• Insulators or transparent (materials with low dielectric loss factor): Microwaves
undergo very low attenuation as they pass through this material (they cannot store
microwave energy in heat form).
• Absorbers (material with high dielectric loss factor): These materials absorb
microwave radiation, and therefore heat up; materials that absorb microwave
radiation are called dielectric materials.
The Lambert and Beer laws (Eq. 3.33) expresses the internal electric field as a
function of the distance from the irradiating source (Falciglia and Vagliasindi 2015;
Robinson et al. 2014).
E d ¼ E 0 e
d
D P
ð3:33Þ
where,
E d : internal electric field at distance d (Vm
À1 )
E 0 : incident electric field (VÁm
À1 )
d: distance from irradiating source (m)
D P : ability of electromagnetic waves to penetrate medium (m)
This energy is transferred into soil using rod, plate, or gauze electrodes. The
conversion yield of radio frequency energy into heat is very high (about 90%)
(Hiester et al. 2013; Roland et al. 2007). The distance between the antennae varies
depending on conditions at the site, but is generally in the order of 3–6 m (Kasevich
et al. 1996).
The two phenomena to consider with RFH are the power absorbed and the
microwave penetration. The power absorbed can be estimated by Poynting’s theorem (average power loss density—Eq. 3.34) (Acierno et al. 2004; Clark et al. 2000):
Q ¼
1
2
ωε 0 ε
0 tan δ E
j j
2 ¼
1
2
ωε 0 ε
00 E
j j
2
ð3:34Þ
where,
Q: power density (JÁm
À3
Ás
À1 )
ω: angular frequency (s
À1 )
ε 0 : vacuum permittivity (FÁm
À1 )
ε
0 : dielectric constant (medium’s electric energy storage capacity) (À)
tan δ: loss tangent parameter (energy loss required to store a given quantity of
energy)
E: magnitude of internal electric field (VÁm
À1 )
ε
00
: dielectric loss factor (medium’s ability to convert electromagnetic energy into
heat from dielectric polarization) (À)
The microwave penetration depth can be calculated as follows (for low-loss
dielectric materials (ε
00
( ε
0
) (Eq. 3.35) (Clark et al. 2000):
3 In Situ Thermal Treatments and Enhancements: Theory and Case Study
183
undergo very low attenuation as they pass through this material (they cannot store
microwave energy in heat form).
• Absorbers (material with high dielectric loss factor): These materials absorb
microwave radiation, and therefore heat up; materials that absorb microwave
radiation are called dielectric materials.
The Lambert and Beer laws (Eq. 3.33) expresses the internal electric field as a
function of the distance from the irradiating source (Falciglia and Vagliasindi 2015;
Robinson et al. 2014).
E d ¼ E 0 e
d
D P
ð3:33Þ
where,
E d : internal electric field at distance d (Vm
À1 )
E 0 : incident electric field (VÁm
À1 )
d: distance from irradiating source (m)
D P : ability of electromagnetic waves to penetrate medium (m)
This energy is transferred into soil using rod, plate, or gauze electrodes. The
conversion yield of radio frequency energy into heat is very high (about 90%)
(Hiester et al. 2013; Roland et al. 2007). The distance between the antennae varies
depending on conditions at the site, but is generally in the order of 3–6 m (Kasevich
et al. 1996).
The two phenomena to consider with RFH are the power absorbed and the
microwave penetration. The power absorbed can be estimated by Poynting’s theorem (average power loss density—Eq. 3.34) (Acierno et al. 2004; Clark et al. 2000):
Q ¼
1
2
ωε 0 ε
0 tan δ E
j j
2 ¼
1
2
ωε 0 ε
00 E
j j
2
ð3:34Þ
where,
Q: power density (JÁm
À3
Ás
À1 )
ω: angular frequency (s
À1 )
ε 0 : vacuum permittivity (FÁm
À1 )
ε
0 : dielectric constant (medium’s electric energy storage capacity) (À)
tan δ: loss tangent parameter (energy loss required to store a given quantity of
energy)
E: magnitude of internal electric field (VÁm
À1 )
ε
00
: dielectric loss factor (medium’s ability to convert electromagnetic energy into
heat from dielectric polarization) (À)
The microwave penetration depth can be calculated as follows (for low-loss
dielectric materials (ε
00
( ε
0
) (Eq. 3.35) (Clark et al. 2000):
3 In Situ Thermal Treatments and Enhancements: Theory and Case Study
183