Viscosities of the ternary mixture (2-butanol+n-hexane+1-butylamine) at 298.15 and 313.15 K

Ž .Fluid Phase Equilibria 169 2000 277–292www.elsevier.nlrlocaterfluid

Viscosities of the ternary mixtureŽ .2-butanolqn-hexaneq1-butylamine at 298.15 and 313.15 K

Magdalena Domınguez, Juan I. Pardo, Ignacio Gascon, Felix M. Royo, Jose S. Urieta)´ ´ ´ ´Departamento de Quımica Organica– Quımica Fısica, Area de Quımica Fısica, Facultad de Ciencias, Seccion de Quımicas,´ ´ ´ ´ ´ ´ ´ ´

UniÕersidad de Zaragoza, Ciudad UniÕersitaria, Plaza San Francisco 50009 Zaragoza, Spain

Received 30 November 1999; accepted 21 February 2000

Abstract

Ž .Viscosities of the ternary mixture 2-butanolqn-hexaneq1-butylamine and of the binary mixturesŽ . Ž .2-butanolqn-hexane at 298.15 and 313.15 K, and 2-butanolq1-butylamine at 313.15 K have beenmeasured at atmospheric pressure. Viscosity deviations and excess Gibbs energy of activation of viscous flowfor the binary and ternary systems were fitted to Redlich–Kister’s and Cibulka’s equations, respectively. Tocorrelate experimental data of ternary system from binary ones, different empirical and semiempirical equations

Ž .have been used Nissan and Grunberg, Hind, Frenkel, McAllister, Katti and Chaudhri, Heric and Iulan and theirŽ .parameters have been calculated. The ‘‘viscosity-thermodynamic’’ model UNIMOD has been applied to

correlate experimental data for the binary mixtures and to predict the viscosity for the ternary system. TheŽ .Group Contribution-Thermodynamic Viscosity model GC-UNIMOD , and the group contribution method

proposed by Wu have been employed to predict the viscosity for the binary and ternary systems. q 2000Elsevier Science B.V. All rights reserved.

Keywords: Viscosity; Alkanol; Alkane; Butylamine; Ternary mixtures

1. Introduction

Knowledge of thermodynamic and transport properties of multicomponent liquid systems isessential in many industrial applications. Experimental viscosity data and methods for the estimationof viscosities of multicomponent mixtures are not only of theoretical but also of great practical

w xinterest. Although a number of predictive equations 1 are available for estimating thermodynamicŽ .excess properties excess volume, excess enthalpy, and excess free energy of multicomponent

) Corresponding author. Tel.: q34-976-76-1298; fax: q34-976-76-1202.Ž .E-mail address: [email protected] J.S. Urieta .

0378-3812r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0378-3812 00 00332-0

( )M. Domınguez et al.rFluid Phase Equilibria 169 2000 277–292´278

systems, such methods are rarely used for viscosity. However, many empirical or semiempiricalw xequations can correlate viscosity data of binary mixtures using several adjustable parameters 2 . The

literature of correlations of flow properties for ternary and multicomponent liquid mixtures is ratherlimited. Recently, the empirical and semiempirical equations for binary mixtures were extended to

w xternary mixtures by introducing a ternary parameter 3 ; also, new models have been developed for thew xprediction of viscosities of mixtures. Some of them are based on a molecular approach 4,5 , while

w xothers are based on the group contribution concept 6,7 . The first type of models require binaryinteraction parameters for each binary system present in the multicomponent mixture, but no ternaryŽ .or higher constants are generally needed.

Ž .In this work, viscosities of the ternary mixture 2-butanolqn-hexaneq1-butylamine and of theŽ . Ž .binary mixtures 2-butanolqn-hexane at 298.15 and 313.15 K, and 2-butanolq1-butylamine at

313.15 K have been measured. The viscosity data have been used to calculate the viscosity deviationsŽ . Ž UE .Dh and excess molar Gibbs energy of activation for viscous flow G . The correlation equations

w x w x w x w x w xof Nissan and Grunberg 8 , Hind et al. 9 , Frenkel 10 , McAllister 11 , Katti and Chaudhri 12 ,w x w xHeric 13 and Iulan et al. 14 were applied to the viscosity data of the ternary system using binary

parameters obtained from the correlation of the binary systems, and a comparison between theoreticaland experimental values was made. The fit parameters of binary and ternary systems, and the root

w xmean square deviations are presented. The UNIMOD model 5 has been employed to correlate theviscosity of the binary systems and then to predict the viscosity of the ternary mixture without

Ž .additional parameters. The Group Contribution-Thermodynamic Viscosity model GC-UNIMODw x w xmodel 7 and the group contribution method proposed by Wu and Marshall 6 have been used to

predict the viscosity of binary and ternary mixtures.Previously, we reported density measurements for these systems as a function of mole fraction and

w xdiscussed their behaviour in terms of molecular interactions 15 .

