Penetration depth, of microwave

Figure 2. Penetration depth of microwave energy as a function of specific resistivity or conductivity of the semiconductor material for microwave radiation of 10 and 40 Gc/s.11...

The penetration depth of waves is defined as the distance from the surface of the material at which the power drops to 1 /e from its value at the surface. The penetration depth of microwaves is equal to 15 mm for water at 20 °C. The electromagnetic energy transfer is ensured by matched alumina windows. The propagated mode within the reactor is theoretically the TEn mode. The interest of this system is to make very specific chemical reaction such as oxidation in aqueous medium under critical conditions. 

On the other hand, it must be kept in mind that a number of critical issues are linked with the application of microwave in chemical scale-up (Ondruschka et al. 2004). Firstly, penetration depth of microwaves in... 

Buschmuller et have demonstrated that microwave resonance can be used effectively as means to monitor the moisture levels in a fluidized-bed dryer during the granulation process. The penetration depth of microwave resonance may be limited to a few microns, and hence this technique may not have any real advantages over NIR which has also been used for monitoring moisture in dryers, and has the advantage of providing chemical information such as solvent levels in addition to water, and other important properties such as polymorphic form, and particle size. 

The key limiting factor is the penetration depth of microwave irradiation, which is only a few centimeters in most solvents at 2.45 GHz. An issue therefore arises in getting sufficient microwave power into the reaction mixture to achieve the desired heating effect. The core of a large reactor vessel will not receive any microwave radiation as it will all have been absorbed by the outer layers. As a result, the center is effectively conductively or convectively heated, and the potential benefits of microwave heating will be lost. Penetration depth does, however, vary with frequency. Only a limited number of Industrial, Scientific, and Medical (ISM) frequencies are allowed so as not to interfere with military and civil aviation frequencies and telecommunications. Alternative frequencies are used for other large-scale applications and thus may provide an alternative solution to the scale-up of micro-wave chemistry. ... 

This shows that the penetration depth decreases dramatically with increasing conductivity of the medium to be penetrated. This has been plotted (Fig. 2) for different specific resistivities of the medium and the frequency of 10-40 Gc/s11 at which microwave conductivity measurements are typically performed. It can be seen that with a specific resistivity of 10 Q cm, a penetration depth of only 2 mm can be expected. Figure 2 furthermore shows the doping densities at which the respective penetration depths can be expected for silicon. Whereas the lower frequency X-band of microwaves (8-12.5 Gc/s) offers some advantages for materials with very low resistance, the high-frequency microwave Ka-band (26.5 10... 

Prohling or imaging of a physical variable, e.g., monitoring of moisture diffusion process through an organic material is readily accomplished with low frequency dielectric sensors. Alternatively, a microwave probe can be used, but the sample penetration depth of the microwave probe would be limited, in many cases, to a few microns, whereas the penetration depth of low frequency dielectric measurements can be controlled by changing the separation between the sensor head electrodes. 

Microwaves sources include electron beams (e.g.. magnetron, klystron), semiconductors (e.g, Gunn diode, transistor) and masers (microwave amplification by stimulated emission of radiation) [88]. The depth of penetration d of microwaves into a dielectric is a function of the lo.ss factor S in the dielectric material and the frequency / of operation (or vacuum wavelength aq) [89] and is given by... 

Z. Peng, J.-Y. Hwang, J. Mouris, R. Hutcheon, X. Huang, Microwave penetration depth of in materials with non-zero magnetic susceptibility, ISIJ Int. 2010, 50(1 I), 1590-1596. 

Materials with relatively high values of the loss factor s") are characterized hy low values of the penetration depth (Dp), and, therefore, microwaves can he totally absorbed within the outer layers of these materials. For example, the penetration depth of water is 1.4 and 5.7 cm at 25 and 95 °C, respectively (Table 3). This means that dining the experiments in a water solution on larger scales, only some parts (outer layers) of the reaction mixture interact with microwaves to generate heat, which is then transported into the rest of the mixture conventionally (i.e., by heat convection and/or conduction mechanism). On the other hand, miaowaves can penetrate and pass through samples of materials with low values of the loss factor (e"). ... 

According to definition, the penetration depth is the point where 37% (1/e) of the initially irradiated microwave power is still present [6]. The penetration depth is in-... 

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