Density and Viscosity from 293.15 to 373.15 K ... - ACS Publications

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Density and Viscosity from 293.15 to 373.15 K, Speed of Sound and Bulk Modulus from 293.15 to 343.15 K, Surface Tension, and Flash Point of Binary Mixtures of Bicyclohexyl and 1,2,3,4Tetrahydronaphthalene or Trans-decahydronaphthalene at 0.1 MPa Dianne J. Luning Prak,*,† Jim S. Cowart,‡ and Paul C. Trulove† †

Chemistry Department, United States Naval Academy 572M Holloway Road, Annapolis, Maryland 21402, United States Mechanical Engineering Department, United States Naval Academy 590 Holloway Road, Annapolis, Maryland 21402, United States

‡

S Supporting Information *

ABSTRACT: In this work, the physical properties of binary mixtures of bicyclohexyl and 1,2,3,4-tetrahydronaphthalene (tetralin) or trans-decahydronaphthalene (trans-decalin) were measured. Densities and viscosities were measured at temperatures from 293.15 to 373.15 K, and speeds of sound were measured at temperatures from 293.15 to 343.15 K. At 303.15 K, pure component values of density (960.9, 878.93, 862.29 kg·m−3), viscosity (1.85, 3.18, 1.79 mPa·s), and speed of sound (1450.2, 1422.7, 1357.5 m·s−1) are consistent with literature values for tetralin, bicyclohexyl, and transdecalin, respectively. Density mole fraction data were fit to second- or thirdorder polynomials. Viscosity mole fraction data were fit using the three-body McAllister model. The bulk modulus ranged from 1206 to 2149 MPa over 293.15 to 343.15 K. For tetralin mixtures, increasing tetralin increased density, speed of sound, bulk modulus, and surface tension and decreased viscosity and flash point. For trans-decalin mixtures, increasing trans-decalin decreased all properties measured. Increasing temperature decreased all properties values. At room temperature, surface tensions ranged from 30.5 to 35.6 mN·m−1. Flash points ranged from 328.7 to 361.2 K. These data are useful for comparing the properties of mixtures of components of coal and wood-based liquid fuels with those of petroleum-based fuels.

1. INTRODUCTION Fuels derived from nonpetroleum sources differ from petroleum-based fuels in their chemical composition, which impacts their physical and chemical properties. For example, petroleum-based jet fuels contain approximately 59% straightchain and branched alkanes, 21% cycloparaffins, 13% alkylbenzenes, 5% indans and tetralins, and 2% naphthalenebased compounds, 1 while coal-based jet fuels contain approximately 1% straight-chain and branched alkanes, 2% cycloparaffins, 4% alkylbenzenes, 59% indans and tetralins, 21% naphthalene-based compounds, and 13% decalins and tricyclics.2 Specific components in coal-based fuels include 1,2,3,4-tetrahydronaphthalene (tetralin), trans-decahydronaphthalene (trans-decalin), methylcyclohexane, and bicyclohexyl.3,5,6 Huber et al.4 developed a five-component surrogate mixture to model a coal-derived liquid fuel using trans-decalin, bicyclohexyl, n-propyl cyclohexane, α-methyldecalin, and nhexadecane. When testing the thermal stability of coal-based and petroleum jet fuels at 450 °C, Song et al.6 reported that trans-decalin and methylcyclohexane were among the most thermally stable of the coal-based fuel components and tetralin was the least stable. Recently, Jiang et al.7 prepared two component mixtures of bicyclohexyl with methylcyclohexane and other cyclohexanes and measured the density, viscosity, © 2015 American Chemical Society

and freezing point of the mixtures in an effort to provide basic data for the preparation of advanced fuels. Other binary mixtures of bicyclohexyl have also been investigated, including those with linear alkanes, cyclohexane, cycloheptane, cyclooctane, and benzene, but no measurements are currently available for mixtures of 1,1′-bicyclohexyl with tetralin and trans-decalin.8−10 The trans-decalin is of interest because it was one of the most thermally stable compound in coal-based fuels, and the tetralin is of interest because it is a component of coalbased fuels and has also been found in new liquid fuels derived from solid wood that has been pyrolyzed and hydrotreated.4,11 The goal of this work was to provide physical property measurements for binary mixtures of bicyclohexyl with tetralin and trans-decalin. The physical properties measured in this study are those that impact the delivery of fuel to an engine and the combustion process itself, namely density, viscosity, speed of sound, surface tension, and flash point. The viscosity, surface tension, and density influence the vaporization of multicomponent fuel droplets.12−15 The bulk modulus, which is calculated from Received: September 14, 2015 Accepted: December 21, 2015 Published: December 31, 2015 650

DOI: 10.1021/acs.jced.5b00790 J. Chem. Eng. Data 2016, 61, 650−661

Journal of Chemical & Engineering Data

Article

Table 1. Sample Information

a

chemical name

CAS number

molar mass (g/mol)a

source/lot number

mole fraction purity

analysis method

bicyclohexyl (C12H22) 1,2,3,4-tetrahydronaphthalene (C10H12) trans-decahydronaphthalene (C10H18)

92-51-3 119-64-2 493-02-7

166.3030(8) ± 0.0047(0) 132.2022(8) ± 0.0046(4) 138.2499(2) ± 0.0060(2)

TCI/VCLTM Aldrich/MKBN2319V TCI/R5K8F

0.997 0.989 0.995

GCb GCb GCb

Calculated using values in ref 25. bGas−liquid chromatography, as specified in the Certificates of Analysis provided by the chemical suppliers.

from which the average and standard deviation were determined. The combined expanded uncertainties of density, viscosity, speed of sound, surface tension, and flash point were determined by multiplying the standard deviations of the measurements (taken at each temperature as described above) by 2. When a normal distribution is assumed, multiplying by a coverage factor of 2 is related to a 95.45% confidence interval. The purity of a sample also impacts how close the measured values are to the true value of the measurements, and this was included in the analysis.24

speed of sound and density, directly affects fuel injection time.16−18 Flash point is an indicator of fuel combustibility and is part of the specifications for military diesel fuel.19 In this work, the density, viscosity, surface tension, speed of sound, and flash point were measured for binary mixtures of 1,1′bicyclohexyl with either tetralin or trans-decalin, and several of these properties were compared to petroleum-based fuels.

2. MATERIALS Bicyclohexyl, 1,2,3,4-tetrahydronaphthalene (tetralin), and trans-decahydronaphthalene (trans-decalin) were used as received from the supplier (Table 1). To prepare the mixtures, each component was weighed at room temperature on a Mettler Toledo AG204 analytical balance with an error of 0.0004 g. On the basis of this error, the combined expanded uncertainties (level of confidence = 0.9545, k = 2) in the mass fraction and mole fractions were calculated to be 0.0001 and 0.0001, respectively.