2. Experimental

Ž Ž . ŽThe compounds used 2-butanol purity better than 99.0 mol% , n-hexane purity better than 99.0. Ž ..mol% and 1-butylamine purity better than 99.0 mol% were obtained from Aldrich. The purities of

the chemicals were checked not only by comparing the measured densities and viscosities with thosereported in the literature but also by gas chromatography using a semicapillary methyl silicone

Ž .column OD: 530 mm and a flame-ionization detector. No further purification was considerednecessary. The butanol and butylamine were dried with activated molecular sieve type 0.3 nm fromMerck. The pure component properties compared with those found in the literature are gathered inTable 1.

Kinematic viscosities, n , of pure components and their binary and ternary mixtures were deter-mined with the aid of an Ubbelohde viscosimeter connected to a Schott–Gerate automatic measuring¨unit model AVS-440, for which the accuracy of the flow time measurement is "0.01 s. A

Ž .thermostatically controlled bath constant to "0.01 K was used. The viscosimeter was calibratedwith deionized doubly distilled water. Kinetic energy corrections were applied to the experimentaldata. The estimated error was "1=10y4 mPa s. Details of calibrations and procedures can be found

w xin an earlier paper 18 .

( )M. Domınguez et al.rFluid Phase Equilibria 169 2000 277–292´ 279

Table 1Properties of the pure components

Component T s298.15 K T s313.15 Ky3 y3Ž . Ž . Ž . Ž .h mPa s r g cm h mPa s r g cm

Experimental Literature Experimental Literature Experimental Experimentala a2-Butanol 3.0804 2.998 0.80239 0.80241 1.7942 0.78939a an-Hexane 0.2944 0.294 0.65493 0.65484 0.2537 0.64108b b1-Butylamine 0.4690 0.470 0.73225 0.73300 0.3831 0.71749

a w xRef. 16 .b w xRef. 17 .

Ž .Densities, r, required for converting kinematic viscosities to absolute or dynamic viscosities,hsnr, were measured by means of an Anton Paar DMA-58 vibrating tube densimeter. The accuracyof the density measurements was "1=10y5 g cmy3, and the corresponding precision "0.5=10y5

g cmy3. The densimeter was calibrated with deionized doubly distilled water and dry air.Ž .The compositions mole fraction of binary and ternary blends were determined by mass using a

Mettler H20T balance with a precision of "0.01 mg. The precision of the mole fraction is estimatedto be better than "1=10y4. The mixtures were completely miscible over the whole compositionrange.

3. Results and discussion

Ž .The experimental viscosities and densities of the binary mixture 2-butanolqn-hexane at 298.15Ž .and 313.15 K, and 2-butanolq1-butylamine at 313.15 K, are given in Table 2. In previous papers,

Ž . w xwe reported the viscosities for the binary mixtures 2-butanolq1-butylamine at 298.15 K 19 andŽ . w xn-hexaneq1-butylamine as a function of mole fraction at the same temperatures 20 .

ŽThe experimental viscosities and densities for the ternary mixture 2-butanolqn-hexaneq1-.butylamine at 298.15 and 313.15K are shown in Table 3.

The viscosity deviations, Dh, and excess Gibbs energies of activation of viscous flow, GUE, forbinary and ternary mixtures were determined through the equations:

n

Dhr mPa s shy x h , 1Ž . Ž .Ý i iis1

nUE y1G r J mol sRT ln n M y x ln n M , 2Ž . Ž . Ž . Ž .Ý i i iž /

is1

where MsÝn x M is the molar mass of the mixture, R is the gas constant, T is the absoluteis1 i i

temperature, h and n are the absolute viscosity and kinematic viscosity of the mixture, respectively,h and n the absolute viscosity and kinematic viscosity of pure component i, x the mole fraction ini i i

component i, and n is the number of components in the mixture.


Table 2Experimental kinematic viscosities, n , and densities, r, and calculated viscosity deviations, Dh, and excess Gibbs energiesof activation of viscous flow, GUE, of the binary mixtures

UEy3 y1Ž . Ž . Ž . Ž . Ž .T K x n cSt r g cm Dh mPa s G J mol1

( ) ( )2-Butanol 1 q n-hexane 2298.15 0.0995 0.4729 0.66404 y0.2576 y400.8

0.1986 0.5097 0.67456 y0.5039 y740.00.2972 0.5630 0.68608 y0.7361 y1016.30.3989 0.6419 0.69901 y0.9570 y1230.90.4977 0.7594 0.71271 y1.1397 y1339.20.5985 0.9520 0.72797 y1.2688 y1315.00.6971 1.2178 0.74423 y1.3302 y1229.60.7987 1.6677 0.76232 y1.2482 y991.90.8978 2.3959 0.78126 y0.9238 y622.6

