Ind. E n g ~Chem. Res 1990, 29,470-475
470 D = spindle speed, rad/s
Registry No. Butyllithium, 109-72-8; styrene, 100-42-5; polystyrene, 9003-53-6.
Literature Cited Abdel-Amin, A. H.; Balke, S. T.; Hamielec, A. E. Flow Properties of Polystyrene Solutions under High Shear Rates. J . Appl. Polym. Sci. 1973, 27, 1431-1442. Beisenberger. J. A.; Sebastion, D. H. Principles of Polymerization Engineering; Wiley-Interscience: New York, 1983; pp 514-572. Broyer, E.; Macosko, C. W.; Critchfield, F. E.; Lawler, L. F. Curing and Heat Transfer in Polyurethane Reaction Injection Molding. Polym. Eng. Sci. 1978, 18, 382-387. Cross, M. M.; Kaye, A,; Stanford, J. L.; Stepto, R. F. T. Rheology of Polyols and Poly01 Slurries in Reinforced RIM. In Reaction Injection Molding, Polymer Chemistry, and Engineering; Kresta, J., Ed.; American Chemical Society: Washington, DC, 1985; pp 97-110.
Einaga, Y.;Osaki, K.; Kurata, M.; Tamura, M. Creep Behavior of Polymer Solutions 11. Steady Shear Compliance of Concentrated Polystyrene Solutions. Macromolecules 1971, 4 , 87-92. Graesslev, W. W. The Entanglement Concept in Polymer Rheology. Adu. Polym Sci. 1974, 1 6 1-179. Graessley. W. W.; Segal, L. Newtonian Viscosity-Molecular Weight Ihlai ionqbio tor Concentrated Solutions of Monodisperse PolysL1rexe. Xiacrcimolecules 1969. 2, 49-57. Graesslcy, !+". W.; Hazieton, R. L.; Lindeman, L. R. The Shear Rate liependencr of Viscosity of Concentrated Solutions of Narrow Distribution Polystyrene. Trans. SOC.Rheol. 1967, 11, 267-285. Howard, D. W. Modern Developments in Viscometers. Ceram. Eng. Fci. Proc. 1985. 6 , 1395-1405. Ide. Y.: White, J.L. Rheological Phenomena in Polymerization Reactors: Rheoiogical Properties and Flow Patterns Around Agitat o r i in Polystyrene-Styrene Solutions. J . Appl. Polym. Sci. 1974. 13, 2997--301s. Levenspiel, 0. Chemical Reaction Engineering; John Wiley: New York. 1972; pp 44-47. Mendelson, R. A, Concentrated Solution Viscosity Behavior a t Elevated Temperatures-Polystyrene in Ethyl Benzene. J . of Rheol. 1980,24. 765-781. Mitschka, P. Simple Conversion of Brookfield RTV Readings into Viscosity Functions. Rheol. Acta 1982, 21, 207-209. Mooney, M. In Rheology, Theory and Applications; Eirich, F. R.. Ed.; Academic: New York, 1958; Vol. 2, pp 192, 193. Morton. M. Anionic Polymerization: Principles and Practice; Arademic Press: New York, 1983.