4. RESULTS 4.1. Density. The measured density values of the NISTcertified toluene standard match the certified values within the reported standard uncertainty of the measurements (Table 2), Table 2. Density and Speed of Sound Measurements for NIST- Certified Toluene Standard at 0.1 MPaa density/ kg·m−3

3. METHODS The densities and speeds of sound of the bicyclohexyl, 1,2,3,4tetrahydronaphthalene, trans-decahydronaphthalene, and their mixtures were measured using an Anton Paar DSA 5000 density and sound analyzer. The viscosities and densities were measured using an Anton Paar SVM 3000 Stabinger viscometer. The methods for cleaning, calibrating, and checking the accuracy of these instruments have been described previously.20,21 The accuracy of the density measurements was tested using a NIST toluene density reference standard. The speed of sound was measured at six temperatures between 293.15 and 343.15 K, and replicate samples were used to determine the standard deviation. The density and viscosity were measured at eight temperatures between 293.15 and 373.15 K, and replicate measurements were used to determine the standard deviation. The DSA 5000 only measures up to 343.15 K, so it was used for the lower-temperature density measurements, and the SVM 3000 was used for the highertemperature measurements 353.15 to 373.15 K. The surface tension of each organic liquid was measured using a Kruss DS100 drop shape analyzer.20−23 In drop shape analysis, a droplet of an organic liquid on the tip of a needle is magnified, recorded, and its shape is fit to the Young−LaPlace equation using input parameters of air density, organic liquid density, and the needle diameter that has been measured using a micrometer (Mitutoyo). More than 15 surface tension measurements were taken of at least 3 droplets of each liquid, and these values were used to calculate the standard deviation of each measurement. The flash point was measured using a Setaflash Series 8 closed cup flash point tester model 82000-0 (Stanhope-Seta) in temperature ramping mode. The manufacturer’s literature specifies that this flash point tester conforms to ASTM D3828 (gas ignition option), ASTM D1655 (gas ignition option), ASTM D3278, ASTM D7236, and ASTM E502. At least two measurements were taken for each mixture

T/K 293.15 303.15 313.15 323.15 333.15 343.15

this studya

literatureb

866.81(7) 857.49(7) 848.11(4) 838.66(4) 829.13(3) 819.50(6) speed of sound/ m·s−1

866.828 857.507 848.131 838.684 829.152 819.516

± ± ± ± ± ±

0.031 0.032 0.033 0.034 0.035 0.037

T/K

this studya

literature

293.15 303.15 313.15 323.15 333.15 343.15

1326.8 1283.6 1241.0 1198.9 1157.5 1116.7

1324.3e, 1326.3 ± 0.3c, 1326.9d, 1281.6e, 1283.3 ± 0.3c 1239.7e, 1240.6 ± 0.3c, 1240.9d, 1198.5e, 1198.6 ± 0.3c, 1198.9d, 1157.2 ± 0.3c, 1157.7d,1158.0e

a

Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainty for the measured values are Uc(ρ) = 0.07 kg·m−3 and Uc(c) = 0.3 m·s−1 (level of confidence = 0.9545, k = 2). The average pressure for these measurements was 0.102 MPa with a combined expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.9545, k = 2). b Reference 26, values for liquid density of SRM 211d “as shipped”. Error bars are the reported standard uncertainties, uN (k = 1). c Reference 27. dReference 66. eReference 67.

demonstrating the accuracy of the DSA 5000. The density values of bicyclohexyl, 1,2,3,4-tetrahydronaphthalene and transdecahydronaphthalene are given as a function of temperature in Table 3 along with literature values. The densities of the pure components match many of the reported values within the combined expanded uncertainty of the measurements. The density values of the 1,2,3,4-tetrahydronaphthalene and bicyclohexyl mixtures and the trans-decahydronaphthalene and bicyclohexyl mixtures are given in Table 4. 651



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Table 3. Comparison of the Measured Values of Density, Speed of Sound, and Viscosity of Bicyclohexyl, 1,2,3,4Tetrahydronaphthalene, and Trans-decahydronaphthalene with Literature Values at 0.1 MPaa density kg·m−3 compound

T/K

this studya

1,2,3,4-tetrahydronaphthalene (tetralin)

bicyclohexyl

293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 293.15

968.8 960.9 953.0 945.0 937.1 929.1 920.9 912.9 904.8 886.13

trans-decahydronaphthalene

303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 293.15

878.93 871.74 864.58 857.43 850.29 843.0 835.9 828.6 869.75

303.15

862.29

313.15 323.15

854.82 847.34

333.15 343.15 353.15 363.15 373.15

839.83 832.30 824.7 817.0 809.4

viscosity mPa·s this studya

literature 968.96 ± 0.02f 961.02 ± 0.02f, 961.7g 952.93p, 953.08 ± 0.02f 944.99p, 945.13 ± 0.02f 937.04p, 937.18 ± 0.02f 929.22 ± 0.02f

2.25 1.85 1.55 1.32 1.14 1.00 0.882 0.789 0.713 4.06

886.0 ± 0.8b, 886.39c, 886.50 ± 0.5d 879.19c 872.01c 858.10 ± 0.5d, 858.7 ± 0.1e

829.9 ± 0.1e 869.67 ± 0.27s, 869.78q 870.01 862.1 ± 0.5h, 862.21 ± 0.27s, 862.34q 854.75 ± 0.29s, 854.88q 847.1 ± 0.5h, 847.28 ± 0.38s, 847.40q 839.82 ± 0.57s 832.36 ± 0.27s, 832.0 ± 0.5h 824.89 ± 0.70s 817.43 ± 0.80s 809.97 ± 0.82s

3.18 2.56 2.10 1.76 1.50 1.29 1.13 1.00 2.14 1.79 1.51 1.30 1.12 0.982 0.867 0.774 0.697

literature 2.22k, 2.259l 1.8143m, 1.847l 1.53k, 1.543l, 1.60u 1.312l 1.133l, 1.13k 0.992l 0.876l 0.7716j 0.698j 3.75i, 3.91j, 4.017c, 4.027j, 3.06i, 3.145c, 3.17j 2.540c, 2.60j 1.995j, 2.16j 1.741j, 1.81j 1.279j 1.116j 0.982j 2.11j,2.103l, 2.128n, 2.128o 1.756l, 1.77j, 1.774n 1.488l, 1.493n, 1.50j 1.277l, 1.28j, 1.282n, 1.289r 1.108l, 1.1j, 1.114n 0.971l, 0.978n 0.859l, 0.865n 0.772n 0.689r, 0.692n

speed of sound this studya 1489.(5) 1450.(2) 1411.(5) 1373.(6) 1336.(4) 1299.(9)

literature 1486.1w, 1488.6y 1447.8v, 1449.3y 1410.7y, 1413p 1372.8y, 1374p 1335p, 1336.4y 1299.5y

1462.3 1422.7 1383.9 1345.9 1308.8 1272.4

1422.3v

1397.9 1357.5

1398.4 ± 0.2%x 1396.7y 1397.1t 1356.1 ± 0.2%x 1356.6t

1317.9 1279.1

1316.2 ± 0.2%x 1278.6 ± 0.2%x

1241.1 1203.8

1238.7 ± 0.2%x 1200.7 ± 0.2%x

a Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc are Uc(ρ) = 0.07 kg·m−3 for T < 353.15 K and Uc(ρ) = 0.2 kg· m−3 for T ≥ 353.15 K for bicyclohexyl and trans-decahydronaphthalene, Uc(ρ) = 0.2 kg·m−3 for the lower purity 1,2,3,4-tetrahydronaphthalene for T < 353.15 K and Uc(ρ) = 0.5 kg·m−3 for T ≥ 353.15 K, Uc(μ) = 0.02 mPa·s, Uc are Uc(c) = 0.5 m·s−1 for bicyclohexyl and transdecahydronaphthalene, and Uc(c) = 0.9 m·s−1 for the lower purity 1,2,3,4-tetrahydronaphthalene, (level of confidence = 0.9545, k = 2). The average pressure for these measurements was 0.102 MPa with a combined expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.9545, k = 2). b Reference 28. cReference 4. dReference 29. eReference 5. fReference 30. gReference 31. hReference 32. iReference 33. jReference 34. kReference 35. l Reference 36. mReference 37. nReference 38. oReference 39. pReference 40. qReference 41. rReference 42. sReference 43. tReference 44. uReference 45. vReference 46. wReference 47. xReference 48. yReference 49.