313.15 0.0995 0.4116 0.64990 y0.1395 y347.70.1986 0.4399 0.66041 y0.2691 y623.60.2972 0.4779 0.67199 y0.3904 y855.20.3989 0.5310 0.68496 y0.5045 y1042.80.4977 0.6154 0.69870 y0.5904 y1108.10.5985 0.7231 0.71407 y0.6593 y1147.20.6971 0.8872 0.73052 y0.6795 y1064.30.7987 1.1484 0.74889 y0.6241 y856.30.8978 1.5490 0.76810 y0.4470 y530.3

( ) ( )2-Butanol 1 q1-butylamine 2313.15 0.0982 0.5929 0.72606 y0.0912 y97.9

0.1983 0.6653 0.73451 y0.1743 y175.40.2986 0.7504 0.74267 y0.2472 y240.20.3960 0.8457 0.75030 y0.3074 y296.20.4996 0.9658 0.75804 y0.3560 y341.20.5950 1.0980 0.76480 y0.3830 y366.90.6953 1.2710 0.77150 y0.3837 y364.20.7966 1.5020 0.77784 y0.3389 y311.50.8955 1.8120 0.78362 y0.2268 y195.9

The viscosity deviations and excess Gibbs energies of activation of viscous flow for binaryw xmixtures were both fitted to a Redlich–Kister’s equation 21 :

ppEY sx x A x yx , 3Ž . Ž .Ýi j i j p i j

ps0

where Y E is Dh or GUE, x denotes the mole fraction of component i of the i, j mixture withi j iŽ .x s1yx , and A are adjustable parameters. The choice of the proper number of coefficients pj i p

was based on the standard deviations, and the F-test as a criterion of goodness with an error lowerthat 1%. The experimental values and Redlich–Kister’s fitted polynomial of Dh and GUE for the

Ž . Ž .binary mixtures at both temperatures, 298.15 and 313.15 K, are plotted in Fig. 1 a and b ,respectively.


Table 3Experimental kinematic viscosities, n , and densities, r, and calculated viscosity deviations, Dh, and excess Gibbs energies

UE Ž . Ž . Ž .of activation of viscous flow, G , of the ternary mixture 2-butanol 1 q n-hexane 2 q1-butylamine 3 at 298.15 and313.15 K

x x T s298.15 K T s313.15 K1 2

U E U Ey3 y1 y3 y1Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .n cSt r g cm Dh mPa s G J mol n cSt r g cm Dh mPa s G J mol

