IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 5, OCTOBER 1998 1201

Sensing Pulverized Material Mixture Proportionsby Resonant Cavity MeasurementsStuart O. Nelson,Fellow, IEEE, and Andrzej W. Kraszewski,Fellow, IEEE

Abstract—Based on differences in the permittivity of coaland limestone rock, a resonant cavity measurement technique ispresented for the rapid determination of the proportions of coaland limestone in powdered mixtures. The ratio of the resonantfrequency shift and the change in the transmission factor whenmixed coal and limestone samples are inserted into the cavityprovides a means for estimating the percentage of coal in themixture relatively independent of the bulk density of the mixture.The technique might be developed for rapid tests of dust in coalmines to determine whether the 65% noncombustible contentrequirement is being met for prevention of coal mine explosions.

Index Terms—Coal, dielectric properties, limestone, mixtures,permittivity, resonant cavity measurements, sensing.

I. INTRODUCTION

ROCK dusting in coal mines is required to reduce explo-sion hazards by providing at least 65% noncombustible

content in the combined coal dust and other dust in the mines[1]. Currently, the noncombustible content is determined byheating processes that burn the coal without decomposing therock dust. Techniques are needed for rapid reliable determi-nations of the rock dust content in samples of dust from coalmines.

Measurements of microwave permittivities of pulverizedcoal and pulverized limestone samples have been used toobtain the permittivities of the solid materials through use ofthe Landau and Lifshitz, Looyenga dielectric mixture equation[2]. This mixture equation implies the linearity of the cuberoot of the dielectric constant with bulk density of an air-particle mixture, and the usefulness of the relationship hasbeen demonstrated with a number of materials [3]–[5]. At11.7 GHz and 20 C the dielectric constants of dry coal andlimestone are 4.2 and 7.6, respectively, while the loss factorsare 0.16 and 0.06, respectively [2]. Thus, both componentsof the relative complex permittivity of coal and limestonerock have significant differences that should be detectable bysuitable measurements. Broad-frequency-range measurementsof coal and limestone permittivity showed reasonably smallvariations in dielectric constants between 200 MHz and 20GHz with both decreasing somewhat at higher frequencies [6].Thus, it appeared reasonable to determine proportions of coaland rock dust by measurements of the permittivities of dustsamples. Therefore, resonant cavity measurements have beenexplored for this purpose.

Manuscript received May 18, 1998; revised November 30, 1998.The authors are with the U.S. Department of Agriculture, Agricultural

Research Service, Russell Resarch Center, Athens, GA 30604 USA.Publisher Item Identifier S 0018-9456(98)09775-7.

II. PRINCIPLES

Resonant cavity measurement techniques are convenient formeasuring the relative dielectric complex permittivity

of materials at single microwave frequencies Here,isreferred to as the dielectric constant andis the dielectric lossfactor. It follows from resonant cavity perturbation theory, thatwhen a dielectric object of low loss, is inserted intothe cavity, the change in the resonant frequency and thechange in the cavity transmission factor can be expressedas follows [7]:

(1)

(2)

where

resonant frequency of the empty cavity;-factor of the empty cavity;

shape factor for the dielectric object;volume of the sample (object);volume of the resonant cavity.

For the sample configuration used in this study, the shapefactor is approximately one.

Use of these equations and the ratio for measure-ments on low-loss dielectric objects has shown that desiredpermittivity-related characteristics of objects can be deter-mined independent of object mass [8], [9]. Thus, the techniquecan be expected to sense permittivities of powdered samplesrelatively independent of the bulk density of the powderedmaterials. This would be an important advantage, since bulkdensities of powdered materials vary greatly, depending onsettling or packing, and carefully controlling the degree ofpacking would be troublesome for a practical measurement.

III. M ATERIALS AND METHODS

Pulverized samples of Pittsburgh coal and limestone %calcium carbonate), with most particle diameters ranging from5 to 100 m, were furnished by the Pittsburgh ResearchCenter, National Institute of Occupational Safety and Health(formerly U.S. Bureau of Mines). Moisture content, deter-mined by drying samples for 24 h at 105in an air oven, was1.4% for the coal and 0.5% for the limestone. Samples of purecoal and pure limestone and mixtures ranging from 10.00% to80.00% coal, by weight, were prepared for the microwaveresonant cavity measurements.

0018–9456/98$10.00 1998 IEEE

1202 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 5, OCTOBER 1998

Fig. 1. Cross section of rectangular waveguide resonant cavity and sampleholder, showing coupling irises (1), waveguide flanges (2), aluminum sleeves(3), 12-mm glass tube (4), and Delrin cap (5) with O-ring seals (6).

