800
C. M. C R A T N D., C. THORN A N D ,J. R. R o w s
Vol. 61
TTTE DIET,ECTR.IC CONSTANT OF SOLID I’ARTICIJI AEROSOLS’ BY CULLEN
M. GRAIN,D O N A L D
c. ‘rE1ORN A N D Jnnms E. BOGGS~
Electrim1 Enginewing Research Laboratory and Deparlments of Ch,emistrU and Electrical Engineering, The University of Texas, Auslin 19, Texas Received FebruarW d f , I957
The tliclwtric constants of aerosols consisting of olystyrene, silver iodide or iron owder Riispondcd in dry nitrogen, or oil smoke aiispended in air have bcen measured a t a Frequency of 0400 megacycles. TEe rcsiilts are fitted well by the simpl? expression oqriation 1, in spite of the complexity and wide diversit,y of the systems Bt,iidicd. The ohRervcd data were well fittiJcdl?y this ccliint’ionw e n in cases where magnctic a s well as electric int,eractions would be expected.
The problem of the effective dielectric constant of a mixture of two substances of different dielectric constants has bcen considered by many authorsa-“ from a theoretical viewpoint. A considerable amount) of simplification is necessary for the mathematical treatment to be successful, and different autJhorshave workcd with quite different models. If considcratioii is restricted to aerosols, where t’he dielectric coiistant of the medium is essentially unitry, the size of the part,icles is small compared with the wave length of the measuring radiation, and interaction between suspended particles may be ncglect>ed,the results of these various invest,igat8ionscan all he expressed in the form A E = 3.0
e1-1C
-X
e1+2p
10-0
where A t is the difference between the dielectric constant of the suspension and that of the medium, el is the dielectric const’ant of the suspended substance, C is the mass concentration of the suspension in micrograms per cc., and p is the density of the suspended material. The derivations of this formula still contain a number of restrictions which are not met by aerosols and by the usual methods of measurement. The derivation of L e ~ i n for ,~ example, assumes that the suspended particles are spheres, that no agglomeration of particles occurs, that the spheres are arranged in a cubical lattice and are stationary, and that the measurement is made with a plane-polarized electromagnetic wave. Numerous studies have been made12on the dielectric constant of two phase mixtures, but these have usually been done with coarse mixtures of high concentration rather than with aerosols, in order to obtain a value of Aa high enough t o measure by the older experimental techniques. The interpretation of the results is less simple than might be anticipated for aerosols where the suspended particles are small, far apart, and essentially independent of each other. I n recent years, techniques for the measurement (1) This work was supportrd by Air Force Contract AF 33(610)2842. (2) The authors would like t o express their appreciation for the valuable assistance of Herbert L. Mitchell and Jnines B . Magee. (3) H. A. Lorentz, Wied. Ann., 9, 041 (1880). (4) L. Lorens, ibid,,11, 70 (1880). (6) J. W. Rayleigh, Phil. M a g . , 34, 481 (1892). (0) K. W. Wagner, Arch. Eleklrolech.. 2 , 371 (1914). (7) D. A. G . Bruggeman, Ann. PhyRik, 24, 636 (1935). (8) R . W. Sillars, J . Inet. Elm. Engrs. ( L o n d o n ) , 80, 378 (1RR7). (9) L. Lewin, ibid., 94, 131, 65 (1947). (IO) H. C . Thacher, Jr., T m s JOURNAL, 56, 795 (1952). (11) J. Fricke. J . A p p l . Phgs., 24, 644 (1953); TIIIRJOURNAL, IT, 934 (1953). (12) C. A , P . Pcarco, Brit. J . A p p l . P h w . ? 6 , 3*58(1955).
