ultrasonic absorption in carbon dioxide-water-vapor mixtures

10.4 Received 21 July 1967

Ultrasonic Absorption in Carbon Dioxide-Water-Vapor Mixtures

ROLAND W. Hmos AND RALPH H. TORBORG

Honeywell Corporate Research Center, Hopkins, Minnesota 55343

The absorption of ultrasound in CO2-H•.O mixtures at 150 ø and 200øC was measured at frequencies of 1.25, 3.3, 4.8, 9.9, and 14.0 MHz for H•.O vapor concentrations from 0.5% to 50%. The measured absorptions are compared with calculated results and agree reasonably well. The effect of H•.O vapor on the relaxation frequency is linear at least up to 20% H20 vapor and a decrease in relaxation frequency is observed with increasing temperature.

INTRODUCTION

HE strong effect of water vapor on the relaxation times for the activation and deactivation of the

vibrational modes of CO2 has been reported by Knudsen and Fricke I and by Lewis and Lee? They found a linear relationship between water vapor concentration and relaxation frequency at low percentages (<1%) of water vapor. Lewis and Lee have shown that the relaxation frequency decreases with temperature. This temperature relationship differs from that predicted by the Landau-Teller theory a and can be attributed to a chemical affinity of a dipole interaction explained in the theory of Widom and Bauer. 4 Because of our measurements of the ultrasonic attenuation in the flue

gases of natural gas-air flames, we were interested in extending the investigation to determine the effect of larger concentrations of water vapor on the sound absorption in carbon dioxide.

I. EXPERIMENTAL METHOD

Figure I shows the experimental apparatus, which consists of a system to produce H20-CO• mixtures and an interferometer. Dry CO•. is bubbled through two frits containing distilled water. The concentration of H, in the CO,depends upon the bath temperature, which is controlled to =t=0.1 øC. The temperature used to calculate the H20 concentration is measured above

• V. O. Knudsen and E. F. Fricke, J. Acoust. Soc. Am. 12, 255-259 (1940).

• J. W. L. Lewis and K. P. Lee, J. Acoust. Soc. Am. 38, 813-816 (1965). Other references to the literature are found in this paper.

a L. Landau and E. Teller, Physik. Z. Sowjetunion 10, 3443 (1936).

4 B. Widom and S. H. Bauer, J. Chem. Phys. 21, 1670-1685 (1953).

the second frit; it is the lowest temperature in a heated line through which the mixture flows to the base of the interferometer.

The interferometer is located in a chimney that is heated to the desired temperature. Temperature gradi- ents are reduced by adjusting the power supplied to heaters located along the length of the chimney. In the region near the interferometer, the temperature read- ings above and below the quartz delay lines differed by approximately 1 øC. A pressure of about 1-2 in. of water was maintained in the chimney to exclude other gases. A double transducer pulse technique is used to measure the absorption and velocity. Two 3-in. long fused quartz rods served to transmit the ultrasound into and out of the high temperature region, thereby allow- ing the transducers to remain at room temperature.

In a given test, the H•.O concentration was varied and the frequency held constant, similar to the technique

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Fro. 1. Equipment assembly.

1038 Volume 42 Number 5 1967

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ABSORPTION IN CO•.-H20 VAPOR MIXTURES

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2 4 6 8 I0 20 40 60

MOLE Yo H20 IN CO 2

Fro. 2. Effect of H20 vapor on the sound absorption in CO2 at 150øC; calculated results--solid line; experimental results-- symbols.

9.9MHz

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0 I I I I I I I i I I • b 2 4 6 8 IO 20 40

MOLE % H20 IN CO 2

Fro. 3. Effect of H•O vapor on the sound absorption in CO• at 200øC; calculated results--solid line; experimental results-- symbols.

reported by Pielemier, Saxton, and Telfair. 5 The velocity was measured by using a time-of-flight technique and absorption determined by measuring the signal attenuation as a function of distance.

The accuracy of our experimental technique was checked by measuring the propagation constants of several gases at room temperature. Absorption coeffi- cients of Ar, N2, and O2 were measured and agreed within q-5% of the values measured by Fujii, Lindsay, and Urushihara. 6 The measured values of ultrasonic

velocities in CH4, N2, and O2 agreed within 4-1.0% of the values published by Kelly 7 and Tempest and Parbrook. a

The H20-CO2 data were analyzed by calculating the classical absorption and the absorption associated with the relaxing vibrational specific heat of CO2, using relations given by Herzfeld and Litovitz. ø The viscosity, ratio of specific heats, and force constants of the mixtures were calculated from relations given by Hirsch- felder, Curtiss, and Bird? The data used were obtained from Ref. 10 and the U.S. NationalBureau of Standards Circular No. 564.