A resonant cavity, constructed from-band (IEC R-22,WR-430) rectangular waveguide for previous work [7], wasconnected through 3-cm-diameter coupling holes in the centerof brass plates at each end of the cavity and waveguide-to-coaxial adapters to a Hewlett-Packard1 8510B MicrowaveNetwork Analyzer for the measurements. The cavity, 65.1cm in length and operating in the TE mode, had 31.75-mm circular openings in the wide walls at the center of thewaveguide with 31.75-mm i.d. aluminum sleeves projecting5.08 cm outside the waveguide walls perpendicular to thelongitudinal waveguide axis (Fig. 1). These openings andsleeves were sized to prevent any energy loss from the cavityand provided an opening for samples to be inserted into thecavity.

Powdered samples were held in a 12-mm Pyrex glasstube positioned vertically and extending through the cavity inalignment with the maximum E field at the center of the cavity(Fig. 1). The glass tube was held firmly in a machined Delrincap that fitted over the lower cylindrical sleeve, concentric withthe bottom opening in the waveguide wall at the center of thecavity, thus holding the glass tube in position in the resonantcavity. O-rings in the Delrin cap facilitated snug fitting of boththe glass tube sample holder and the sleeve projecting fromthe waveguide to hold the sample precisely in position. Theresonant frequency of the cavity with the empty glass-tubesample holder in the cavity was 2.473 GHz.

A reference line 1.27 cm from the top of the glass tube wasprovided for accurate volumetric determinations for samplesheld in the tube. Powdered coal and limestone samples werepoured slowly into the glass tube sample holder with the aidof a glass funnel. The sample and sample holder, consisting ofthe 15.9-cm-long glass tube and the Delrin cap, were weighedto 0.01 g for determination of sample mass, the sample wassettled to the reference line, and the sample holder assemblywas placed in the cavity for the microwave measurements.Then, additional sample material was added, and the wholeprocedure was repeated several times to provide the numberof densities desired for the measurement sequence.

With the network analyzer set for proper ranges of thefrequency and the voltage transmission coefficient the“marker-to-maximum” command provided the coordinates of

1Mention of company or trade names is for purpose of description onlyand does not imply endorsement by the U.S. Department of Agriculture.

the peak of the resonance curve both with the sample holderempty and with the sample in place. Thus, the informationnecessary for the ratio was obtained.

Preliminary measurements on powdered samples of purecoal and limestone and mixtures ranging from 10% to 80%coal showed that the ratio was relatively insensitiveto the mixture bulk density, particularly at higher percentagesof coal in the mixture [10]. There is some decrease in the

value with increasing density, and that slope increasesslightly with increasing limestone percentage [10].

Therefore, for subsequent measurements, the density ofpowdered samples was not determined, but a uniform pro-cedure for filling the glass tube sample holder was followedto minimize the remaining influence of sample bulk density.The 12-mm glass sample holder was filled by pouring thepowdered samples through a glass funnel. Then the sampleholder, consisting of the 12-mm glass tube and the Delrin capin which it was held, was tapped vertically on the laboratorybench three times before it was placed into the resonant cavityby inserting it through the opening in the lower wide wallof the cavity and raising it until the Delrin cap was seatedover the sleeve projecting from the bottom of the cavitywaveguide section.

A series of resonant cavity measurements was taken toprovide a calibration curve. Powdered coal–limestone mixturesamples of 0, 10, 20, 40, 60, 80, and 100% coal, were eachpoured into the sample holder and inserted into the cavity, aftersettling as described, five times each, and four measurementswere taken with the network analyzer for each of the fivereplications. This provided 20 measurements at each of sevencoal percentages for the calibration. The calibration data werefitted by a least-squares regression technique, by using all 140data points, to an exponential equation that could be easilyused as a calibration equation.

To test the performance of the measurement for determiningcoal percentage in mixed samples of coal and limestone,additional samples were mixed to provide 30.00 and 50.00%coal samples, and another series of resonant cavity measure-ments was performed on samples of 10–60% coal by 10%increments. For these performance tests, three replicate mea-surements were used with five repeated measurements with thenetwork analyzer on each for a total of 15 measurements foreach of the six mixture percentages. Predicted coal percentagesfor each measurement were then calculated according to theexponential calibration equation.

