|MadSci Network: Physics|
1. S. Ramo, J. R. Whinnery, T. Van Duzer,
Fields and Waves in Communications Electronics
John Wiley & Sons, New Your, 1967
2. A. Von Hippel, Dielectric Materials and Applications
The Technology Press of MIT and John Wiley & Sons, NY, 1954
The answer to your question involves complex mathematical physics; however, I will
try to answer your question in words.
Before discussing particle size, relative to the length of an electromagnetic (EM) wave
there is a much more important issue in discussing the ability to heat any material.
The ability to heat a material depends on the material's transmission, absorption
and reflection properties at the EM wavelengths used for the heating. Technically this
is known as the Complex Permittivity of the material which has a real parameter
and an imaginary (mathematical) parameter.
The complex permittivity (CP) of a material is the same if the material is a dust,
a powder, or a solid. If the material is liquefied or vaporized then the CP
usually changes. The CP is also wavelength dependent; however, the particle size is not
a factor in the wavelength dependent characteristics of the material's CP. The CP
is dependent on the molecular structure of the material. What is important is to
determine if the material CP is a conductor, an imperfect dielectric or a near
perfect dielectric. For example graphite powder (and solid graphite) would be a
more absorptive material than silica sand which in a pure form as quartz is an
almost perfect dielectric. Thus bulk graphite powder could be heated easily at
any wavelength ranging from microwaves to infrared (IR) or visible light
wavelengths. Quartz (fused silica) in powder form would be very difficult to heat
at any wavelength. Thus quartz is transparent to both microwaves and to IR and
visible wavelengths and absorbs extremely small amounts of energy from an EM wave.
Technically the part of the CP related to a materials absorption is determined by
the ratio of the imaginary part of the CP divided by the real part of the CP. This
ratio is called the Loss Tangent of the material (labeled tangent (d) in text
books using the lower case Greek letter delta in place of d). A material with a high
loss tangent (approaching 1.0 ) at a given frequency is easy to heat. A material with
a small loss tangent (< 0.001) at a given wavelength is very difficult to heat.
Most materials are imperfect dielectrics and they transmit, reflect and absorb EM
waves. To heat the material you want to know it's absorption at a given wavelength.
There are many reference books that list the loss tangent of hundreds of materials
at microwave frequencies including References 1 and 2. Reference 2 is a classic in
the field and may contain the material that you are interested in.
The size of the electromagnetic (EM) wavelength relative to the particle size is
important only if the powder particles are individually suspended in air or a gas
as in a dust. Then for efficient heating you would want to have the heating
wavelength equal to or less than the particle diameter. In your example, a carbon
dioxide laser operating at wavelengths near 10 micrometers would be useful for
heating. A number of lasers operating at near one micrometer would be even be
better heaters. However, the loss tangent of the particle material remains the
primary factor that determines the efficiency in heating the particle with an EM wave. The EM wavelength can enhance the coupling of energy into
the CP of the particle if the wavelength is less that the particle size.
A general comment: most dry powdered materials, such as packaged food products, are not
easily heated in a microwave oven because they have low loss tangents at microwave
frequencies. To overcome this problem some water or oil with a large loss tangent
is added to and absorbed within the particles or they are immersed in the oil
or water before microwave heating. You can find a number of discussions about
microwave ovens and heating materials by searching the Mad Science Archives.
Best regards, Your Mad Scientist
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