procedure was conducted using Microsoft Excel 2010, and the results are given in Table 5. The fits are good with R2 > 0.9999 as shown in Figure 1. A third-order fit was used instead of a second-order because the standard error for the second order fit was approximately 0.3, which is much higher than that of the third-order model, which was approximately 0.07. A secondorder polynomial was used to fit the density and mole fraction data for the trans-decahydronaphthalene mixtures

For the mixtures, the density increased as mole fraction of the 1,2,3,4-tetrahydronaphthalene increased (Figure 1), and it decreased as the mole fraction of trans-decahydronaphthalene increased (Figure 2), but the changes were not linear. A thirdorder polynomial was used to fit the density and mole fraction data for the 1,2,3,4-tetrahydronaphalene mixtures ρ /kg·m−3 = AX13 + BX12 + CX1 + D

(1)

In this equation X1 is the mole fraction of the 1,2,3,4tetrahydronaphthalene and A, B, C, and D are fitting parameters, which are given in Table 5. The standard error of the fit was calculated using σ=

ρ /kg·m−3 = AX12 + BX1 + C

In this equation X1 is the mole fraction of the transdecahydronaphthalene and A, B, and C are fitting parameters, which are given in Table 6. The fits are good with R2 > 0.9999 as shown in Figure 2. The fractional deviations of the fitted density values from the measured values are given in the Supporting Information. The densities of these mixtures can provide basic data for determining how alternative fuels containing these components could be utilized by the U.S. Navy. The military specification

∑ (Pmeasured − Pm,cal)2 N−n

(3)

(2)

in which Pmeasured is the measured density, Pm,cal is the fitted density, N is the number of experimental data, and n is the number of parameters in the fitting equation. The fitting 652



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Table 4. Densities (kg·m−3) of Mixtures of 1,2,3,4-Tetrahydronaphthalene (1) + Bicyclohexyl (2) and Transdecahydronaphthalene (1) + Bicyclohexyl (2), T = 293.15−373.15 K and 0.1 MPaa temperature/K W1

X1

293.15

0.1000 0.2001 0.3001 0.4000 0.5002 0.6000 0.6998 0.8001 0.9001

0.1226 0.2394 0.3504 0.4561 0.5573 0.6536 0.7457 0.8343 0.9189

893.3 900.8 908.4 916.3 924.5 932.8 941.4 950.3 959.4

0.1005 0.2000 0.3003 0.4000 0.5000 0.5999 0.7001 0.8001 0.8999

0.1185 0.2312 0.3405 0.4451 0.5460 0.6433 0.7374 0.8280 0.9154

884.26 882.51 880.73 879.03 877.41 875.78 874.19 872.67 871.18

303.15

313.15

323.15

333.15

1,2,3,4-Tetrahydronaphthalene (1) + Bicyclohexyl (2) 886.1 878.9 871.6 864.4 893.5 886.2 878.9 871.6 901.1 893.7 886.4 879.0 908.9 901.4 894.0 886.6 917.0 909.4 901.9 894.4 925.1 917.6 910.0 902.4 933.7 926.0 918.3 910.6 942.5 934.8 927.0 919.2 951.6 943.7 935.9 928.0 Trans-decahydronaphthalene (1) + Bicyclohexyl (2) 877.04 869.84 862.67 855.50 875.28 868.07 860.86 853.67 873.50 866.27 859.04 851.81 871.80 864.55 857.30 850.04 870.13 862.84 855.56 848.28 868.48 861.17 853.85 846.53 866.85 859.51 852.16 844.80 865.30 857.92 850.53 843.13 863.76 856.34 848.90 841.45

343.15

353.15

363.15

373.15

857.2 864.3 871.6 879.1 886.9 894.8 902.9 911.5 920.1

850.0 857.1 864.3 871.7 879.3 887.2 895.4 903.8 912.1

842.7 849.7 856.8 864.2 871.7 879.4 887.6 895.8 904.1

835.6 842.4 849.5 856.7 864.2 872.0 879.9 888.0 896.3

848.33 846.47 844.60 842.78 840.98 839.20 837.42 835.70 833.97

841.2 839.3 837.4 835.5 833.7 831.9 830.0 828.3 826.5

833.9 832.1 830.1 828.2 826.3 824.5 822.5 820.7 818.9

827.0 824.9 822.9 820.9 819.0 817.0 815.1 813.2 811.3

a

W1 is the mass fraction of 1,2,3,4-tetrahydronaphthalene or trans-decahydronaphthalene in mixtures with bicyclohexyl and X1 is the mole fraction of 1,2,3,4-tetrahydronaphthalene or trans-decahydronaphthalene in mixtures with bicyclohexyl. Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc is Uc(ρ) = 0.2 kg·m−3 for 1,2,3,4-tetrahydronaphthalene mixtures for T < 353.15 K and Uc(ρ) = 0.5 kg·m−3 for T ≥ 353.15 K and Uc(ρ) = 0.07 kg·m−3 for trans-decahydronaphthalene mixtures for T < 353.15 K and Uc(ρ) = 0.2 kg·m−3 for T ≥ 353.15 K (level of confidence =0.9545, k = 2). The average pressure for these measurements was 0.102 MPa with a combined expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.9545, k = 2).

Figure 2. Densities of trans-decahydronaphthalene (1) + bicyclohexyl mixtures at □, 293.15 K; ■, 303.15 K; Δ, 313.15 K; ▲, 323.15 K; ◊, 333.15 K; ⧫, 343.15 K; ○, 353.15 K; ●, 363.15 K; and x, 373.15 K. Error bars, which are the combined expanded uncertainties with 0.9545 level of confidence (k = 2), are smaller than the symbols. Lines shown are second-order fits using eq 3 with the coefficients in Table 6.

Figure 1. Densities of 1,2,3,4-tetrahydronaphthalene (1) + bicyclohexyl mixtures at □, 293.15 K; ■, 303.15 K; Δ, 313.15 K; ▲, 323.15 K; ◊, 333.15 K; ⧫, 343.15 K; ○, 353.15 K; ●, 363.15 K; and x, 373.15 K. Error bars, which are the combined expanded uncertainties with 0.9545 level of confidence (k = 2), are smaller than the symbols. Lines shown are third-order fits using eq 1 with the coefficients in Table 5.