IV. RESULTS AND DISCUSSION

The calibration curve provided by measurements on thecalibration data set of coal–limestone mixture samples isshown in Fig. 2, where the points are the mean values of the20 measurements at each mixture percentage. The followingtractable equation was fitted to the data with high precision,

where is the coefficient of determination

(3)

The resonant frequency shift change in the transmis-sion factor and ratio, along with the standard

NELSON AND KRASZEWSKI: SENSING PULVERIZED MATERIAL MIXTURE PROPORTIONS 1203

Fig. 2. Relationship between�f=�T (y) and coal percentage incoal–limestone powder mixture (x) for calibration data set:y = aeb=(c+x);wherea = 6:949; b = 102:8; and c = 43:82:

TABLE IMEAN VALUES OF 20 MEASUREMENTS FOR

EACH MIXTURE (CALIBRATION DATA SET)

deviation of that ratio, are shown for the calibration data inTable I. The precision of the measurements is on theorder of 1%, ranging from 0.5 to 2% over the entire range ofmixture percentages.

Solving (1) for the independent variable—coal percentagein the mixture—provides the following calibration equation:

(4)

By using (4), the percentage of coal in the coal–limestonemixture samples for the performance data set can be predicted.Results are summarized for the six different mixtures in theperformance data set in Table II. Precision of the repeatedmeasurements was very similar to the figures in Table I and aretherefore not included. The mean difference values for the 15measurements (predicted minus known mixture percentages)represent the bias present for each mixture percentage. Theoverall standard deviation of the differences for the wholeperformance data set includes the effect of the bias values ateach mixture percentage, and therefore constitutes a standarderror of performance (SEP) for this test of the calibration andmeasurement technique in predicting the mixture percentagefrom the determinations with the resonant cavitymeasurements. This (SEP) value was 1.84%, and the meanbias for all measurements was 0.22%.

In this performance test, the range of coal percentagein the coal–limestone mixture was limited to the 10–60%range, because the region of major interest is the 35–65%

TABLE IIMEAN VALUES OF 15 CAVITY MEASUREMENTS

FOR EACH MIXTURE (PERFORMANCE DATA SET)

coal–rock dust ratio at which level the minimum noncom-bustible content of 65% must be maintained. With calibrationover a narrower range than the total range investigated in thisstudy, the accuracy of the coal–rock dust ratio determinationcould probably be improved. The 1.8% standard error ofperformance obtained in this initial study, however, is certainlyof interest for practical use. Many other factors must alsobe considered, including the variation in moisture content ofdust samples in the coal mines, temperature variations thatmight be encountered, etc. The technique warrants furtherinvestigation, because the convenience of a rapid mixture-ratiodetermination, relatively independent of bulk density, offers anattractive advantage in the routine use of a practical instrumentwhich might be developed for testing such powdered samples.

V. CONCLUSIONS

The usefulness of a resonant cavity measurement and useof the resonant frequency-shift to transmission factorratio for determining the proportions of coal and limestonein pulverized coal–limestone mixtures has been demonstrated.The ratio provides a means for this determinationrelatively independent of the mixture bulk density. Initialcalibration and performance testing of the technique at 24has shown that the coal percentage in coal–limestone mixturesbetween 10 and 60% coal can be determined with a standarderror of performance of 1.8%. Although further research isrequired to study the influence of additional factors, thesimplicity of the measurement and accuracy demonstratedindicate promise for consideration of development work aimedat practical use of the technique. Further research is required todetermine the ultimate suitability of such measurements andthe performance that might be achieved with practical coalmine samples.

ACKNOWLEDGMENT

The authors are grateful to Dr. S. Trabelsi and Dr. K. C.Lawrence for their assistance.

REFERENCES

[1] CFR 30, Code of Federal Regulations, Mineral Resources 30, Part 75,Par. 75.403, 492, 1995.

[2] S. O. Nelson, “Determining dielectric properties of coal and limestoneby measurements on pulverized samples,”J. Microw. Power Electro-magn. Energy, vol. 31, no. 4, pp. 215–220, 1996.

[3] , “Estimating the permittivity of solids from measurements ongranular or pulverized materials,” inMater. Res. Soc. Symp. Proc., W.H. Sutton, M. H. Brooks, and I. J. Chabinsky, Eds., vol. 124, 1988, pp.149–154.

1204 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 5, OCTOBER 1998

[4] , “Estimation of permittivities of solids from measurements onpulverized or granular materials,”Dielectric Properties of Heteroge-neous Materials, A. Priou, Ed., vol. 6,Progress in ElectromagneticsResearch, J. A. Kong, Chief Ed. New York: Elsevier, 1992, Ch. 6.

[5] S. O. Nelson and T.-S. You, “Relationships between microwave permit-tivities of solid and pulverized plastics,”J. Phys. D: Appl. Phys., vol.23, pp. 346–353, 1990.

[6] S. O. Nelson and P. G. Bartley, Jr., “Estimating properties of solids frompermittivity measurements on pulverized samples,” inProc. Microwaveand High Frequency Heating 1997, Conf., Fermo, Italy, 1997, pp.488–491.