0.0495 0.0497 0.6549 0.73086 y0.1109 y119.0 0.5469 0.71648 y0.0547 y84.00.0502 0.1002 0.6361 0.72549 y0.1211 y148.5 0.5328 0.71121 y0.0621 y113.70.0506 0.8456 0.4727 0.66513 y0.1391 y231.4 0.4123 0.65110 y0.0766 y200.10.0503 0.9018 0.4666 0.66187 y0.1341 y214.3 0.4075 0.64787 y0.0734 y187.10.0987 0.0488 0.6955 0.73488 y0.2071 y189.1 0.5776 0.72067 y0.0998 y128.10.1000 0.1003 0.6741 0.72931 y0.2209 y225.7 0.5615 0.71520 y0.1097 y164.80.0990 0.1988 0.6359 0.71911 y0.2355 y277.1 0.5328 0.70500 y0.1215 y218.40.0999 0.2981 0.6036 0.70979 y0.2494 y321.6 0.5087 0.69557 y0.1317 y263.10.1003 0.4004 0.5750 0.70083 y0.2580 y353.1 0.4883 0.68652 y0.1376 y290.40.0992 0.5016 0.5495 0.69241 y0.2600 y371.7 0.4694 0.67810 y0.1399 y309.90.0987 0.5956 0.5294 0.68504 y0.2601 y379.8 0.4550 0.67082 y0.1401 y316.20.1004 0.6941 0.5123 0.67786 y0.2627 y383.3 0.4424 0.66378 y0.1413 y320.00.0983 0.8012 0.4934 0.67032 y0.2551 y375.1 0.4280 0.65632 y0.1372 y316.50.0988 0.8499 0.4850 0.66717 y0.2550 y378.2 0.4215 0.65314 y0.1372 y321.40.1984 0.0993 0.7608 0.73694 y0.4090 y363.5 0.6257 0.72308 y0.1978 y254.90.1995 0.1990 0.7136 0.72643 y0.4368 y437.4 0.5912 0.71263 y0.2176 y326.50.1988 0.3007 0.6707 0.71649 y0.4551 y497.2 0.5594 0.70265 y0.2317 y386.80.2002 0.4001 0.6359 0.70757 y0.4720 y547.5 0.5333 0.69370 y0.2439 y438.10.1970 0.4960 0.6034 0.69909 y0.4750 y579.0 0.5090 0.68522 y0.2481 y472.40.1972 0.5961 0.5749 0.69078 y0.4827 y612.5 0.4882 0.67695 y0.2537 y504.20.1990 0.6972 0.5473 0.68272 y0.4933 y654.9 0.4679 0.66885 y0.2607 y543.90.3000 0.1012 0.8637 0.74434 y0.5918 y498.4 0.6993 0.73065 y0.2824 y347.00.2987 0.2002 0.8005 0.73338 y0.6270 y592.0 0.6544 0.71975 y0.3077 y435.30.2998 0.2978 0.7487 0.72360 y0.6581 y675.6 0.6167 0.70996 y0.3298 y516.30.2979 0.4012 0.6979 0.71361 y0.6788 y749.8 0.5796 0.69995 y0.3459 y589.10.2962 0.4966 0.6559 0.70472 y0.6935 y812.3 0.5483 0.69103 y0.3579 y652.70.2987 0.5945 0.6161 0.69594 y0.7164 y893.2 0.5179 0.68215 y0.3744 y734.80.3967 0.1009 0.9795 0.75138 y0.7513 y616.2 0.7832 0.73780 y0.3520 y416.90.3969 0.2008 0.8980 0.74004 y0.8058 y742.6 0.7239 0.72650 y0.3913 y542.50.3963 0.2948 0.8298 0.73003 y0.8466 y851.9 0.6756 0.71647 y0.4201 y645.20.3930 0.3985 0.7626 0.71928 y0.8772 y954.8 0.6260 0.70566 y0.4444 y749.50.3981 0.4988 0.7075 0.70941 y0.9196 y1075.3 0.5844 0.69567 y0.4738 y869.50.4971 0.0995 1.1220 0.75848 y0.8987 y726.5 0.8772 0.74500 y0.4182 y501.60.4982 0.2012 1.0130 0.74649 y0.9786 y893.4 0.8031 0.73301 y0.4714 y654.00.4945 0.2977 0.9198 0.73541 y1.0319 y1030.2 0.7375 0.72186 y0.5100 y785.20.4954 0.3989 0.8402 0.72425 y1.0845 y1169.1 0.6767 0.71055 y0.5497 y932.90.5975 0.1000 1.2980 0.76490 y1.0190 y810.6 0.9914 0.75157 y0.4682 y561.30.5941 0.1996 1.1510 0.75232 y1.1196 y1004.0 0.8908 0.73889 y0.5374 y747.20.5936 0.2991 1.0390 0.74029 y1.1977 y1167.0 0.8140 0.72669 y0.5905 y901.00.6931 0.1018 1.5120 0.77038 y1.0963 y855.2 1.1210 0.75719 y0.4992 y600.50.7124 0.1896 1.4120 0.75985 y1.2233 y1031.7 1.0410 0.74650 y0.5867 y795.70.7828 0.1115 1.7880 0.77402 y1.1098 y829.1 1.2640 0.76089 y0.5115 y618.50.8356 0.0502 2.2120 0.78555 y0.9047 y591.3 1.5070 0.77263 y0.3914 y409.20.8475 0.1018 2.1080 0.77876 y1.0227 y717.0 1.4230 0.76566 y0.4763 y561.80.8950 0.0518 2.5610 0.78856 y0.7776 y490.4 1.6710 0.77561 y0.3433 y363.0


Ž . Ž . Ž . Ž .Fig. 1. a Viscosity deviations Dh mPa s for the binary mixtures: 2-butanol 1 q n-hexane 2 ; `, at 298.15 K, v, atŽ . Ž . Ž w x. Ž .313.15 K; 2-butanol 1 q1-butylamine 2 ; ^, at 298.15 K Ref. 19 , ', at 313.15 K; Redlich–Kister’s

Ž . UE Ž y1.correlation. b Excess Gibbs energy of activation of viscous flow G J mol for the binary mixtures: 2-butanolŽ . Ž . Ž . Ž .1 q n-hexane 2 ; `, at 298.15 K, v, at 313.15 K; 2-butanol 1 q1-butylamine 2 ; ^, at 298.15 K, ', at 313.15 K;Ž . Redlich–Kister’s correlation.