VmE =

for diesel fuel requires that the fuel have a density of less than 876 kg·m−3 at 288.15 K.19 All the 1,2,3,4-tetrahydronaphthalene mixtures studied here exceed this specification, and only the mixtures of trans-decalin in bicyclohexyl with mole fractions greater than 0.8280 will meet this specification. For mixtures, such as those studied herein, to be used in military applications, they must be mixed with petroleum-based fuels or other components to lower the density. The excess molar volumes (VmE) of bicyclohexyl with either 1,2,3,4-tetrahydronaphthalene or trans-decahydronaphthalene were calculated using the following equation20,21

M1X1 + M 2X 2 MX MX − 1 1 − 2 2 ρm ρ1 ρ2

(4)

in which ρm is the density of the mixture, ρ1 and ρ2 are the pure component densities, M1 and M2 are the molar masses, and X1 and X2 are the mole fractions of 1,2,3,4-tetrahydronaphthalene or trans-decahydronaphthalene as component 1 and bicyclohexyl as component 2. The calculated excess molar volumes for the 0.5573 mole fraction of 1,2,3,4-tetrahydronaphthalene in bicyclohexyl (weight fraction = 0.5002) are given in Table 5. These excess molar volumes are positive values that do change over the temperature range studied within the combined 653



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Table 5. Parameters for Equation 1, ρ/kg·m−3 = AX13 + BX12 + CX1 + D, That Correlates Density to Mole Fraction of 1,2,3,4Tetrahydronaphthalene (X1) in (1,2,3,4-Tetrahydronaphthalene + Bicyclohexyl) Mixtures and the Excess Molar Volume (VmE) at w1 = 0.5002, T = 293.15−373.15 K, and 0.1 MPaa T/K 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

A 11.1 11.3 11.4 11.1 11.0 10.9 9.8 10.3 9.8

± ± ± ± ± ± ± ± ±

B 1.1 1.5 1.4 1.4 1.4 1.4 2.0 1.9 2.1

14.2 13.5 13.0 13.0 12.8 12.6 13.3 12.4 12.5

± ± ± ± ± ± ± ± ±

C 1.8 2.2 2.2 2.1 2.1 2.1 3.0 2.8 3.3

57.4 57.1 56.8 56.3 55.8 55.2 54.8 54.2 53.8

± ± ± ± ± ± ± ± ±

D 0.7 0.9 0.9 0.9 0.9 0.9 1.3 1.2 1.4

886.11 878.90 871.71 864.55 857.40 850.26 843.0 835.9 828.7

± ± ± ± ± ± ± ± ±

0.08 0.11 0.10 0.10 0.10 0.10 0.1 0.1 0.2

R2

σ

VmE/cm3·mol−1

0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999

0.04 0.05 0.05 0.05 0.05 0.05 0.07 0.06 0.07

0.20 0.20 0.20 0.20 0.20 0.20 0.17 0.19 0.16

a The “±” symbols for the coefficients A, B, C, and D represent the 95% confidence interval. The σ is the standard error of the fit as given by eq 2. The combined expanded uncertainty (level of confidence = 0.9545, k = 2) for the excess molar volume is 0.03 cm3·mol−1 for temperatures less than 353.15 K and 0.05 cm3·mol−1 for temperatures equal to or above 353.15 K.

Table 6. Parameters for Equation 3, ρ/kg·m−3 = AX12 + BX1 + C, That Correlates Density to Mole Fraction of Transdecahydronaphthalene (1) in (Trans-decahydronaphthalene + Bicyclohexyl) Mixtures, and the Excess Molar Volume (VmE) at w1 = 0.5000, T = 293.15−373.15 K, and 0.1 MPaa T/K 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

A −0.8 −1.1 −1.4 −1.6 −1.8 −2.1 −2.7 −2.9 −3.3

± ± ± ± ± ± ± ± ±

B 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.3 0.6

−15.6 −15.5 −15.6 −15.6 −15.8 −15.9 −15.7 −15.9 −16.0

± ± ± ± ± ± ± ± ±

C 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.3 0.7

886.13 878.92 871.73 864.56 857.41 850.26 843.0 835.8 828.7

± ± ± ± ± ± ± ± ±

0.03 0.03 0.02 0.02 0.03 0.03 0.1 0.1 0.2

R2

σ

VmE/cm3·mol−1

0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998

0.02 0.01 0.01 0.01 0.02 0.02 0.03 0.03 0.08

0.09 0.08 0.07 0.06 0.05 0.05 0.02 0.01 −0.02

The “±” symbols for the coefficients A, B, C, and D represent the 95% confidence interval. The σ is the standard error of the fit as given by eq 2. The combined expanded uncertainty (level of confidence = 0.9545, k = 2) for the excess molar volume is 0.03 cm3·mol−1 for temperatures less than 353.15 K and 0.05 cm3·mol−1 for temperatures equal to or above 353.15 K. a

ment. The combined expanded uncertainty of 1,2,3,4tetrahydronaphthalene, which is based in part on impurities, may be overestimated in this case. The speed of sound values for the NIST toluene standard compare favorably to previously measured values as shown in Table 2. The speed of sound values of the 1,2,3,4-tetrahydronaphthalene and bicyclohexyl and trans-decahydronaphthalene and bicyclohexyl mixtures are given in Table 7 as a function of the mole fraction of 1,2,3,4tetrahydronaphthalene or trans-decahydronaphthalene (X1). As the mole fraction of the 1,2,3,4-tetrahydronaphthalene increased, the speed of sound increased as shown in Figure 3 but the trend is not linear. As the mole fraction of the transdecahydronaphthalene increased, the speed of sound decreased as shown in Figure 4, and its trend is also not linear. The experimental data for the 1,2,3,4-tetrahydronaphthalene were fit with a third-order model

expanded uncertainty of the measurements. The positive values indicate that the molecules are less closely packed in the mixture than they are as pure liquids, and this packing does not change with temperature. Positive values of excess molar volume have also been found for mixtures of 1,2,3,4tetrahydronaphthalene with cyclohexane.50 The calculated excess molar volumes for the 0.5460 mole fraction of transdecahydronaphthalene in bicyclohexyl (weight fraction = 0.5000) are given in Table 6. The excess molar volumes are small positive values that decrease as temperature increases and become negative at 373.15 K. The values are not statistically different from zero at temperatures above 333.15 K. Researchers have shown that the excess molar volume of trans-decalin with linear alkanes becomes less negative as the carbon number on the linear alkane increases41 is negative for cyclohexane and only becomes zero for cyclooctane at a few mixture compositions.51,52 In the current study, the slightly positive excess molar volumes for trans-decalin suggest that the more asymmetric nature of the bicyclohexyl may cause it to pack with trans-decalin less well than cyclohexane packs with trans-decalin. 4.2. Speed of Sound and Bulk Modulus. The speed of sound values of 1,2,3,4-tetrahydronaphthalene, bicyclohexyl, and trans-decahydronaphthalene measured herein are given as a function of temperature in Table 3 along with literature values. The values measured herein agree with the reported values within the combined expanded uncertainty of the measure-

c /m·s−1 = AX13 + BX12 + CX1 + D

(5)

In this equation, X1 is the mole fraction of the 1,2,3,4tetrahydronaphthalene, and A, B, C, and D are fitting parameters. Initial analysis showed that the “B” was essentially zero, so that term was omitted and the data were fit without the “B” term. The values of A, C, and D from the fit are given in Table 8. The standard error for the fit (σ) was determined by eq 2, where Pmeasured is the measured speed of sound and Pm,cal is the fitted speed of sound. The model fits the data well (with R2 > 0.999) as shown in Figure 3. The experimental data for the 654



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Table 7. Speeds of Sound (m·s−1) of Mixtures of 1,2,3,4Tetrahydronaphthalene (1) + Bicyclohexyl and Transdecahydronaphthalene (1) + Bicyclohexyl, T = 293.15− 343.15 K and 0.1 MPaa X1 0.1226 0.2394 0.3504 0.4561 0.5573 0.6536 0.7457 0.8343 0.9189 0.1185 0.2312 0.3405 0.4451 0.5460 0.6433 0.7374 0.8280 0.9154

