_ *εr*

, *tan*(*δ*) <sup>=</sup> *<sup>ε</sup><sup>r</sup>*

), both of them are complex quantities. The real

Microwave Technology in Freeze-Drying Process http://dx.doi.org/10.5772/intechopen.74064 151

″ |*E*|<sup>2</sup> (4)

, which are known as dielectric constant and loss factor, are related

′, *pd* = <sup>0</sup> *ε<sup>r</sup>*

of moisture content of agricultural products [12].

ecules reacted to the applied field.

as an ability of structure to be polarized.

) and magnetic permeability (*μr*

to stored and dissipated electrical energy in the material, respectively [12]:

′ − *j ε<sup>r</sup>* ″

**Figure 8.** The arrangement of molecules when dielectric is subjected in external electric field.

ing [12].

permittivity (*ε<sup>r</sup>*

and imaginary parts of *ε<sup>r</sup>*

*ε<sup>r</sup>* = *ε<sup>r</sup>*

Also, [3] presents a microwave freeze-drying setup in a laboratory scale.
