Introduction - Microwave-Assisted Concrete Technology: Production, Demolition and Recycling - page 27

4000

2.45 GHz
10.6 GHz
18 GHz

3500

3000

2500

2000

1500

1000

500

0

0 2 4 6 8 10

Distance from the Microwave Exposed Surface (cm)

Figure 1.18 Variation of the electric field norm within a saturated concrete specimen.

frequencies is shown in Figure 1.18. As can be seen, the electric field norm
and thus the microwave power in the concrete seem to attenuate expo-
nentially within a concrete specimen. In addition, the penetration depth
decreases substantially with an increase in microwave frequency.

1.8.1 Lambert's law
Lambert's law is the most common approximation used to estimate micro-
wave power dissipation. This method considers an exponential decay of
microwave energy absorption inside the dielectric material. The original
form of Lambert's law may be written as

() =

− 2β x

Ix Ie (1.34)

0

where I ( x ) is the transmitted power flux into the medium, and I 0 is the
incident power of microwaves. Equation 1.34 may be used to predict the
variations in the microwave energy with distance x from the microwave-
exposed surface of the material. Hence, the microwave energy dissipated at
a specific point inside a dielectric material may be estimated by differentiat-
ing I ( x ) with respect to x which results in

() =− ∂ ()
∂

Ix
x

− 2 β x

PL x = 2 β Ie (1.35)

0

Lambert's law, when applicable, is easy to use. However, prior to using
Lambert's law for microwave power estimation in a specific microwave