T/K 293.15

T/K 303.15

T/K 313.15

T/K 323.15

T/K 333.15

1,2,3,4-Tetrahydronaphthalene (1) + Bicyclohexyl (2) 1463.4 1423.8 1385.0 1347.0 1309.8 1464.7 1425.2 1386.4 1348.4 1311.3 1466.5 1427.0 1388.2 1350.2 1313.1 1468.4 1429.0 1390.2 1352.3 1315.1 1471.0 1431.4 1392.1 1354.0 1316.6 1473.7 1434.2 1395.2 1357.2 1319.9 1476.7 1437.4 1398.8 1360.8 1323.6 1480.3 1441.1 1402.5 1364.6 1327.4 1484.6 1445.3 1406.8 1368.9 1331.7 Trans-decahydronaphthalene (1) + Bicyclohexyl (2) 1455.2 1415.6 1376.8 1338.8 1301.6 1448.6 1408.9 1370.1 1332.0 1294.7 1442.1 1402.4 1363.5 1325.3 1287.9 1435.6 1395.8 1356.8 1318.6 1281.1 1429.3 1389.4 1350.3 1312.0 1274.4 1422.9 1382.9 1343.7 1305.3 1267.7 1416.6 1376.5 1337.2 1298.7 1261.0 1410.4 1370.2 1330.8 1292.2 1254.4 1404.0 1363.8 1324.3 1285.6 1247.7

T/K 343.15 1273.4 1274.8 1276.6 1278.6 1280.0 1283.4 1287.0 1290.8 1295.1

Figure 4. Speeds of sound of trans-decahydronaphthalene (1) + bicyclohexyl mixtures at □, 293.15 K; ■, 303.15 K; Δ, 313.15 K; ▲, 323.15 K; ◊, 333.15 K; and ⧫, 343.15 K. Error bars, which are the combined expanded uncertainties with 0.9545 level of confidence (k = 2), are smaller than the symbols. Lines shown are 2nd order fits using eq 6 with the coefficients in Table 9.

1265.0 1258.6 1251.2 1244.3 1237.6 1230.7 1223.9 1217.2 1210.5

Table 8. Parameters for Equation 5, c = AX13 + CX1 + D, That Correlates Speed of Sound, c (m·s−1) to Mole Fraction of 1,2,3,4-Tetrahydronaphthalene (X1) in (1,2,3,4Tetrahydronaphthalene + Bicyclohexyl) Mixtures and Associated Standard Error, σ, Over Temperature Range T = 293.15−343.15 Ka

a

X1 is the mole fraction of 1,2,3,4-tetrahydronaphthalene or transdecahydronaphthalene in mixtures with bicyclohexyl. Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc is Uc(c) = 1 m·s−1 for 1,2,3,4-tetrahydronaphthalene mixtures and 0.5 m·s−1 for trans-decahydronaphthalene mixtures (level of confidence = 0.9545, k = 2). The average pressure for these measurements was 0.102 MPa with a combined expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.9545, k = 2).

T/K 293.15 303.15 313.15 323.15 333.15 343.15

A/m·s−1 16.9 17.2 17.7 18.0 18.3 18.5

± ± ± ± ± ±

0.8 0.5 0.8 1.2 1.4 1.4

C/m·s−1 10.2 10.3 10.0 9.8 9.4 9.1

± ± ± ± ± ±

0.9 0.5 0.9 1.3 1.5 1.5

D/m·s−1 1462.2 1422.6 1383.8 1345.9 1308.8 1272.4

± ± ± ± ± ±

0.8 0.2 0.3 0.4 0.5 0.5

R2

σ

0.999 0.999 0.999 0.999 0.999 0.999

0.16 0.10 0.16 0.23 0.27 0.28

The “±” symbols for the coefficients A, C, and D represent the 95% confidence interval. The σ is the standard error of the fit as given by eq 2. a

of sound and Pm,cal is the fitted speed of sound. The model fits the data well (with R2 > 0.999) as shown in Figure 4. The fractional deviations of the fitted speed of sound values from the measured values are given in the Supporting Information. The isentropic bulk modulus of each 1,2,3,4-tetrahydronaphthalene and trans-decahydronaphthalene mixture, Ev, was calculated at each temperature and ambient pressure from the speed of sound (c) and density (ρ) by20−23 Ev /Pa = (c 2/m 2·s−2)(ρ /kg·m−3)

The calculated values are given Table 10. The bulk modulus decreases with increasing temperature and increasing mole fraction of trans-decahydronaphthalene and decreasing mole fraction of 1,2,3,4-tetrahydronaphthalene. The values of bulk modulus for all the mixtures studied herein exceed those reported for a petroleum-based diesel fuel.18 For example, all the mixtures in Table 10 at 293.15 K have values of bulk modulus that exceed the 1610 MPa reported for petroleumbased diesel fuel at the same temperature.18 Higher values of bulk modulus can cause the start of injection time in mechanical injection diesel engines to occur sooner (advance relative to piston Top Dead Center), which can further impact the timing of combustion. 4.3. Viscosity. The viscosity values of 1,2,3,4-tetrahydronaphthalene, trans-decahydronaphthalene, and bicyclohexyl are

Figure 3. Speeds of sound of 1,2,3,4-tetrahydronaphthalene (1) + bicyclohexyl mixtures at □, 293.15 K; ■, 303.15 K; Δ, 313.15 K; ▲, 323.15 K; ◊, 333.15 K; and ⧫, 343.15 K; Error bars, which are the combined expanded uncertainties with 0.9545 level of confidence (k = 2), are smaller than the symbols. Lines shown are 3rd order fits using eq 5 with the coefficients in Table 8.

1,2,3,4-tetrahydronaphthalene were fit with a second-order model c /m·s−1 = AX12 + BX1 + C

(7)

(6)

In this equation X1 is the mole fraction of the transdecahydronaphthalene, and A, B, and C are fitting parameters, which are given in Table 9. The standard error for the fit (σ) was determined by eq 2, where Pmeasured is the measured speed 655



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Table 9. Parameters for Equation 6, c = AX12 + BX1 + C, That Correlates Speed of Sound, c (m·s−1) to Mole Fraction of Transdecahydronaphthalene (X1) in (Trans-decahydronaphthalene + Bicyclohexyl) Mixtures and Associated Standard Error, σ, Over Temperature Range T = 293.15−343.15 Ka A/m·s−1

T/K

−8.5 −9.0 −9.6 −10.0 −10.2 −10.5

293.15 303.15 313.15 323.15 333.15 343.15 a

± ± ± ± ± ±

B/m·s−1 −55.6 −55.9 −56.1 −56.5 −57.2 −57.9

1.2 1.1 1.0 0.9 1.0 1.2

± ± ± ± ± ±

C/m·s−1

1.3 1.2 1.0 1.0 1.0 1.3

1462.1 1422.5 1383.7 1345.7 1308.6 1272.3

± ± ± ± ± ±

0.3 0.3 0.2 0.2 0.2 0.3

R2

σ

0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

0.15 0.14 0.12 0.11 0.13 0.16

The “±” symbols for the coefficients A, C, and D represent the 95% confidence interval. The σ is the standard error of the fit as given by eq 2. ln νm = X13 ln ν1 + 3X12X 2 ln ν1,2 + 3X1X 22 ln ν2,1 + X 23 ln ν2

