Ind. Eng. Chem. Res. 1988,27, 1743 Thermodynamics of Fluid-Phase Equilibria, 2nd ed.; PrenticeHall: Englewood Cliffs, NJ, 1986. Rabe, A. E.; Harris, J. F. “Vapor-Liquid Equilibrium Data for the Binary Systems, Sulfur Dioxide and Water”. J. Chem. Eng. Data 1963,8, 333-336. Reid, R. C.; Prausiniz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. Vimalchand, P. “Thermodynamics of Multi-polar Molecules”. Ph.D. Dissertation, The Johns Hopkins University, Baltimore, MD, 1986.
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Vimalchand, P.; Donohue, M. D.; Celmins, I. “Thermodynamics of Dipolar Molecules: The Perturbed-Anisotropic-Chain Theory”. In Equations of State: Theories and Applications; Chao, K. C., Robinson, Jr., R. L., Eds.; American Chemical Society: Washington, DC, 1985; pp 297-313. Xu, Y. N.; Hu, Y. “Prediction of Henry’s Constants of Gases in Electrolyte Solutions”. Fluid Phase Equilib. 1986, 30, 221-228. Received for review February 2, 1988 Accepted April 21, 1988
CORRESPONDENCE Comments on “Ultrasonic Technique for Dispersed-Phase Holdup Measurements” Sir: Your journal recently published a paper by Bonnet and Tavlarides (1987) concerning the ultrasonic technique for dispersed-phase holdup measurements, where our work on this topic (HavliEek and Sovovd, 1984) was quoted; however, it was not quoted quite correctly. Bonnet and Tavlarides report that we have correlated experimental data by a linear relationship between the velocities of the sound in the dispersion and in the individual phases and the fractional holdup. In fact, we have found a linear dependence of the sound pulse transmission time on the holdup, described by eq 6 in our paper: L / V = L X / V , + L(1- X ) / V , (1) Substituting 4 for X , t+fcir L / V , t2 for L / V l , and tl for L / V,, one obtains, after rearrangement,
their experiments with the transducers located outside the vessel and the shaft in the middle of the accoustic path, in spite of a significant distortion of the signal from the receiving transducer. For the on-line measurement with automatic evaluation, a sufficient quality of the signal is achieved far easier with the transducers immersed in the dispersion. Using the ultrasonic technique for holdup measurement, one can choose from both alternatives-either the noninvasive technique with the output on the oscilloscope,which is suited for the measurements on the laboratory scale, or the technique with the sensing probe immersed in the liquid and with the automatic evaluation of the transmission time, which can be used in larger equipment up to industrial scale for holdup monitoring and control.
Acknowledgment This is relationship 8 used by Bonnet and Tavlarides to correlate the results of their measurements, and it is called, according to Kuster and Toksoz (1974), the time-average model. In this way, Bonnet and Tavlarides confirmed our finding that the velocity of ultrasound in a dispersion under conditions typical for extraction is independent of the drop size and is described by eq 1 or 2. We would like to add that we used the frequency of ultrasound as 2 MHz and the size of drops as 0.1-2 mm. Accordingly, the maximum ratio of the sound wavelength to the drop diameter was equal to 10, as in the work by Bonnet and Tavlarides. Kuster and Toksoz concluded in their investigation of the velocity of sound in suspensions of solid particles that the time-averaged model was valid only when the ratio of the sound wavelength to the particle diameter was smaller than 0.03, as indicated in Figure 8 of their paper. This shows that the propagation of sound through liquid dispersions differs significantly from that through the suspensions of solids. The ultrasonic technique with a sensing probe immersed in the dispersion and with an automatic evaluation of holdup has been patented and used in our laboratory for continuous holdup measurement since 1982. It enabled us to measure the transient behavior of holdup in a reciprocating plate column extractor (Sovovd and HavliEek, 1986) and to control the holdup automatically. Bonnet and Tavlarides measured the pulse travel times directly on the oscilloscope screen. This method does not require as sharp and distinct signals as the automatic evaluation. This fact permitted them to perform part of OSSS-5SS5/SS/2627-1743$01.50/0
The technique for continuous measurement of the volume ratio of two unmiscible or partially miscible liquids in dispersion is given in Czech. Patent A 0 247 852.
Nomenclature L = acoustic path length, m t+ = sound pulse transmission time through the dispersion, S
tl = sound pulse transmission time through the continuous phase, s t2 = sound pulse transmission time through the dispersed phase, s V = velocity of sound in the dispersion, m/s Vl = velocity of sound in the dispersed phase, m/s V2= velocity of sound in the continuous phase, m/s X,4 = fractional volume dispersed-phase holdup Literature Cited Bonnet, J. C.; Tavlarides, L. L. Znd. Eng. Chem. Res. 1987,26, 811. HavliEek, A,; Sovovi, H. Collect. Czech. Chem. Commun. 1984.49, 378. Kuster, G. T.; Toksoz, M. N. Geophysics 1974,39, 607. Sovovi, H.; HavliEek, A. Chem. Eng. Sci. 1986, 41, 2579.
H. SovovP,* A. HavliEek Institute of Chemical Process Fundamentals Czechoslovak Academy of Sciences Prague, Czechoslovakia 0 1988 American Chemical Society
