444 Chapter 25
relatives to air, and for this reason, the vari-
able is dimensionless (Eq. 25.2 ).
εεεr= * 0 (25.2)
In this equation ε 0 represents the air per-
mittivity (8,8542 × 1 0^ −^12 F/m).
When complex permittivity is drawn as a
vector (Fig. 25.2 ), real and imaginary parts
are diphase 90 °. The sum vector forms a δ
angle with real axis ( ε ′ ). The ratio between
real and imaginary parts of permittivity rep-
resents another important parameter, the loss
tangent (Eq. 25.3 , which represents a measure
of the food ability to the energy dissipation
(Ponne and Bartels 1995 ; I ç ier and Baysal
2004 ).tanδ
ε
ε=
′′
′==D
Q1
(25.3)In Equation 25.3 , D is called the dissipa-
tion factor, and Q the quality factor. Tan δ
can be defi ned as the energy lost per cycle
divided by energy stored per cycle (Grimnes
and Gr ø ttem - Martinsen 2008 ).Figure 25.1 presents the electromagnetic
spectrum, which is characterized by different
types of radiation on the basis of wavelength
and frequency.
Electromagnetic waves are composed of
an electric and a magnetic fi eld. Due to the
fact that foods do not present components
that can interact with the magnetic fi eld, it is
possible to assume that food permeability is
similar to that of free space ( μ 0 = μ = 4 π
10 −^7 H/m) (Regier and Schubert 2005 ) and to
consider only the complex permittivity ( ε (^) r ) as
the dielectric property that describes the
behavior of the food when it is subjected to
an electromagnetic fi eld (Metaxas and
Meredith 1993 ; Nelson and Datta 2001 ).
Complex permittivity is defi ned by the next
equation:
εε εr= ′−⋅j ′′ (25.1)
In this equation,
j=−^1
the real part of complex permittivity is
called the dielectric constant ( ε ′ ) and the
imaginary part is called the loss factor ( ε ′′ ).
The dielectric constant is related with the
capacitance of the material and its ability
to store energy (polarization). Foods are
nonideal dielectrics and polarization has
associated dissipation phenomena, producing
energy absorptions and the decay of the
dielectric constant. The parameter that
refl ects the absorption and dissipation of
electromagnetic energy is the loss factor. The
subscript “ r ” indicates that the values are
Figure 25.1. The electromagnetic spectrum.
Figure 25.2. Diagram of loss tangent vector.