Table 10. Values of Bulk Modulus (MPa) of Mixtures of 1,2,3,4-Tetrahydronaphthalene (X1) + Bicyclohexyl and Trans-decahydronaphthalene (X1) + Bicyclohexyl, T = 293.15−343.15 K and 0.1 MPaa X1 0.000 0.1226 0.2394 0.3504 0.4561 0.5573 0.6536 0.7457 0.8343 0.9189 1.000 0.1185 0.2312 0.3405 0.4451 0.5460 0.6433 0.7374 0.8280 0.9154 1.000

T/K 293.15

T/K 303.15

T/K 313.15

T/K 323.15

T/K 333.15

1,2,3,4-Tetrahydronaphthalene (1) + Bicyclohexyl (2) 1895 1779 1669 1566 1469 1913 1796 1686 1581 1483 1933 1815 1703 1598 1499 1954 1835 1722 1616 1516 1976 1856 1742 1635 1533 2001 1879 1763 1653 1550 2026 1903 1786 1676 1572 2053 1929 1812 1701 1596 2082 1957 1839 1726 1620 2114 1988 1868 1754 1646 2149 2021 1899 1783 1674 Trans-decahydronaphthalene (1) + Bicyclohexyl (2) 1872 1757 1649 1546 1449 1852 1737 1629 1527 1431 1832 1718 1610 1509 1413 1812 1698 1591 1491 1395 1792 1680 1573 1473 1378 1773 1661 1555 1455 1360 1754 1642 1537 1437 1343 1736 1624 1519 1420 1327 1717 1606 1502 1403 1310 1699 1589 1485 1386 1294

⎛1⎛ ⎛ M ⎞ M ⎞⎞ − ln⎜X1 + X 2 2 ⎟ + 3X12X 2 ln⎜⎜ ⎜2 + 2 ⎟⎟⎟ M1 ⎠ M1 ⎠⎠ ⎝ ⎝3⎝ ⎛1⎛ ⎛M ⎞ M ⎞⎞ + 3X1X 22 ln⎜⎜ ⎜1 + 2 2 ⎟⎟⎟ + X 23 ln⎜ 2 ⎟ M1 ⎠⎠ ⎝ M1 ⎠ ⎝3⎝

T/K 343.15

(8)

Here νm is the kinematic viscosity of the binary mixture, X1 and X2 are the mole fractions, ν1 and ν2 are the kinematic viscosities of the pure components, and M1 and M2 are the molar masses of 1,2,3,4-tetrahydronaphthalene or trans-decahydronaphthalene as component 1 and bicyclohexyl as component 2. To determine the interaction parameters ν2,1 and ν1,2, the GRG nonlinear engine of the SOLVER function in Microsoft Excel 2010 was used to minimize the sum of the square of the difference between the value calculated by the model in eq 8, νm,calc, and the measured kinematic viscosity of the binary mixture, νmeasured20,21,23

1377 1390 1405 1420 1437 1453 1474 1496 1519 1543 1570 1357 1341 1322 1305 1288 1271 1254 1238 1222 1206

min ∑ (νm,calc − νmeasured)2

(9)

The standard error for the fit (σ) was determined by eq 2, in which Pmeasured is the measured viscosity and Pm,cal is the fitted viscosity. Both the fitted values of ν2,1, and ν1,2, and the standard errors of the fits are given in Table 12 at each temperature. Figures 5 and 6 show that the model fits the data well. The viscosity deviation (Δν) was also calculated for the two component systems using

a

X1 is the mole fraction of 1,2,3,4-tetrahydronaphthalene or transdecahydronaphthalene in mixtures with bicyclohexyl. Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc is Uc(bulk modulus) = 1 MPa, (level of confidence = 0.9545, k = 2). The average pressure for these measurements was 0.102 MPa with a combined expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.9545, k = 2).

Δν = νm − (X1ν1) − (X 2ν2)

(10)

νm is the kinematic viscosity of the binary mixture, ν1 and ν2 are the kinematic viscosities of the pure components, and X1 and X2 are the mole fractions of 1,2,3,4-tetrahydronaphthalene or trans-decahydronaphthalene as component 1 and bicyclohexyl as component 2. The calculated values of the viscosity deviations for all two-component mixtures are given in Tables S1 and S2 of the Supporting Information. Figures 7 and 8 show that the viscosity deviations for all the mixtures are negative. The negative viscosity deviations indicate that the molecules in the mixture are sliding past each other more easily than would be predicted by a simple linear addition of viscosities using pure liquid values. As the temperature increases, the viscosity values deviate less from ideal mixing. The viscosity deviations were fit using a Redlich−Kister type expression54

given as a function of temperature in Table 2 along with literature values. The viscosities of the pure components match reported values within the combined expanded uncertainty of the measurements. The dynamic and kinematic viscosity values of the 1,2,3,4-tetrahydronaphthalene, trans-decahydronaphthalene, bicyclohexyl, and their mixtures are given in Table 11 as a function of the mole fraction (X1) of 1,2,3,4-tetrahydronaphthalene or trans-decahydronaphthalene in bicyclohexyl. The value for pure bicyclohexyl (w = 0) is only reported once in the table but applies to both mixtures. The McAllister three-body model53 was used to fit the kinematic viscosity data 656



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Table 11. Viscosities of Mixtures of 1,2,3,4-Tetrahydronaphthalene (X1) + Bicyclohexyl and Trans-decahydronaphthalene (X1) + Bicyclohexyl, T = 293.15−373.15 K and 0.1 MPaa T/K X1

Viscosity

0.0000 0.1226 0.2394 0.3504 0.4561 0.5573 0.6537 0.7470 0.8343 0.9189 1.000

0.1185 0.2312 0.3405 0.4451 0.5460 0.6433 0.7374 0.8280 0.9154 1.000

293.15

μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1

4.06 4.58 3.67 4.11 3.35 3.72 3.08 3.39 2.87 3.14 2.70 2.92 2.55 2.74 2.44 2.59 2.34 2.47 2.28 2.37 2.25 2.32

μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1

3.72 4.21 3.43 3.89 3.17 3.60 2.96 3.36 2.77 3.15 2.60 2.97 2.45 2.81 2.33 2.67 2.21 2.54 2.14 2.46

303.15

313.15

323.15

333.15

1,2,3,4-Tetrahydronaphthalene (1) + Bicyclohexyl (2) 3.18 2.56 2.10 1.76 3.62 2.93 2.43 2.05 2.91 2.36 1.95 1.64 3.28 2.68 2.24 1.90 2.67 2.19 1.82 1.54 2.99 2.47 2.07 1.77 2.48 2.04 1.71 1.45 2.76 2.29 1.93 1.66 2.33 1.93 1.62 1.38 2.56 2.14 1.81 1.56 2.20 1.83 1.54 1.32 2.40 2.01 1.71 1.48 2.09 1.75 1.48 1.27 2.26 1.90 1.63 1.41 2.00 1.68 1.43 1.23 2.15 1.81 1.55 1.35 1.93 1.62 1.38 1.19 2.05 1.74 1.49 1.30 1.88 1.58 1.35 1.16 1.98 1.67 1.44 1.26 1.85 1.55 1.32 1.14 1.93 1.63 1.40 1.22 Trans-decahydronaphthalene (1) + Bicyclohexyl (2) 2.95 2.39 1.98 1.66 3.37 2.75 2.29 1.94 2.74 2.24 1.87 1.58 3.14 2.58 2.17 1.85 2.56 2.11 1.77 1.50 2.93 2.43 2.05 1.76 2.40 1.99 1.68 1.43 2.76 2.30 1.96 1.68 2.27 1.89 1.60 1.36 2.60 2.19 1.86 1.61 2.15 1.80 1.52 1.31 2.47 2.09 1.78 1.54 2.03 1.71 1.46 1.25 2.35 1.99 1.71 1.48 1.94 1.64 1.40 1.21 2.24 1.91 1.64 1.43 1.85 1.57 1.34 1.16 2.14 1.83 1.58 1.38 1.79 1.51 1.30 1.12 2.07 1.77 1.53 1.34