of dielectric constants a t microwave frequency have bcen developed which make possible the detection of very small differences in dielectric constant with relative ease. D ~ r a i has n ~ ~measured the dielectric const’ants of liquid drop aerosols of dioctyl phthalate and triethylene glycol di-(2-ethyl butyrate) suspended in air. His measurements show good agreement with equation 1 over the concentration range of 0 t o 0.8 microgram per cc. The problem of the dielectric coiistant of solidparticle aerosols would appear to be more complex than that studied by Dorain, since here the suspended particles may be far from spherical and considerable agglomeration of the particles into clusters may exist. We have studied a number of such systems to see how well experimental measurements agree with the simple theory. The aerosols chosen exhibit a wide range of particle size and shape, degree of clustering, and density, dielectric constant, conductivity and permeability of the suspended substance. Experimental Apparatus.-All of the measurements were made a t a frequency of 9400 megacyclcs, using a Crain microwave refractometer.Id In this instrument, the resonance frequency of a microwave cavity, which depends on the dielectric const,ant of the material within the cavity, is used to stabilize a Klystron oscillator. The resulting fro uency is beat against that of a similar reference cavity an] oscillator, the beat frequency being a measure of the diberence in the dielectric constants of the materials in the two cavities. For our experiments, the aerqsol was passed through one cavity of the refractometer, then through a Cambridge “abnolute” filter,16then through the other cavity of the refractometter. The filter used will remove 99.95% of partiFles of 0.3 p size or larger. Thus the refractometer reading gives the difference between the dielectric constant of the suspension and that of the gas hose, or the contribution due t o the suspended particles. iffter passing through the second cavity, the gas was passed through a wet-test gas meter t o measure its volume. The weight of the suspended material i n the aerosol used was determined from the increase of weight of the filter during the run. From these two mea8urements, the averagc concentration of the aerosol during the experiment could be determined. The frequency difference between the two cavities was converted to a voltage and recorded continuously, giving a plot from which the average dielectric constant difference could be calculated. The pressure drop across the filter was measured, so that if a significant pressure difference developed between the two cavities, the run could be terminated. Aerosols.-Polystyrenc spheres with an average diameter of about 3 p were obtained from the Wright Air Development, Center. Under high magnification these were seen t80 be nearly perfect spheres with quite a narrow range of particle size. There was very little clust,ering. The powder (13) P. B . Dorain, “The Dielectric Propertiea of Aerosols,” Ph.D. Dissertation, Indiana Univerait,y, 1964. (14) C. M. Crain, R m . Sa. Inetr., 21, 466 (1950); C. M. Crain and C. E. Williams. Electronics, 29, 150 (1966). (15) D. H. Northrup, Chem. Eng. Progr., 49, 513 (1953).
12 was placed in a flask with a conical bottom and srtb,iected to moderate agit,atioii with an est,ernal vilxntor. A stream of carefully dried nitjrogcn was passed through tlir flnsk, t81iror~gli a scttling chnniber, through tlic iefrar~t~ometcr cavities, and then through the wet-test motcr. 7’110 nrrosol densit,y could be varied by dilut,ing tlic :wow1 strcittrn with drird 8 nitrogen, or, to some cst,erit, I,y vnryiiig tlic flow velocity 7’ and extent of agitation. 2 A silver iodide aerosol was grncrat,etl by heating solid X silver iodide in a zirr,onium oxide comlirist,ion tulw lirnted by a small tuhe furnace. Ihicd riit,rogcn w n ~passrtl over 4 4 the heated silver iodide, through n sriflicient length of t,iibinp: t o bring the temperature back to rooni t,cmpcraturc!, tlirorigh the refractometer cavities, through the wet,-tcst meter, then through a vacuum pump. IGlectJron micrographs of t)hc rcsulting silver iodide particles showctl t’liem t’o have an irregular shape with a moderate degrec of clustering and con0 siderable variation in size around an avcrnge diamet,er of 0 4 8 12 about 0.1 U , for the individual particles. pg./cc. An oil smoke aerosol was generate! I)y burning dicscl oil constant increment for polystyrene in an inadequate supply of air, uaing an asbestos wir,k. Fig. 1 .--Dielectric aero~olsas a function of mass concentration. The smoke was passed through a cold trap to remove water, and drawn through the refractometer cavities as before. Great care must be taken to remove all traces of water vapor, since it will be absorbed to some ext,ent by the filter and it, has such a high dielectric constant that sma.11 tr:Lces of it can give highly erroneous results. Electron micrographs showed this aerosol to have a strongly clustered structure, the clusters averaging about 1 micron in diameter witJh individual particles about 0.05 M . , 12 A sus ension of iron particles was obtnined, using “SF” I carbony? iron powder obtained from Antara Chemicals Co. 2 These particles average 3 p in diameter, 94’34 of them falling in the size range from 1.5 to 5 p . They contain W.2-W870 X 8 iron, the remainder being mainly carbon and nitrogen with d about 0.2y0 oxygen. The articles are nearly spherical and show lit’tle clustering. &he powdcr was diRpersed by ,i the same technique used for the polystyrene. A moderate amount of iron powder was found to set,tle out in the first refractometer cavity, giving a gradual shift in the base line 0 of the refractometer tracing for which a correction had to be made. 0 10 20 30 40 50 a./cc. Results Fig. 2.-Dielectric constant increment for silver iodide The density of polystyrene is 1.032 g./cc. The aerosols as a function of mass conceatrat.ion,
.
refractive index a t optical frequencies is 1.592, the square of which gives 2.54 for the dielectric constant. This agrees well with measurement,s a t one megacycle, and may be taken as the value of 9400 megacycles. Using these values, equation 1 becomes Ae = 0.98C X This line is plotted in Fig. 1, together with the measured points. The best line through the experimental points ha,s exactly the proper slope, but an intercept of A e = This presumably corresponds to a -0.5 X constant error in measurement and is within the error which can be expected in the absolute value of AB.