Morton, M.; Fetters, L. J. Anionic Polymerization of Vinyl Monomers. Rubber Chem. Technol. 1975, 48, 359-409. Morton, M.; Bostick, E. E.; Livigni, R. Advances in Anionic Polymerization. Rubber Plastics Age 1961, 97-401. Nielsen, L. E. Mechanical Properties of High Polymers: Van Nostrand Reinhold: New York, 1962. Nishimura, N. Viscosities of Concentrated Polymer Solutions. J . Polym. SCL.1965, A:3, 237-253. Penwell, R. C.; Graessley, W. W. Difference in Viscosity Among Narrow Distribution Polystyrenes of Comparable Molecular Weight. J . Polym. Sci., Polym. Phys. Ed. 1974, 12, 213-216. Penwell, R. C.; Graessley, W. W.; Kovacs, A. Temperature Dependence of Viscosity-Shear Rate Behavior in Undiluted Polystyrene. J . Polym. Sci., Polym. Phys. Ed. 1974, 12, 1771-1783. Perry, S. J.; Castro, J. M.; Macosko, C. W. A Viscometer for Fast Polymerizing Systems. J . Rheol. 1985, 29 (l),19-36. Quirk, R. P.; McFay, D. Solvation of Alkyllithium Compounds. Heats of Interaction of Tetrahydrofurans with Poly(is0propeny1)lithium and Poly(styry1)lithium. Makromol. Chem.. Rapid Commun. 1980, 1, 71-73: Ree. T.: Evrine. H. Theorv of Non-Newtonian Flow. I. Solid Plastic Systems. Appl. Phis. 1955, 26, 793-800. Richter, E. B.; Macosko, C. W. Viscosity Changes During Isothermal and Adiabatic Urethane Network Polymerization. Polym. Eng. S C ~1980, . 20, 921-924. Roller, M. B. Characterization of the Time-Temperature-Viscosity Behavior of Curing B-Staged Epoxy Resin. Polym. Eng. Sci. 1975, 15, 406-414. Roller, M. B. Rheology of Curing Thermosets: A Review. Polym. Eng. Sci. 1986, 26, 432-440. Rosen, S.L. Fundamental Principles of Polymeric Materials; Wiley-Interscience: New York, 1982; pp 199-212. Schwab, F. C.; Murray, J. G. Anionic Dispersion Polymerizaton of Styrene. In Aduances in Polymer Synthesis; Culbertson, B. M., McGrath, J. E., Eds.; Plenum Press: New York, 1985; pp 381-404. Taylor, G. I. Fluid Friction Between Rotating Cylinders I. Torque Measurements. Proc. R. Soc. London 1936, A157, 546-564. Tung, L. H.; Moore, J. C. Gel Permeation Chromatography. In Fractionation of Synthetic Polymers. Principles and Practices; Tung, L. H., Ed.; Marcel Dekker: New York, 1977; Chapter 6. Worsfold, D. J.; Bywater, S. Anionic Polymerization of Styrene. Can. ,I. Chem. 1960, 38, 1891-1900. Your, J.-J. A,; Karles, G. D.; Ekerdt, J. G.; Trachtenberg, I.; Barlow, ,J, W.Development of a RIM Encapsulant System. 1. Kinetic Studies of Butyl Lithium Catalyzed Styrene Polymerization. Ind. Eng. Chem. Res. 1989, 28. 1456-1463. I
I
0; H E > 0). Contrary to 1, solutes 2 and 3 reveal the small deviations from additivity in the hexane + 1-butanol binary solvent system, and no synergetic effect has been observed, as is shown in Figure 2, for solute 2, as an example. The solubility measurements of solute 3 have been done only in one mixture of hexane + 1-butanol (49.31 mol 70 l-butanol), just for exhibiting that 3 does not reveal the synergetic effect of solubility. Evidently, compounds 2 and 3 are able to form new intermolecular solutebinary solvent mixture association, and only small deviations from additivity are observed. The measured solubilities of the solutes in all solvents (even binary) are lower than the calculated values for ideal solubility, and they show positive deviations from idealsolution behavior (yl > 1). The solubility of solid 1 in a liquid may be expressed in a very general manner by
n
Ci n
I
7.. =
&ij -
I
'11
' xkG k j X k \
'-
Ck G k j X k
7 , .=
&ji -
RT IC RT where Agij = gij- gji and Agji = gji - gii are two adjustable parameters for the molar energy of interaction between i and j . In the present work, also the prediction of the solubility of benzoyl-substituted naphthols in binary solvent mixtures has been done by the Wilson, UNIQUAC, and NRTL equations. Parameters in binary solute-solvent systems were regressed from solid-liquid equilibrium data, whereas
474
Ind. Eng. Chem. Res., Vol. 29, No. 3, 1990