The viscosity deviations and excess Gibbs energies of activation of viscous flow for the ternaryw xmixture have been fitted to the Cibulka equation 22 :

E EY sY qx x 1yx yx B qB x qB x , 4Ž . Ž .bin 1 2 1 2 1 2 1 3 2


where

Y E sY E qY E qY E , 5Ž .bin 12 13 23E Ž . Ž . Ž .and Y are given by Eq. 3 . The coefficients A Eq. 3 , B Eq. 4 , and the standard deviations, s ,i j P P

obtained by the least-squares method, are gathered in Table 4. This standard deviation is calculatedŽ .applying Eq. 6 , where the property values, number of experimental data, and number of parameters

are represented by z, m and p, respectively.1r2m

2z yzŽ .Ý exptl calc

is1s z s . 6Ž . Ž .

myp� 0UE Ž .Three-dimensional surfaces of Dh and G calculated from Cibulka’s equation Eq. 4 for the

Ž . Ž .ternary system, at 298.15 and 313.15 K, have been plotted in Fig. 2 a and b , respectively. Theisolines at constant values of Dh and GUE have been drawn in Figs. 3 and 4.

Table 4Ž . Ž .Coefficients of the Redlich–Kister’s Eq. 3 , A , Cibulka’s Eq. 4 , B , and the corresponding standard deviations, s , forp p

viscosity deviations and excess molar Gibbs energy of activation of viscous flow of the binary and ternary systems at 298.15and 313.15 K

Ž .T K A A A A A s0 1 2 3 4

( ) ( )2-Butanol 1 q n-hexane 2Ž .298.15 Dh mPa s y4.5698 y3.1302 y1.9632 y2.1300 y1.6353 0.0049

UE y1Ž .G J mol y5306.4 y1007.0 y385.7 y730.0 – 10Ž .313.15 Dh mPa s y2.3666 y1.5650 y1.2544 y0.7922 – 0.0050

UE y1Ž .G J mol y4502.1 y1172.6 y447.1 – – 11

( ) ( )2-Butanol 1 q1-butylamine 3a Ž .298.15 Dh mPa s y3.1867 y2.1026 y1.4678 y0.7384 – 0.0061

UE b y1Ž .G J mol y2136.4 y1383.4 y334.6 – – 12Ž .313.15 Dh mPa s y1.4248 y0.7728 y0.4857 y0.1725 – 0.0003

UE y1Ž .G J mol y1367.1 y751.9 y474.9 193.0 166.8 1

( ) ( )n-Hexane 2 q1-butylamine 3c Ž .298.15 Dh mPa s y0.1693 0.0314 y0.0252 – – 0.0003

UE d y1Ž .G J mol y770.6 y15.5 y102.0 – – 2.2c Ž .313.15 Dh mPa s y0.1233 0.0256 y0.0388 y0.0071 0.0423 0.0004

UE d y1Ž .G J mol y700.3 y18.6 y100.1 – – 4.0

Ž .T K B B B s1 2 3

( ) ( ) ( )2-Butanol 1 q n-hexane 2 q1-butylamine 3Ž .298.15 Dh mPa s 0.7796 8.6385 1.4435 0.0082

UE y1Ž .G J mol 1065.2 y665.9 8688.9 10.5Ž .313.15 Dh mPa s 0.5434 3.7492 0.4512 0.0048

UE y1Ž .G J mol 1437.6 2340.3 5254.0 9.1

a w xRef. 19 .b w xCorrelated with experimental data of Ref. 19 .c w xRef. 20 .d w xCorrelated with experimental data of Ref. 20 .


Ž . Ž . Ž . Ž . Ž .Fig. 2. a Three-dimensional surface of Dh mPa s for the ternary system 2-butanol 1 q n-hexane 2 q1-butylamine 3 ,Ž . Ž . Ž . Ž .correlated with the Cibulka’s Eq. 4 , at the temperatures 298.15 and – – – 313.15 K. b Three-dimensional

UE Ž y1. Ž . Ž . Ž .surface of G J mol for the ternary system 2-butanol 1 q n-hexane 2 q1-butylamine 3 , correlated with theŽ . Ž . Ž .Cibulka’s Eq. 4 , at the temperatures 298.15 and – – – 313.15 K.

UE Ž . ŽThe values of Dh and G for the binary mixture 2-butanolqn-hexane and 2-butanolq1-.butylamine at 298.15 and 313.15 K are negative over the entire composition range. A rise of

UE Ž .temperature makes both Dh and G increase less negative values .The ternary viscosity deviations and excess Gibbs energies of activation for viscous flow are also

Ž . Ž . UEnegative over the whole composition range. In Fig. 2 a and b , the surfaces of Dh and G have thesame shape at both temperatures. According to these figures, it can be observed that an increase oftemperature considerably modifies Dh of the ternary mixture; however, GUE scarcely changes. Atboth temperatures, the GUE surfaces and the corresponding Dh surfaces do not have a minimumbecause the lowest value correspond to the binary minimum of 2-butanolqn-hexane mixtureŽ UE y1Ts298.15 K, x s0.704, Dh sy1.326 mPa s, x s0.551, G sy1339.4 J mol ;1 minimum 1 minimum

