in considering potential dielectric heating applications. General principles ... of radio-frequency dielectric heating to agricultural problems. The first quantitative ...
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S. O. Nelson: Agricultural Applications of Dielectric Measurements
Agricultural Applications of Dielectric Measurements Stuart O. Nelson U. S. Department of Agriculture, Agricultural Research Service Athens, Georgia, 30604-5677, U. S. A.
ABSTRACT A brief historical perspective on dielectric properties of agricultural products is presented, including their use for rapid measurement of moisture content in grain and in considering potential dielectric heating applications. General principles are discussed as they relate to dielectric properties of materials and energy absorption from radio-frequency and microwave electric fields. Measurement principles and techniques for determining the dielectric properties of agricultural materials are described, and appropriate references are cited for detailed information. Dielectric properties data for some grain, insects, fruits, and vegetables are presented that relate to applications for selective heating of insects in grain and potential maturity and quality sensing in fresh fruits and vegetables. Principles are discussed for the use of microwave dielectric properties for sensing moisture content in grain, and relationships between dielectric properties of granular and powdered materials and their bulk densities are described. Index Terms - Dielectric properties, agricultural products, grain, moisture measurement, insects, fruits, vegetables, permittivity, granular materials, powders, permittivity-density relationships.
1 INTRODUCTION Electrical properties of agricultural products have been of interest for at least 100 years. One of the earliest applications for purposeful use of electrical properties was the study of dc electrical resistance of grain for rapidly determining its moisture content. Briggs [1] found a logarithmic increase in resistance between two brass rod electrodes inserted into a wheat sample as the moisture content of the wheat decreased. He also noted a nonlinear increase in resistance as the grain temperature decreased. In later studies with ac measurements, changes in the capacitance of sample-holding capacitors, when wheat and rye samples were introduced between the capacitor plates, were correlated with grain moisture content and used for grain moisture measurement [2, 3]. The subsequent development of electrical grain moisture meters has been treated in earlier reviews [4-7]. Use of electrical properties of grain for moisture measurement has been the most prominent agricultural application for dielectric properties data. In the early work, no quantitative data on the dielectric properties of the grain were reported. Interest generally focused on the influence of a grain sample on the response of an electrical circuit, and the instrument readings were calibrated with values measured by drying-oven techniques or other standard procedures for Manuscript received on 30 January 2005, in final form 26 May 2005.
moisture determination. The need for quantitative values of the dielectric properties arose from research on the application of radio-frequency dielectric heating to agricultural problems. The first quantitative data on the dielectric properties of grain were reported for barley along with a method for reliable measurement of those properties in the 1 to 50 MHz frequency range [8]. Quantitative dielectric properties data, obtained for similar reasons, were soon reported in the USSR for wheat and other grain and crop seeds [9]. Extensive measurements on grain and crop seeds in the 1 to 50 MHz range, taken over a decade of research on radio-frequency (RF) heating applications, were summarized and made available for use in electric moisture meter design and other applications [10]. The other principle use for dielectric properties of agricultural materials has been for use in research on potential dielectric heating applications. One of these was the possible selective dielectric heating for control of insects that infest stored grain [11]. The dielectric properties, or permittivity, of a material determine the interaction of the material with electromagnetic fields. For practical use, the dielectric properties of usual interest are the dielectric constant and the dielectric loss factor, the real and imaginary parts, respectively, of the relative complex permittivity, ε = ε ′ − jε ′′ = ε e − jδ where δ is the loss angle of the dielectric. Hereafter in this article, "permittivity" is understood
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IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 13, No. 4; August 2006
to represent the relative complex permittivity, i.e., the permittivity relative to free space, or the absolute permittivity divided by the permittivity of free space, ε 0 = 8.854 ×10 −12 F/m. Often, the loss tangent, tan δ = ε ′′ / ε ′ , or dissipation factor, is also used as a descriptive dielectric parameter, and sometimes the power factor § tan δ / 1 + tan 2 δ · is used. The ac conductivity of the ¨ ¸ © ¹ dielectric in S/m is σ = ωε 0 ε ′′ , where ω = 2πf is the angular frequency, with frequency f in Hz. In this article, ε ′′ is interpreted to include the energy losses in the dielectric due to all operating dielectric relaxation mechanisms and ionic conduction.