Table V. Correlation and Prediction of the Solubility Data of Benzoylnaphthols in One-Component and Two-Component Solvent Mixtures Using the Wilson, UNIQUAC, and NRTL Equations parameterse w UNIQUAC NRTLC deviationsb ( U T ) , K no. of g12 - g11 A42 &12 _________ system xson data pts g,, - gZ2 A41 &21 W UNIQUAC NRTL 2-benzoyl-l-naphthol/hexane + 1-butanol 0.0 5 192.7194 -5.8081 701.8805 1.44 1.16 1.16 5792.9758 1716.1555 7470.2644 0.3029 7 -192.9625d 4055.5501d 7299.4543d 1.01 10.95 14.09 -418.5033 7641.6280 -1 370.3551 2.72 9.31 0.4932 -192.9625d 4055.5501d 7299.4543d 3.45 8 418.5033 7641.6280 -1 370.3551 5.14 4.17 -192.9625d 4055.5501d 7299.4543d 3.80 0.6998 8 -418.5033 7641.6280 -1 370.3551 0.47 0.46 4653.5143 702.7827 -194.2403 0.44 9 1.0 1268.2745 8495.8749 5666.5968 9 158.4789 17440.980 3.97 5.15 5.52 3500.6810 7 l-benzoyl-2-naphthol/hexane+ 1-butanol 0.0 125853.358 -992.7009 4718.1720 5.09 4.91 -192.9625d 4055.5501d 7299.4543d 8.99 8 0.3029 -418.5033 7641.6280 -1 370.3551 2.29 2.74 -192.9625d 4055.5501d 7299.4543d 5.79 0.5039 9 -418.5033 7641.6280 -1 370.3551 n 1.30 5.86 -192.9625d 4055.5501d 7299.4543d 2.11 0.6994 -418.5033 7641.6280 -1 370.3551 0.63 7 -3007.1753 3 542.0239 10491.154 0.61 0.58 1.0 -1 419.4020 -1 687.6636 11 698.968 3.35 1.37 10327.799 3 107965.91 18077.994 3.72 4-benzoyl-l-naphthol/hexane+ 1-butanol 0.0 318.4005 11577.156 61846.276 3.80 8.33 -192.9625d 4055.5501d 7299.4543d 4.05 0.4931 8 7641.6280 -1 370.3551 -418.5033 0.59 0.59 1246.1522 -1 251.7678 -3 571.9398 0.96 11 I .o 1359.8890 3431.3235 -835.2020 ~
‘ I
n x t is the mole fraction of the second-named component in the solute-free mixed solvent. uT given by eq 14. ‘Parameter a I z = 0.289, taken from Gmehling et al. (1978). dGmehling et al. (1978). e I n Jemol-’. for binary mixed solvents they were taken from literature data of the vapor-liquid equilibrium. Recommended values of the solventsolvent binary interaction parameters were taken from Gmehling et al. (1978). (See Table V.) The root-mean-square deviation of temperature defined by eq 14 was used as a measure of the goodness of fit of the solubility curves .
l”=l -
where Tical and Ti are respectively the calculated and experimental temperatures of the ith point and n is the number of experimental points, which include the melting point. The calculated values of the equation parameters and corresponding root-mean-square deviations in binary and ternary systems are presented in Table V. It can be noted that a good description has been obtained for most of the one-component solvents, as a result of correlation. All deviations are in the oT range from 0.5 to 5.5 K, being especially bad in the 2-hexane system, probably due to the small solubility of 2 in hexane. The results of the solubility prediction in ternary systems are not satisfactory in all the cases studied (ar is from 2 to 14 K). Too large values of the root-mean-square deviations are observed in different mixtures, predicted by different equations. Generally, the results of the solid solubility prediction, obtained by using the Wilson, UNIQUAC, and NRTL equations, are comparable with each other. Conclusions The effect of intra- and intermolecular solute-solvent hydrogen bonding on the solubility in a binary solvent system as well as its influence on the synergetic effect of solubility in hydrocarbon + alcohol mixtures has been tested. Therefore, 2-benzoyl-1-naphthol has revealed the
synergetic effect of solubility in the hexane + 1-butanol binary solvent system, contrary to 1-benzoyl-2-naphthol and 4-benzoyl-1-naphthol. The increase of 1-benzoyl-2naphthol and 4-benzoyl-1-naphthol solubility with an increase of alcohol concentration in the binary hydrocarbon alcohol solvent system due to the existence of new intermolecular hydrogen bonds between solid and solvent has been observed. The prediction of the solubility in ternary systems by means of the Wilson, UNIQUAC, and NRTL correlation equations that describe the Gibbs excess free energy of mixing (G E) using parameters for binary solvents taken from the literature VLE data gives results of the same order for all the equations and describes the solubility curves to within an average root-mean-square deviation (ii,) of 5.2 K.