The ideal-gas formula was used to calculate the low- frequency velocity for the various mixtures and the relations given by •'Herzfeld and Litovitz were used to calculate velocities as a function of frequency.

* W. H. Pielemier, H. L. Saxton, and D. J. Telfair, J. Chem. Phys. 8, 106-115 (1940).

0 y. Fujii, R. B. Lindsay, and K. Urushihara, J. Acoust. Soc. Am. 35, 961-966 (1963).

7 B. T. Kelly, J. Acoust. Soc. Am. 29, 1005-1008 (1957). a W. Tempest and H. D. Parbrook, Acustica 7, 354-362 (1957). 0 K. F. Herzfeld and T. A. Litovitz• Absorption and Dispersion

of Ultrasonic Waves (Academic Press Inc., New York, 1959), Topic 15.

•0 j. O. Hirschfelder, C. F. Curriss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954), pp. 529-530, 120, 168.

II. RESULTS

Measurements on CO2-H20 mixtures were made at 150 ø and 200øC for frequencies of 1.25, 3.3, 4.8, 9.9, and 14.0 MHz. The H20 concentration varied from 0.5%-50 mole %. Measurements of absorption at the two temperatures are shown in Figs. 2 and 3. The frequency is kept constant and the concentration varied; this amounts to varying the relaxation time, or relaxation frequency. The maximum absorption occurs where the relaxation frequency equals the driving frequency. The relaxation frequency is plotted as a function of the H20:concentration in Fig. 4 and found to be linear at both temperatures. The equations of the straight lines fitted to the data are at 150øC,

f0= 0.03+0.570m, (1)

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Pz•. •. •elaxation œzequency of CO•-H•O m•xtures at 150 ø and 200øC.

The Journal of the Acoustical Society of America 1039


HIGGS AND TORBORG

35000

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.%2 000 • • I I I i I I l 8 I 0 2 4 6 8 I0 12 14 16 I 20 22

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FIG. 5. Calculated velocity dispersion at 150øC.

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I I I I I I • I I 0 4 8 •2 •6 20 24 8 •2 36

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Fro. 6. Calculated velocity dispersion at 200øC.

o

and at 200øC, f0= 0.05+0.439m, (2)

where f0 is the relaxation frequency and m is the per- centage water vapor. The values of f0 for 0% water vapor were obtained by extrapolation and are consistent with previously published values n at these temperatures.

The fit to the data was obtained by calculating the relaxation strength. Additivity of the relaxing specific heats of CO2 and H20 was assumed; however, the specific heat of H20 vapor makes a negligible contribu- tion because of its low value and because of the concentrations used. The fit to the data for 9.9 and 14 MHz

in Fig. 2 is poor; both experimental curves have their maxima at nearly the same concentration of water vapor.

The experimental velocity data were widely scattered and, therefore, the velocities shown in Figs. 5 and 6 were calculated for 150 ø and 200øC using relations given by Herzfeld and Litovitz •2 and the ideal gas formula. The relaxation frequencies were obtained from the peaks in the absorption data. Our velocity data at 14 MHz and 150øC were in fair agreement with the calculated curve, and the value of the high-frequency velocity for carbon dioxide at 150øC compares favorably with the value shown in curves published by Henderson and

n F. D. Shiel•ts, J. Acoust. Soc. Am. 29, 450-454 (1957). x2 Ref. 9, Topic 12.

Klose la at 146øC. The shape of the velocity curves are the result of changes in the molecular weight, ratio of specific heats, and relaxation times with changes in H•O concentrations.

In mixtures of two excitable gases, one should expect two different relaxation processes--one associated with CO2 and one associated with H20. The relaxation of the vibrational degrees of freedom in H•O are not de- tectable because of the low specific heat of H•O compared to the specific heat of CO•. Further, the relaxation frequency of H20 is higher than those used in these ex- periments as shown by Yamada and FujiiJ 4 We assumed, then, that the relaxation frequencies associated with absorption peaks are those of the vibrational degrees of freedom of CO• and the agreement of our data with the calculated absorption substantiates this. Thus, the effect of H•O vapor on the relaxation frequency is linear at least up to 20% H•O vapor and a decrease in relaxation frequency is observed with increasing temperature.

ACKNOWLEDGMENT

The research reported in this paper was sponsored by Consolidated Natural Gas Service Corporation, Cleve- land, Ohio.

x8 M. C. Henderson and J. Z. Klose, J. Acoust. Soc. Am. 31, 29-33 (1959).

x4 K. Yamada and Y. Fujii, J. Acoust. Soc. Am. 39, 250-254 (1966).

1040 Volume 42 Number 5 1967


ultrasonic absorption in carbon dioxide-water-vapor mixtures

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