For silver iodide, the density is 5.67 g./cc. and the square of the optical index of refraction is 2.21. A crude measurement of the dielectric constant a t 9400 megacycles gave substy,e approaches infinity and (e - l)/(t 2) approaches 1 . At the same time, the effective p approaches0 and ( p - l)/(,u 2) approaches 1/2. Thus, for conducting particles, the magnetic effect should lower the observed frequency change below that’ predicted considering electric interaction alone. These considerations apply strictly only if one can assume that the e1ect)ricfield lines do not enter the conductor. At 9400 megacycles the depth of penetration is of about the same order as the diameter of tjhe particles used, and we have not tried to make a prediction of the quantitative effect of high electrical conductivity. Oil smoke is a rather indefinite thing chemically, hut we may assume that its density is around 1.95 g./cc., an average of a number of reported values for amorphous carbon. Amorphous carbon is a moderately good conductor, so the effective dielectric constant should be high. If el is h k e n as infinity,
+
+
(16) J. G . Linhart and 100 (1056).
-
T. H. B. Baker, Brit. J . A p p l . Phya.,
6,
NOTES
808 32
24
20.
I
s? X 16
4 8
0 0
5
10 16 20 25 pg./cc. Fig. 3.-Dielrctric constant increment for oil smoke aerosols as a function of mass concentration.
0 0
20 30 40 50 rg./cc. Fig. 4.-Dielect,ric constant increment for iron powder aerosols as a function of mass concentration. 10
equation 1 becomes A E = 1.54C X A € becomes rather insensitive t,o variations in el if z1 is large. Thus, a value of 50 for the dielectric constant of oil smoke would reduce the slope of the line by only about 6% from that calculated for an infinite dielectric constant. The predicted line and the observed points are compared in Fig. 3. It can be seen that the agreement is good in spite of the fact that no allowance has been made for magnetic interaction caused by the conductivity of the particles. Minor effects might not appear in our experi-
Vol. 61
ment because of the uncertainties involved jn our selection of the density and dielectric constant values. The density of the "SF" iron particles is 7.81 g./ cc. If the dielectric constant is taken as infinity, equation 1 becomes A e = 0.3%' X Figure 4 shows this line, together with the ohserved points. Our measurements on iron are probably less accurate than those on the other aerosols because of the refractometer background drift caused by settling of iron particles in the first cavity. It was assumed that this drift was linear with time, but this may not be exactly true. The best line which can be drawn through the experimental points will have an intercept of +0.6 X IOw8 for Ae, which can reasonably be attributed to instrumental error, and a slope of 0.28. This, qualitatively, is the effect we have seen should be observed for an aerosol made up of conducting particles, but it is doubtful here whether it is beyond the limits of experimental error. Conclusions Equation 1, developed by different authors on the basis of various highly restrictive models, has been shown to have surprisingly wide applicability in predicting the dielectric constant of aerosols. It is to be expected that this relationship might break down at high aerosol concentrations, because of interaction between the charge distribution in closely adjacent particles. Although we have tried to produce very dense aerosols, and have measured concentrations 65 times as high as those studied by Doraiii,lawe have seen no evidence of such a deviation. While it is recognized that suspensions of materials with high electrical conductivity or permeability will have a magnetic as well as an electric interaction with electromagnetic radiation, no such effect was observed with oil smoke and only a small effect, possibly not beyond experimental error, for iron powder. Our measurements have been made on substances with densities ranging from 1.032 to 7.81 g./cc., with dielectric constants from 2.21 t o infinity, with and without high permeability, on aerosols in concentrations from 2 to 50 micrograms per cc.,. having particles of widely different sizes and distributions of sizes and of widely varying degrees of clustering.
NOTES that in general the surface tension of liquids decreases with increasing gas pressures. Theoretical treatments of the effect are more numerous, with BY EMIL J. SLOWINSKI, JR.,ERNEST E. GATESA N D CHARLES Gibbs,2 Guggenheims and Rice' among those who E. WARINO have made important contributions. The effect Chsmislrs Department, (Iniveraitg of Connecticut, Storm, Connecticut is attributed to adsorption of the pressurizing gas
THE EFFECT OF PRESSURE ON THE SURFACE TENSIONS OF LIQUIDS
Received August 10, 1068
The only reported experimental measurements of the effect of pressurizing gases on the surface tensions of liquids are those of Kundt.' He found
( 1 ) A. Kundt, Ann. phveik. Chem., 12, 638 (1881). (2) J. W. Gibbs, "Collected Works," Vol. I, Yale Univeraity Preus, New Haven, Conn., 1948, pp. 219-269. (3) E. A. Guggenheim, J . Chem. Soc., 128 (1940). ( 4 ) 0. K.Rioe, J . Chem. Phyr., 16, 333 (1847).