[7] A. W. Kraszewski and S. O. Nelson, “Contactless mass determinationof arbitrarily shaped dielectric objects,”Meas. Sci. Technol., vol. 6, pp.1598–1604, 1995.

[8] A. W. Kraszewski, S. O. Nelson, and T.-S. You, “Use of a microwavecavity for sensing dielectric properties of arbitrarily shaped biologicalobjects,” IEEE Trans. Microwave Theory Tech., vol. 38, pp. 858–863,July 1990.

[9] A. W. Kraszewski and S. O. Nelson, “Resonant cavity perturbationsomenew applications of an old measuring technique,”J. Microw. PowerElectromagn. Energy, vol. 31, no. 3, pp. 178–187, 1996.

[10] S. O. Nelson and A. W. Kraszewski, “Resonant cavity measurementsfor sensing pulverized material mixture proportions,” inProc. IEEEInstrumentation and Measurement Technology Conf., St. Paul, MN, May18–21, 1998.

Stuart O. Nelson (SM’72–F’98) was born in Stan-ton County, NE, in 1927. He received the B.S.and M.S. degrees in agricultural engineering andthe M.A. degree in physics from the Universityof Nebraska, Lincoln, in 1950, 1952, and 1954,respectively, and the Ph.D. degree from Iowa StateUniversity, Ames, in 1972.

From 1954 to 1976, he was a Research Engineerwith the U.S. Department of Agriculture, Lincoln,NE. He was also Professor of Agricultural Engineer-ing and Graduate Faculty Fellow at the University

of Nebraska. In 1976, he transferred his laboratory to the USDA’s RichardB. Russell Agricultural Research Center, Athens, GA, where he is an AdjunctProfessor and a member of the Graduate Faculty at The University ofGeorgia, Athens. His research interests include the use of radio-frequency andmicrowave dielectric heating for seed treatment, stored-product insect control,and agricultural product conditioning; studies of the dielectric propertiesof grain, seed, insects, coal, and minerals; methods of dielectric propertiesmeasurement; dielectric properties and density relationships in granular andpulverized materials; and moisture measurement through sensing dielectricproperties of agricultural products. These studies have been documented inmore than 350 publications.

Dr. Nelson is a member of ASAE, IMPI, AAAS, NSPE, CAST, OPEDA,Sigma Tau, Sigma Xi, Gamma Sigma Delta, and Tau Beta Pi. He is a Fellowof ASAE and IMPI. Honors include the IMPI Decade Award, NSPE Founder’sGold Medal as the 1985 Federal Engineer of the Year, USDA Superior ServiceAward, Professional Achievement Citation in Engineering from Iowa StateUniversity, the OPEDA Professional-of-the-Year Award, and election to theNational Academy of Engineering. He was awarded an honorary Doctor ofScience degree by the University of Nebraska, Lincoln, in 1989.

Andrzej W. Kraszweski (M’89–SM’91–F’96) wasborn in Poznan, Poland, on April 22, 1933. He re-ceived the B.Sc. and M.Sc. degrees in electrical en-gineering from the Technical University of Warsaw,Warsaw, Poland, in 1954 and 1958, respectively,and the D.Sc. degree in technical sciences fromthe Polish Academy of Sciences (PAN), Warsaw,in 1973.

In 1953, he joined the Telecommunication In-stitute (PIT), Warsaw, where he did research anddevelopment of microwave systems and compo-

nents. In 1963, he joined UNIPAN Scientific Instruments, a subsidiary ofthe Polish Academy of Sciences, as Head of the Microwave Laboratory. In1972, he became the Manager of the Microwave Department of WILMERInstruments and Measurements, a subsidiary of the Polish Academy ofSciences in Warsaw, where he codeveloped microwave instruments formoisture content measurement and control. Beginning in November 1980, hewas a Visiting Professor at the University of Ottawa, Ottawa, Ont., Canada,where he did research on RF and microwave dosimetry. In January 1987 hejoined the Richard B. Russell Agriculture Research Center (U.S. Departmentof Agriculture) in Athens, GA, where he is involved in research on plantstructure and composition and quality assessment of agriculture products usingelectromagnetic fields. He is the author of several books on microwave theoryand techniques, has published well over 200 technical papers on the subject,and holds 20 patents.

Dr. Kraszewski is a member of Sigma Xi, the International MicrowavePower Institute, the Materials Research Society, the New York Academy ofSciences, and the Polish Electricians Association (SEP). He received severalprofessional awards, among them the State Prize in Science in Poland in 1980.