2 GENERAL PRINCIPLES The dielectric properties of materials dictate, to a large extent, the behavior of the materials when subjected to RF or microwave electric fields for purposes of heating or drying the materials. The power in W/m3 dissipated per unit volume in the dielectric can be expressed as
P = E σ = 55.63 × 10 2
−12
fE ε ′′ 2
where
(2)
ρ is its density in kg/m3. In drying applications, the latent heat of vaporization for water removed from the material must also be taken into account, because energy must be supplied for that purpose. From (1) it is obvious that the power dissipation is directly related to the dielectric loss factor ε ′′ ; however, it may also be dependent on the dielectric constant ε ′ in that, depending on the treating arrangement, the electric field intensity may be a function of ε ′ . Two simple examples illustrate this influence of relative values. In the RF dielectric heating of a layer of material of permittivity ε 1 of uniform thickness d1 between parallel-plate electrodes, with an air gap of permittivity ε 2 and thickness d 2 between the material and one electrode, the rms electric field intensity in the material is
V
d1 + d 2 (ε1 / ε 2 )
§ 3ε 1 · ¸¸ E 2 = E1 ¨¨ © 2ε1 + ε 2 ¹
(4)
where E1 is the electric field intensity in the infinite medium [12]. Thus, the value of the dielectric constants can have an important influence on the electric field intensity in the material to be heated, which according to equation (1) has an important influence on the power dissipation in that material. The absorption of microwave energy propagating through a material depends upon the variables of equation (1). Thus, the dielectric properties of the material are important. The frequency of the wave is also a factor, and the power absorption also depends on the square of the electric field intensity. For a plane wave, the electric field intensity E , which has an e jωt dependence, can be given as [13] (5)
(1)
c p is the specific heat of the material in kJ/(kg °C), and
E1 =
embedded in an infinite medium of permittivity ε 1 will have an electric field intensity in the spherical material of
E( z ) = E 0 e jωt −γz
where E represents the rms electric field intensity in V/m. The time rate of temperature increase, dT/dt in °C/s, in the dielectric material caused by the conversion of energy from the electric field to heat in the material is
dT P = dt cpρ
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where E0 is the rms electric field intensity at a point of reference, t is time, γ is the propagation constant for the medium in which the wave is traveling, and z is the distance in the direction of travel. The propagation constant γ is a complex quantity, and for nonmagnetic materials
γ = α + jβ = j
ε (6) λ0 where α is the attenuation constant, β is the phase constant, and λ0 is the free-space wavelength. The attenuation constant α and phase constant β are related to the dielectric properties of the medium as follows [13]:
α=
β=
ε′ §
λ0
· 2 ¨ 1 + tan δ − 1¸ 2© ¹
(7)
2π
ε′ §
(8)
2π
λ0
· 2 ¨ 1 + tan δ + 1¸ 2© ¹
As the wave travels through a material that has a significant dielectric loss, its energy will be attenuated. For a plane wave traversing a dielectric material, the electric field intensity at the site of interest can be obtained by combining equations (5) and (6) as follows: αz
(3)
where V is the rms potential difference between the electrodes. In a second example, a spherical inclusion of permittivity ε 2
2π
E( z ) = E 0 e − e j (ωt − βz )
(9)
where the first exponential term controls the magnitude of the electric field intensity at the point of interest, and it should be noted that the magnitude of this term decreases as the wave
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S. O. Nelson: Agricultural Applications of Dielectric Measurements
propagates into the material. Since the power dissipated is proportional to E 2 , P ∝ e −2αz . The penetration depth, D p , is defined as the distance at which the power drops to e −1 = 1 / 2.7183 of its value at the surface of the material. Thus, D p = 1 / 2α . If attenuation is high in the material, the dielectric heating will taper off quickly as the wave penetrates the material. Attenuation is often expressed in decibels/meter (dB/m). In terms of power densities and electric field intensity values, this can be expressed as [13]
§ P · § E · 10 log10 ¨¨ 0 ¸¸ = 20 log 10 ¨¨ 0 ¸¸ = 8.686αz P ( z ) © ¹ © E( z ) ¹
(10)
where P0 is the incident power, and P( z ) is the power at distance z into the material. The dielectric properties of the materials are very important in evaluating the penetration of energy that can be achieved. The attenuation in dB/m, combining (7) and (10), can be expressed in terms of the dielectric properties, ε ′′