+
Acknowledgment
I thank the Institute of Physical Chemistry, Polish Academy of Sciences, for its financial aid of Project CPBR 3.20.62. Nomenclature AC m l = difference between heat capacities of the solute in t i e solid and liquid states g , = molar energy of interaction between i and j U12, Ag = binary interaction parameters G E = excess 6ibbs free energy AHml = molar enthalpy of fusion of the solute 1, = bulk factor of pure component i as defined by I, = (2/2)(r1 - ql) - (r, - 1) n = number of experimental points q z = surface parameter of pure component i r, = size parameter of pure component i R = universal gas constant T = experimental equilibrium temperature Tea' = calculated equilibrium temperature
Ind. Eng. Chem. Res. 1990,29, 475-482
T,, = melting point temperature of the pure solute Au12,Aual, Auji = binary interaction parameters Vi, V j = molar volume of the solute or solvent x1 = mole fraction of the solute 2 = lattice coordination number, a constant set to 10 Greek L e t t e r s a12,aij = proportionality constant similar to the nonrandom-
ness constant of the NRTL equation y1 = activity coefficient of the solute Bi = surface fraction of component i T ~ T~ ~ ,= , coefficients defined by eq 10 Qi = segment fraction of component i Aij, Aji = parameters of the Wilson equation uT = root-mean-square deviation of temperature
Literature Cited Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J . 1975, 21, 116-128. Barton, A. F. M. Solubility Parameters. Chem. Rev. 1975, 75, 731-753. Bisanz, T. Fries Rearrangement of @-NaphtholEsters and of their Derivatives. I. Evidence for the Mechanism of Reaction. Rocz. Chem. 1956, 30, 87-102. Buchowski, H.; Domadska, U. Solubility and Hydrogen Bonding. Part VI. Evidence for Intramolecular Hydrogen Bond. Polish J. Chem. 1980,54, 97-102. Buchowski, H.; Domahka, U.; Ksigczak, A. Solubility and Hydrogen Bonding. Part V. Synergic Effect of Solubility in Mixed Solvents. Polish J . Chem. 1979, 53, 1127-1138. Dean, F. M.; Locksley, H. D. Spirans. Part V. Diastereoisomeric Grisenones Obtained by Oxidative Cyclisation. J . Chem. Soc. 1963, 97, 393-401. Domdska, U. Solubility and Hydrogen Bonding. Part VII. Synergic Effect of Solubility of Naphthalene in Mixed Solvents. Polish J . Chem. 1981,55, 1715-1720. DomaAska, U. Correlation and Prediction of the Solubility of Acetyl-Substituted Naphthols in Binary Solvent Mixtures. International Meeting on Phase Equilibrium Data, Meeting No. 3, Paris, France, Sept 11-13 1985; pp 745-749. Domhska, U. Vapour-Liquid-Solid Equilibrium of Eicosanoic Acid in One- and Two-Component Solvents. Fluid Phase Equilib. 1986, 26, 201-220. DomaAska, U. Solid-Liquid Phase Relations of Some Normal Long-chain Fatty Acids in Selected Organic One- and Two-component Solvents. Znd. Eng. Chem. Res. 1987,26, 1153-1162. DomaAska, U. Solubility of 2,5-Dimethylphenol and 3,4-Dimethylphenol in Binary Solvent Mixtures Containing Alcohols. Fluid Phase Equilib. 1988, 40, 259-277.