UE y1.Ts313.15 K, x s0.692, Dh sy0.681 mPa s, x s0.568, G sy1145.9 J mol .1 minimum 1 minimumw xAccording to Kauzman and Eyring 23 , the viscosity of a mixture strongly depends on entropy of

Žmixture, which is related to liquid structure and enthalpy and consequently to molecular interactions.between the components of the mixture . So, the viscosity deviations are functions of molecular


Ž . Ž . Ž . Ž . Ž .Fig. 3. Isolines at constant Dh mPa s for the ternary system 2-butanol 1 q n-hexane 2 q1-butylamine 3 :Ž . Ž . Ž . Ž .correlated with Cibulka’s Eq. 4 ; – – – predicted by UNIMOD model. a At T s298.15 K; b at T s313.15 K.

w xinteractions as well as size and shape of molecules. Vogel and Weiss 24 affirm that mixtures withŽ E .strong interactions between different molecules H -0 and negative deviations from Raoult’s law

present positive viscosity deviations; whereas, for mixtures with positive deviations of Raoult’s lawand without strong specific interactions, the viscosity deviations are negative. In this way, Meyer et

w xal. 25 state that excess Gibbs energy of activation of viscous flow, like viscosity deviations, can beused to detect molecular interactions. The breaking of hydrogen bonding of alcohols and aminesmakes the mixture to flow more easily. At the same time, the OH–NH interactions increase the2

viscosity, but the effect is not as important as the breaking of self-associations, given that the negativevalues observed for Dh and GUE of the ternary system under study point out the easier flow of


UE Ž y1. Ž . Ž . Ž .Fig. 4. Isolines at constant G J mol for the ternary system 2-butanol 1 q n-hexane 2 q1-butylamine 3 correlatedŽ . Ž . Ž .with Cibulka’s Eq. 4 . a At T s298.15 K; b at T s313.15 K.

mixture compared with the behaviour of pure liquids. This is also in accordance with the conclusionsw xof Fort and Moore 26 about the behaviour of systems containing an associated component.

Comparing the values for the present ternary mixture with those reported for the systemŽ . w x UE1-butanolqn-hexaneq1-butylamine 20 , it can be seen that the Dh and G values are morenegative for the mixture with 2-butanol. This agrees with the fact that hydrogen bonding in secondarybutanol is not as strong as in primary butanol and their breaking is less difficult during the mixingprocess.

The correlation equations of Nissan and Grunberg, Hind, Frenkel, McAllister, Katti and Chaudhri,w xHeric and Iulan et al. have been developed for binary mixtures. Recently however, Canosa et al. 3

introduced a new parameter to correlate ternary systems.


Nissan and Grunberg:n n n n n n

ln h s x ln h q x x A q x x x A , 7Ž . Ž . Ž .Ý Ý Ý Ý Ý Ýi i i j i j i j k i jki i j)i i j)i k)j

Hind et al.:

n n n n n n2hs x h q2 x x A q x x x A , 8Ž .Ý Ý Ý Ý Ý Ýi i i j i j i j k i jkž /

i i j)i i j)i k)j

Frenkel:

n n n n n n2ln h s x ln h q2 x x ln A q x x x ln A , 9Ž . Ž . Ž .Ž . Ž .Ý Ý Ý Ý Ý Ýi i i j i j i j k i jkž /

i i j)i i j)i k)j

McAllister:n n n n n n

3 2ln hV s x ln h V q3 x x ln A q6 x x x ln A , 10Ž . Ž . Ž .Ž . Ž .Ý Ý Ý Ý Ý Ýi i i i j i j i j k i jki i j/i i j)i k)j

Katti and Chaudhri:n n n n n n

ln hV s x ln h V q x x A q x x x A , 11Ž . Ž . Ž .Ý Ý Ý Ý Ý Ýi i i i j i j i j k i jki i j)i i j)i k)j

Heric:

n n n 1 n n nkln hV s x ln h V q x x A x yx q x x x A , 12Ž . Ž . Ž . Ž .Ý Ý Ý Ý Ý Ý Ýi i i i j k i j i j k i jkž /

i i j)i ks0 i j)i k)j

Iulan et al.:

n n n 3 n n nkln hV s x ln h V q x x A x yx q x x x A . 13Ž . Ž . Ž . Ž .Ý Ý Ý Ý Ý Ý Ýi i i i j k i j i j k i jkž /

i i j)i ks0 i j)i k)j

where, for each equation, x is the mole fraction, h and h are the dynamic viscosity of the mixturei

and of the pure components, respectively, V and V are the molar volume of the mixture and of thei

pure components, respectively, A and A are the binary correlation parameters, and A is thei j k i jk

ternary correlation parameter. Eqs. 11–13 have the same shape and only differ in the number ofparameters. Correlation parameters and standard deviations for these equations are shown in Table 5.Our analysis shows that a rise of the number of parameters in Eqs. 11–13 leads to a smaller standard