343.15

353.15

363.15

373.15

1.50 1.76 1.40 1.64 1.32 1.53 1.25 1.44 1.20 1.36 1.15 1.29 1.11 1.24 1.07 1.19 1.04 1.14 1.02 1.11 0.998 1.07

1.29 1.53 1.22 1.43 1.15 1.34 1.09 1.27 1.05 1.20 1.01 1.15 0.973 1.10 0.944 1.05 0.920 1.02 0.901 0.987 0.882 0.958

1.13 1.35 1.07 1.27 1.01 1.19 0.967 1.13 0.928 1.07 0.895 1.03 0.866 0.985 0.841 0.948 0.821 0.917 0.804 0.890 0.789 0.865

0.997 1.20 0.948 1.13 0.903 1.07 0.865 1.02 0.832 0.97 0.803 0.93 0.778 0.893 0.758 0.861 0.740 0.834 0.726 0.810 0.713 0.788

1.42 1.67 1.35 1.60 1.29 1.53 1.23 1.46 1.18 1.41 1.14 1.35 1.09 1.30 1.05 1.26 1.02 1.22 0.982 1.18

1.23 1.46 1.17 1.40 1.12 1.34 1.08 1.29 1.04 1.24 0.996 1.20 0.960 1.16 0.927 1.12 0.897 1.09 0.867 1.05

1.08 1.29 1.03 1.24 0.990 1.19 0.952 1.15 0.917 1.11 0.884 1.07 0.853 1.04 0.825 1.01 0.799 0.976 0.774 0.947

0.957 1.16 0.919 1.11 0.883 1.07 0.850 1.04 0.820 1.00 0.792 0.969 0.765 0.939 0.741 0.911 0.718 0.885 0.697 0.861

a

X1 is the mole fraction of 1,2,3,4-tetrahydronaphthalene or trans-decahydronaphthalene in mixtures with bicyclohexyl. Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc is Uc(μ) = 0.02 mPa·s and Uc(ν) = 0.02 mm2·s−1 (level of confidence = 0.9545, k = 2). The average pressure for these measurements was 0.102 MPa with a combined expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.9545, k = 2).

is the mole and bicyclohexyl. The standard error for the fit (σ) was determined by eq 2, where Pmeasured is the calculated viscosity deviation and Pfit is the fitted viscosity deviation. The fitted values of A0, A1, and A2, and the standard errors of the fits are given in Table 13 for each temperature. The model fits the data well as shown in Figures 7 and 8. The viscosities of these mixtures can provide basic data for determining how alternative fuels containing these components could be used by the U.S. Navy. The military specification for

2

Δν = X1X 2 ∑ Aj (X1 − X 2) j j=0

= X1X 2{A 0 + [A1(X1 − X 2)] + [A 2 (X1 − X 2)]2 } (11)

where Aj are adjustable parameters, j is the order of the polynomial, and X1 is the mole fraction of either 1,2,3,4tetrahydronaphthalene or trans-decahydronaphthalene and X2 657



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Table 12. Values of the Coefficients for McAllister Equation (Equation 8) and Associated Standard Error (Equation 2) for Binary Mixtures of 1,2,3,4-Tetrahydronaphthalene + Bicyclohexyl and Trans-decahydronaphthalene + Bicyclohexyl, T = 293.15−373.15 K and 0.1 MPa T/K 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

ν12 /mm2·s−1

ν21 /mm2·s−1

103·σ /mm2·s−1

1,2,3,4-Tetrahydronaphthalene (1) + Bicyclohexyl (2) 2.59 3.41 5.3 2.16 2.77 2.5 1.83 2.30 0.96 1.58 1.94 0.22 1.37 1.66 0.74 1.21 1.44 0.49 1.08 1.27 0.54 0.969 1.13 0.42 0.878 1.02 0.30 Trans-decahydronaphthalene (1) + Bicyclohexyl (2) 2.84 3.63 7.1 2.39 2.95 3.3 2.03 2.45 1.4 1.75 2.06 0.37 1.53 1.76 0.70 1.34 1.53 0.44 1.19 1.34 0.39 1.07 1.20 0.42 0.961 1.08 0.34

Figure 6. Viscosities of trans-decahydronaphthalene (1) + bicyclohexyl mixtures at □, 293.15 K; ■, 303.15 K; Δ, 313.15 K; ▲, 323.15 K; ◊, 333.15 K; ⧫, 343.15 K; ○, 353.15 K; ●, 363.15 K; and x, 373.15 K. Error bars, which are the combined expanded uncertainties with 0.9545 level of confidence (k = 2), are smaller than the symbols. Lines shown are fits using eq 8 with the coefficients in Table 12.

Figure 7. Viscosity deviations of 1,2,3,4-tetrahydronaphthalene (1) + bicyclohexyl mixtures as calculated by eq 9 at □, 293.15 K; ■, 303.15 K; Δ, 313.15 K; ▲, 323.15 K; ◊, 333.15 K; ⧫, 343.15 K; ○, 353.15 K; ●, 363.15 K; and x, 373.15 K. Lines shown are fits to eq 11 with the coefficients in Table 13. Data can be found in the Supporting Information. Error bars, which are the combined expanded uncertainties with 0.9545 level of confidence (k = 2), are not shown (∼0.02 mm2·s−1). Figure 5. Viscosities of 1,2,3,4-tetrahydronaphthalene (1) + bicyclohexyl mixtures at □, 293.15 K; ■, 303.15 K; Δ, 313.15 K; ▲, 323.15 K; ◊, 333.15 K; ⧫, 343.15 K; ○, 353.15 K; ●, 363.15 K; and x, 373.15 K. Error bars, which are the combined expanded uncertainties with 0.9545 level of confidence (k = 2), are smaller than the symbols. Lines shown are fits using eq 8 with the coefficients in Table 12.

the surface tension of 1,2,3,4-tetrahydronaphthalene vary significantly as shown in Figure 9. The value measured herein of 36.1 ± 0.2 mN·m−1 at 294.1 ± 0.5 K, shown as an “X” in Figure 9, falls along the temperature trend of four of the referenced values.58−61 As can be seen from the data in Table 14, the surface tension increases as the mole fraction of 1,2,3,4tetrahydronaphthalene increases and as the mole fraction of trans-decahydronaphthalene decreases. The flash point of bicyclohexyl, 364.7 ± 2 K, agrees with literature values of 365 and 365.15 K,62,63 and the value for trans-decahydronaphthalene, 326.7 ± 2 K, agrees with the reported values of 326.8 and 330.2 K41,63 within the combined expanded uncertainty of the measurements. The flash point of 1,2,3,4-tetrahydronaphthalene, 347.7 ± 2 K, falls between values reported in the literature of 344 and 350 K.42,63 The flash point values decrease as the mole fraction of either 1,2,3,4tetrahydronaphthalene or trans-decahydronaphthalene increases. The flash point of these mixtures can provide basic data for determining how alternative fuels containing these components could be incorporated into use by the U.S. Navy. The military

diesel fuel requires that the fuel have a viscosity between 1.7 and 4.3 mm2·s−1 at 313.15 K.19 The 1,2,3,4-tetrahydronaphthalene mixtures with mole fractions ranging from 0 to 0.8343 and all the trans-decahydronaphthalene mixtures studied herein would meet this specification. 4.4. Surface Tension and Flash Point. The surface tension and flash point values are given in Table 14 for the mixtures studied herein as a function of the mole fraction of 1,2,3,4-tetrahydronaphthalene or trans-decahydronaphthalene, X1, in bicyclohexyl. The surface tension of bicyclohexyl, 32.7 ± 0.2 mN·m−1 at 294.0 ± 0.5 K agrees with the literature values of 32.74 and 32.5 mN·m−1 at 293.2 K,55,56 while the surface tension of trans-decahydronaphthalene, 30.5 ± 0.2 mN·m−1 at 294.0 ± 0.5 K, is slightly higher than the literature values of 29.89 and 30.15 mN·m−1 at 293.2 K.57,64 Literature values for 658