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Domafmka, U. Solubility of Long-chain Fatty Acid Esters in Selected Organic One- and Two-Component Solvents. J . Solution Chem. 1989a, 18, 173-188. Domadska, U. Solubility of n-Alkanols (CI6, CIS, C,) in Binary Solvent Mixtures. Fluid Phase Equilib. 198913, 46, 223-248. Domadska, U. Enhancement of Solid Solubility in Binary Solvent Mixtures. The System o-Toluic Acid-Cyclohexane + Methylene Iodide. J . Solution Chem. 1989c, in press. Domhska, U. Solubility of Acetyl-Substituted Naphthols in Binary Solvent Mixtures. Fluid Phase Equilib. 1990, in press. D o m ~ s k aU.; , Hofman, T. Correlation for the Solubility of Normal Alkanoic Acids and o-Toluic Acid in Binary Solvent Mixtures. J . Solution Chem. 1985, 14, 531-547. Gmehling, J.; Onken, U.; Arlt, W. Vapor Liquid Equilibrium Data Collection Organic Hydroxy Compounds: Alcohols and Phenols; DECHEMA F.R.G., 1978; Vol. I, Part 2b, p, 200. Gordon, L. J.; Scott, R. L. Enhancement Solubility in Solvent Mixtures. I. The System Phenanthrene-Cyclohexane-Methylene Iodide. J. Am. Chem. SOC.1952, 74, 4138-4140. Hofman, T.; Nagata, J. Determination of Association Constants for Alcohols Based on Ethers as HomomorDhs. Fluid Phase Eouilib. 1986, 25, 113-128. Konstam, A. H.; Feairheller, W. R., Jr. Calculation of Solubility Parameters of Polar ComDounds. AZChE J . 1970, 16, 837-840. Renon, H.; Prausnitz, J. M. Lical Compositions in Thermodynamics Excess Functions for Liquid Mixtures. AZChE J . 1968, 14, 135-144. Riddick, J. A.; Bunger, W. B. Organic Solvents Physical Properties and Methods of Purification. Techniques of Chemistry; WileyInterscience: New York, London, Sydney, Toronto, 1970; Vol. 11. Skulski, L. Ultraviolet Absorption Spectra of Acetyl- and Benzoylsubstituted Naphthols. Bull. Acad. Pol. Sci., Ser. Sci. Chim. 1969, I 7,253-258. Skulski, L.; Adamska, G. UV-VIS Absorption Spectra of Some Benzoyl-Substituted Naphthols and of Their Acetates and oMethyl Ethers. Bull. Acad. Pol. Sci., Ser. Sci. Chim. 1973, 21, 849-857. Skulski, L.; Waclawek, W. Correlations Between the Spectral Solvent Effects and “Dioxan Effect” in the dipolometric Measurements. Studies on Intramolecular Hydrogen Bonding by Ultraviolet-Visible Absorption Spectroscopy. Bull. Acad. Pol. Sci., Ser. Sci. Chim. 1971, 19, 277-286; Part VIII. Vera, J. H.; Sayegh, G. S.; Ratcliff, G. A. A Quasi Lattice Local Composition Model for the Excess Gibbs Free Energy of Liquid Mixtures. Fluid Phase Equilib. 1977, I, 113-135. Wilson, G. M. Vapor-Liquid Equilibrium. XI. A New Expression 1964, for the Excess Free Energy of Mixing. J . Am. Chem. SOC. 86, 127-130. Witt, 0. N.; Braun, 0. Uber Umlagerungen in der Gruppe der Aceto-Naphthole: Ber. Dtsch. Chem. Ces. A 1914, 47, 3216-3232. Received f o r review May 23, 1989 Accepted November 20, 1989
Model for Hold-Up Measurements in Liquid Dispersions Using an Ultrasonic Technique J o n g h e o p Yi a n d L a w r e n c e L. Tavlarides* Department of Chemical Engineering a n d Materials Science, Syracuse University, Syracuse, New York 13244
The spherical droplet correction time-averaged (SDTA) model is proposed, which permits estimation of the dispersed-phase holdup from the transmission time of the ultrasound wave through the dispersions. T h e SDTA model considers the effects of spherical and polydispersed drops on the path length of ultrasound wave transmission and the physical properties of both phases. This analysis also suggests that an estimate of phase inversion holdup can be made. The validity of this model is investigated for the two chemical systems of saturated water with toluene and saturated 0.2 M nitric acid solution with 30 vol % tributyl phosphate in n-dodecane. Experimental results show that the true holdup can be accurately measured with a relative error range between 0% and 7.7%. I t is also shown that the ultrasonic technique can be employed on steel wall vessels of a n extraction unit in a noninvasive and nonintrusive manner for continuous and safe monitoring. Solvent extraction has been a key operation in many processes for product purification and raw material re0888-5885/90/2629-0475$02.50/0
covery. One key factor in the control and analysis of extractor operations is the ability to monitor the dispersed@ 1990 American Chemical Society