Ž .deviation, while with the other equations less number of parameters , the best correlation method forthese binary and ternary systems is found using the McAllister equation and the worst using the Hindmodel. For the ternary system, the viscosity predictions obtained with these empirical and semiempiri-cal equations with only binary coefficients have bigger standard deviations than those obtainedintroducing the ternary parameter A .i jk


Table 5Adjustable parameters and standard deviations of several empirical and semiempirical equations for the binary and ternarymixtures

Ž . Ž . Ž .T K Equation Binary correlation parameters s h mPa s

( ) ( )2-Butanol 1 q n-hexane 2298.15 A Ai j ji

aNissan and Grunberg y2.4514 0.0336bHind et al. y0.7748 0.3120

bFrenkel 0.2795 0.0336cMcAllister 58.1791 45.2162 0.0092

A A A A0 1 2 3aKatti and Chaudhri y2.3747 0.0337

aHeric y2.1491 y0.6190 0.0092aIulan et al. y2.1448 y0.4550 y0.0185 y0.0192 0.0027

313.15 A Ai j jiaNissan and Grunberg y1.9858 0.0205

bHind et al. y0.2482 0.1474bFrenkel 0.2500 0.0205

cMcAllister 46.4801 38.5137 0.0040A A A A0 1 2 3

aKatti and Chaudhri y1.9057 0.0207aHeric y1.7490 y0.5167 0.0040

aIulan et al. y1.7364 y0.4545 y0.0183 0.0006 0.0019

( ) ( )2-Butanol 1 q1-butylamine 2298.15 A Ai j ji

aNissan and Grunberg y1.0127 0.0498bHind et al. 0.0791 0.1871



aHeric y0.8780 y0.5963 0.0070aIulan et al. y0.8661 y0.6144 y0.0149 0.0183 0.0067

313.15 A Ai j jiaNissan and Grunberg y0.5821 0.0183

bHind et al. 0.3420 0.0659bFrenkel 0.6197 0.0183

cMcAllister 78.0541 58.6092 0.0036A A A A0 1 2 3


aIulan et al. y0.5336 y0.2987 y0.0148 0.0110 0.0018

( ) ( )n-Hexane 1 q1-butylamine 2298.15 A Ai j ji




Ž .Table 5 continued

Ž . Ž . Ž .T K Equation Binary correlation parameters s h mPa s

( ) ( )n-Hexane 1 q1-butylamine 2A A A A0 1 2 3


aIulan et al. y0.3132 0.0012 y0.0037 y0.0025 0.0005313.15 A Ai j ji




aHeric y0.2746 0.0097 0.0006aIulan et al. y0.2718 0.0195 y0.0028 y0.0043 0.0006

Ž . Ž . Ž .T K Equation Ternary correlation s h mPa sparameter

Predicted from Correlated withbinary parameters ternary parameter

( ) ( ) ( )2-Butanol 1 q n-hexane 2 q1-butylamine 3298.15 Ai jk

aNissan and Grunberg 1.9666 0.0400 0.0323bHind et al. 2.4823 0.2067 0.1799

bFrenkel 2.6735 0.0400 0.0323cMcAllister 57.0818 0.2327 0.0079

aKatti and Chaudhri 1.9259 0.0397 0.0322aHeric 1.1870 0.0296 0.0144

aIulan et al. 1.0969 0.0178 0.0114313.15 Ai jk

aNissan and Grunberg 1.9740 0.0239 0.0142bHind et al. 1.1462 0.0901 0.0768

bFrenkel 2.6820 0.0239 0.0142cMcAllister 51.3201 0.1792 0.0028

aKatti and Chaudhri 1.9129 0.0234 0.0142aHeric 1.5548 0.0156 0.0028

aIulan et al. 1.4046 0.0143 0.0033

a Ž .A Dimensionless .ib Ž .A mPa s .i jc 3 Ž 4 y1 y1.A 10 kg m s mol .i j

w xThe ‘‘viscosity-thermodynamic’’ model UNIMOD 5 is used for correlating the viscosities ofbinary mixtures, and from these results to predict the viscosities of multicomponent systems. Adetailed description of the model is provided in the original paper. In this model, U yU are theji ii

Ž . w xinteraction potential energies the adjustable parameters obtained using a Simplex method 27 , whichŽ . Ž .are shown with standard deviations in Table 6. Fig. 3 a and b present the isolines of constant Dh


