Ultrasonic Velocity and Thermal Relaxation in Dry CO2 at Moderate Pressures

Abstract

The velocity and absorption of ultrasound in dry CO2 have been measured along the 50.8 ø isotherm with a Hubbard-type, variable path, recording acoustic interferometer at six frequencies from 300 kc to 7 mc and from 0.3 to 250 atmos, i.e., up to liquid densities. Velocity dispersion is clearly shown in addition to the change in velocity attributable to the nonideality of the gas. The values of the frequency/density ratio at which the transition from V02 to V• 2 is half-completed as the pressure is lowered, and at which the maximum absorption per wavelength occurs, were measured wherever possible. From these determinations the relaxation time of the gas has been determined as a function of the density. It proves to be inversely proportional to the density up to the highest density reached (0.8 g/ml), indicating that ternary collisions have not become important and that the number of binary collisions required to excite the internal vibrations does not vary with density. At 50.8 ø and one atmosphere the relaxation frequency 1/2,rr is about 26 kc and the number of collisions required to excite the molecule is 48 500. The extra absorption (in excess of the classical) remains a consequence of thermal relaxation up to liquid densities, and no new mechanism need be postulated to explain it. Further work at higher densities and other temperatures is in progress.

Melting curve and fluid equation of state of carbon dioxide at high pressure and high temperature

“…As a consequence, for ωτ v ∼ 1 the sound velocity goes from its low-frequency ("static") value v 0 s to an unrelaxed value v ∞ s . The presence of a thermal relaxation in gaseous and liquid CO 2 is a long-known and well documented phenomenon 34,35,36 . The relaxation frequency ω r was found to be a linear function of density in the gas phase, whereas it increases more rapidly in the liquid.…”

“…The presence of a thermal relaxation in gaseous and liquid CO 2 is a long-known and well documented phenomenon 34,35,36 . The relaxation frequency ω r was found to be a linear function of density in the gas phase, whereas it increases more rapidly in the liquid.…”

Speed of Sound in (Carbon Dioxide + Propane) and Derived Sound Speed of Pure Carbon Dioxide at Temperatures between (248 and 373) K and at Pressures up to 200 MPa

“…The high-density experimental data, along with relevant low-density results, are compared with the present model in Figure . The results of Henderson and Peselnick at T = 323 K are scattered but agree with the model on the average, while those of Bass and Lamb are between 7 % and 14 % greater than the model predicts. The measurements of Madigosk and Litovitz agree with our model to within ±7 % .…”

“…Although somewhat oversimplified, this approach is expect to provide a reasonable estimate of the vibrational-relaxation time in gas, liquid, and supercritical states. Although related to compressed CO 2 , the results of Bass and Lamb and Henderson and Peselnick all fall at densities below ρ cross and hence they were not relevant to the estimation of the parameter a .…”

“…Vibrational relaxation times in dense CO2 have been reported by Bass and Lamb, 23 Henderson and Peselnick, 24 We now have a basis for modelling the absorption and dispersion of ultrasound in pure carbon dioxide as functions of both frequency and the thermodynamic state of the fluid. In figure 3, we plot the absorption coefficient α as a function of T along isobars at pressures up to 200 MPa and at frequencies of (0.5, 1, 2 and 5) MHz.…”