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Table 14. Surface Tensions and Flash Points of Mixtures of 1,2,3,4-Tetrahydronaphthalene + Bicyclohexyl and Transdecahydronaphthalene + Bicyclohexyla X1

Figure 8. Viscosity deviations of trans-decahydronaphthalene (1) + bicyclohexyl mixtures as calculated by eq 9 at □, 293.15 K; ■, 303.15 K; Δ, 313.15 K; ▲, 323.15 K; ◊, 333.15 K; ⧫, 343.15 K; ○, 353.15 K; ●, 363.15 K; and x, 373.15 K. Lines shown are fits to eq 11 with the coefficients in Table 13. Data can be found in the Supporting Information. Error bars, which are the combined expanded uncertainties with 0.9545 level of confidence (k = 2), are not shown (∼0.02 mm2·s−1).

Table 13. Parameters for Redlich−Kister Equation, Equation 11, for Excess Viscosities of Binary Mixtures of 1,2,3,4Tetrahydronaphthalene + Bicyclohexyl and Transdecahydronaphthalene + Bicyclohexyl and Associated Standard Error (Equation 2) at 0.1 MPa

293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

A0·10 mm2·s−1

A1·10 mm2·s−1

A2·10 mm2·s−1

± ± ± ± ± ± ± ±

1 1 1 1 1 1 1 1

± ± ± ± ± ± ± ± ±

1 1 3 5 3 6 3 2 1

a X1 is the mole fraction of 1,2,3,4-tetrahydronaphthalene in (1,2,3,4tetrahydronaphthalene + bicyclohexyl) or trans-decahydronaphthalene in (trans-decahydronaphthalene + bicyclohexyl). Combined expanded uncertainties Uc are U(x1) = 0.0001, for surface tension Uc(surface tension) and flash point Uc(flash point) are indicated by the symbol “±”. Surface tension measurements were taken at room temperature, 294.1 ± 1 K. The average pressure for these measurements was 0.102 MPa with a combined expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.9545, k = 2).

σ·103 mm2·s−1

1,2,3,4-Tetrahydronaphthalene (1) + Bicyclohexyl (2) −16.5 1.56 −1.95 −11.4 0.925 −0.869 −8.07 0.601 −0.269 −5.92 0.456 0.017 −4.45 0.332 0.154 −3.44 0.289 0.094 −2.72 0.289 0.118 −2.17 0.147 0.141 −1.75 0.024 0.136 Trans-decahydronaphthalene (1) + Bicyclohexyl (2) −11.0 0.354 −1.70 −6.96 0.088 −4.06 −4.49 0.061 −0.058 −3.00 0.121 0.017 −2.10 0.133 0.199 −1.49 0.155 0.046 −1.13 0.131 0.098 −0.83 0.039 0.148 −0.61 0.061 0.118

flash point (K)

1,2,3,4-Tetrahydronaphthalene (1) + Bicyclohexyl (2) 32.91 ± 0.2 361.2 33.25 ± 0.2 358.2 33.41 ± 0.2 356.5 33.86 ± 0.2 354.2 34.02 ± 0.2 353.8 34.38 ± 0.2 351.2 34.71 ± 0.2 350.7 35.56 ± 0.2 349.2 Trans-decahydronaphthalene (1) + Bicyclohexyl (2) 0.1185 32.20 ± 0.4 355.5 0.2312 31.88 ± 0.22 349.8 0.3405 31.58 ± 0.2 346.5 0.4449 31.29 ± 0.2 342.7 0.5000 31.06 ± 0.2 340.2 0.5999 30.82 ± 0.2 337.9 0.7001 30.73 ± 0.2 335.6 0.8001 30.67 ± 0.2 330.7 0.8999 30.53 ± 0.2 328.7 0.1226 0.2394 0.3504 0.4561 0.5573 0.6536 0.7459 0.9189

T/K

surface tension (mN·m‑1)

4.0 2.3 1.0 0.50 0.58 0.84 0.61 0.47 0.35 4.8 3.4 1.7 0.53 0.66 0.53 0.29 0.34 0.39

Figure 9. Surface tension values for 1,2,3,4-tetrahydronaphthalene: x, current measurement; ◊, ref 61; ⧫, ref 60; ○, ref 58; ●, ref 59; □, ref 65; and ▲, ref 55.

specification for diesel fuel requires that the fuel have a flash point greater than 333.15 K.19 All of the 1,2,3,4-tetrahydronaphthalene mixtures and the trans-decahydronaphthalene mixtures with mole fractions ranging from 0 to 0.7001 studied herein would meet this specification.

function of mole fraction of 1,2,3,4-tetrahydronaphthalene. Second-order polynomials were used to fit the density and speed of sound data and for trans-decahydronaphthalene mixture as a function of mole fraction of trans-decahydronaphthalene. The excess molar volumes were positive for 1,2,3,4tetrahydronaphthalene mixtures with bicyclohexyl, which is consistent with previous studies that showed that 1,2,3,4tetrahydronaphthalene had positive molar volume with cyclohexane. The excess molar volumes were also positive for transdecahydronaphthalene except at the highest temperature, which differs from previous work that showed that mixtures of transdecahydronaphthalene with cyclohexane had negative molar volumes. It may be that the structure of bicyclohexyl does not

5. CONCLUSIONS In this work, the physical properties of mixtures of bicyclohexyl with 1,2,3,4-tetrahydronaphthalene or trans-decahydronaphthalene were measured. Most of the pure component measurements fell within values reported in the literature. Third-order polynomials were used to fit the density and speed of sound data and for 1,2,3,4-tetrahydronaphthalene mixtures as a 659



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allow it to pack as trans-decahydronaphthalene packs with cyclohexane. Viscosity values of the mixtures at each temperature were well modeled using the McAllister three-body model. These data can be used to determine how the properties of mixtures of components found in coal-based fuels compare with those of petroleum-based fuels. In the case of the mixtures studied herein, the densities of most of the mixtures are larger than allowed by the U.S. Navy, so other components would have to be added for it to be acceptable. The viscosity and flash point data suggest that several mixtures would be meet the criteria for Navy fuels.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00790. The values of the viscosity deviation for the mixtures. Fractional deviations of fitted density values. Fractional deviations of fitted speed of sound values. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (410) 293-6339. Fax: (410) 293-2218. Funding

This work was funded by the Office of Naval Research and a Kinnear Fellowship awarded to D.J.L.P. Notes

The authors declare no competing financial interest.

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REFERENCES

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