Table 6Ž . Ž .Adjustable parameters U yU and standard deviations s h of the UNIMOD model for the binary and ternary mixturesji ii

at 298.15 and 313.15 Ky1 y1Ž . Ž . Ž . Ž . Ž .T K U yU J mol U yU J mol s h mPa s21 11 12 22

( ) ( )2-Butanol 1 q n-hexane 2298.15 y205.2819 y2.2100 0.0063313.15 y202.4603 17.9091 0.0023

( ) ( )2-Butanol 1 q1-butylamine 2a298.15 y306.7801 238.6556 0.0219

313.15 y266.8451 218.8956 0.0090

( ) ( )n-Hexane 1 q1-butylamine 2b298.15 y39.6335 38.1476 0.0019b313.15 y37.9274 36.7534 0.0013

( ) ( ) ( )2-Butanol 1 q n-hexane 2 q1-butylamine 3298.15 – – 0.0166313.15 – – 0.0142

a w xParameters obtained from data of Ref. 19 .b w xRef. 20 .

Ž . Žpredicted with UNIMOD model dashed lines and compared with the experimental values continu-.ous lines .

w x w xThe GC-UNIMOD 7 and the Wu’s model 6 have been used as predictive models for both,binary and ternary mixtures. The van der Waals properties for the different subgroups and the group

Table 7Standard deviations of GC-UNIMOD model and Wu’s model for the binary and ternary systems at 298.15 and 313.15 K

Ž . Ž . Ž .T K s h mPa s

GC-UNIMOD Wu

UNIFAC ASOG

As1 As2.45 As1 As2.45

( ) ( )2-Butanol 1 q n-hexane 2298.15 0.3353 0.1343 0.2880 0.1363 0.2883313.15 0.1863 0.0520 0.1485 0.0529 0.1479

( ) ( )2-Butanol 1 q1-butylamine 3298.15 0.1292 0.7102 0.4149 0.6111 0.3807313.15 0.0258 0.3627 0.1959 0.3407 0.1881

( ) ( )n-Hexane 2 q1-butylamine 3298.15 0.0159 0.0348 0.0021 0.0298 0.0011313.15 0.0119 0.0266 0.0018 0.0255 0.0015

( ) ( ) ( )2-Butanol 1 q n-hexane 2 q1-butylamine 3298.15 0.1677 0.2908 0.2665 0.2638 0.2565313.15 0.0714 0.1380 0.1281 0.1330 0.1262


interaction energy parameters used in the GC-UNIMOD model have been obtained from Hansen et al.w x28 . The free energy of mixing needed in Wu’s model is obtained using the UNIFAC and ASOG

w x w xparameters proposed by Gmehling et al. 29 and Tochigi et al. 30 , respectively. Table 7 shows thestandard deviations for binary and ternary mixtures at two temperatures, 298.15 and 313.15 K,

Ž .obtained by application of GC-UNIMOD and Wu’s model. Comparing these values with s h of theUNIMOD model for the same mixtures, we can see that the last model yields smaller deviations, andalso it is capable to predict the viscosity of the ternary mixture rather well without other additionalparameters that those obtained for binary mixtures.

List of symbols

A empirical factor of Wu’s modelŽ .A adjustable coefficients of Eq. 3p

A binary adjustable coefficients of Eqs. 12 and 13k

A binary adjustable coefficients of Eqs. 7–11i

A ternary adjustable coefficients of Eqs. 7–13i jkŽ .B adjustable coefficients of Eq. 4p

UE Ž y1.G excess Gibbs energy of activation for viscous flow J molM molar mass of the mixtureM molar mass of pure component ii

m number of experimental pointsn number of components in the mixturep number of adjustable coefficientsR gas constant

Ž .T absolute temperature KU yU adjustable parameters of UNIMOD modelji ii

Ž 3 y1.V molar volume of the mixture cm molŽ 3 y1.V molar volume of pure component i cm moli

x mole fraction of component ii

Greek lettersŽ .h dynamic viscosity mPa s of the mixtureŽ .h dynamic viscosity mPa s of pure component iiŽ .Dh viscosity deviations mPa s of the mixture

Ž y3.r density of mixture g cmŽ y3.r density of pure component i g cmi

s standard deviationŽ .n kinematic viscosity cSt of the mixtureŽ .n kinematic viscosity cSt of pure component ii

Subscriptscalc calculatedexptl experimentallit literature


Acknowledgements

M. Domınguez gratefully acknowledges the support of Departamento de Educacion y Cultura del´ ´ŽGobierno de Navarra. The authors also thank the support of the CONSIqD of D.G.A Project

.PCB0894 .

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Viscosities of the ternary mixture (2-butanol+n-hexane+1-butylamine) at 298.15 and 313.15 K