Measurement and correlation of density and viscosity of n-hexadecane with three fatty acid ethyl esters

J. Chem. Thermodynamics 97 (2016) 127–134

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Measurement and correlation of density and viscosity of n-hexadecane with three fatty acid ethyl esters Xiaojie Wang, Xiaopo Wang ⇑, Hanxiao Lang Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an 710049, China

a r t i c l e

i n f o

Article history: Received 6 November 2015 Received in revised form 17 January 2016 Accepted 24 January 2016 Available online 4 February 2016 Keywords: n-Hexadecane Ethyl caprylate Ethyl caprate Ethyl laurate Density Viscosity

a b s t r a c t This work reports the density and viscosity of binary mixtures for n-hexadecane with three fatty acid ethyl esters (ethyl caprylate, ethyl caprate, and ethyl laurate) in the overall composition range at temperatures from 298.15 to 323.15 K and at atmospheric pressure (0.1 MPa). Excess molar volumes and viscosity deviations have been obtained. In addition, the viscosities of the binary mixtures were correlated using a rough hard-sphere model. The average absolute relative deviations between the experimental data and the calculated values were 0.26% for n-hexadecane/ethyl caprylate, 0.30% for n-hexadecane/ ethyl caprate, and 0.24% for n-hexadecane/ethyl laurate with optimized adjustable parameters. It indicates that the rough hard-sphere model is able to reproduce the viscosity behavior of the studied binary mixtures very well. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Biodiesels consist of mixtures of alkyl esters of fatty acid (typically methyl or ethyl) obtained by a transesterification reaction where a vegetable oil or an animal fat is combined with a short chain alcohol such as methanol or ethanol [1]. Biodiesel has a high cetane number, wherefrom reduced solid particle and hydrocarbons emissions. It is, therefore, considered as a renewable and environmental friendly alternative diesel fuel for diesel engine. In the last few years, researchers have made effort to establish novel approaches to improve the production or purification of biodiesels [2–4]. In addition, to study the thermophysical properties of fatty esters or biodiesels have attracted more and more attention [5–8]. Due to the complete miscibility of biodiesel with diesel oil, the blending of both fuels in any proportion may improve fuel qualities and engine performance [9]. The knowledge of the thermodynamics and transport properties of the mixtures of biodiesel + diesel oil is essential to optimize the diesel engine. Density and viscosity are the most important properties of a fuel, influencing especially the injection system, atomization quality and combustion quality. Several investigations on the density and viscosity of biodiesel + diesel oil mixtures have been reported in the literature [10–13]. As biodiesels and diesel oils are all multi-component mixtures, changes in compounds profile affect their densities and viscosities. The ⇑ Corresponding author. Tel.: +86 29 82668210; fax: +86 29 82668789. E-mail address: [email protected] (X. Wang). http://dx.doi.org/10.1016/j.jct.2016.01.021 0021-9614/Ó 2016 Elsevier Ltd. All rights reserved.

knowledge of the properties of the pure compounds or its mixtures enables the prediction of the properties of biodiesel + diesel oil mixtures. To the best of our knowledge, the density and viscosity of n-hexadecane (a reference molecule for modeling diesel oil thermodynamics properties) with pure fatty acid ethyl esters (for example, ethyl caprylate, ethyl caprate, or ethyl laurate) have not been reported in the literature. In this work, the density and viscosity of binary mixtures of n-hexadecane with ethyl caprylate, ethyl caprate, and ethyl laurate at temperatures from 298.15 to 323.15 K over the entire composition range were reported, and the excess molar volumes and viscosity deviations were obtained.

2. Experimental section 2.1. Samples n-Hexadecane (CH3(CH2)14CH3), ethyl caprylate (CH3(CH2)6COOCH2CH3), ethyl caprate (CH3(CH2)8COOCH2CH3), and ethyl laurate (CH3(CH2)10COOCH2CH3) were supplied by Aladdin Chemistry and the mass purity was better than 99%. All samples were used without further purification. Table 1 shows the sample descriptions used in the present work. The densities and viscosities of the pure components were measured and compared to the literatures [14–26], as indicated in table 2. The data obtained in this work have a good agreement with the literature values. The preparation of binary mixtures was done by weighing using an analytical balance (model AB204 N, Mettler-Toledo) with an accuracy of

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X. Wang et al. / J. Chem. Thermodynamics 97 (2016) 127–134

TABLE 1 Sample descriptions in this work.

a

Chemical name

CAS

Source

n-Hexadecane Ethyl caprylate Ethyl caprate Ethyl laurate

544-76-3 106-32-1 110-38-3 106-33-2

Aladdin Aladdin Aladdin Aladdin

Chemistry Chemistry Chemistry Chemistry

Mass fraction puritya

Purification method

0.99 0.99 0.99 0.99

None None None None

As stated by the supplier.

TABLE 2 Comparison between the experimental and literature values for the densities and viscosities of the pure components from T = (298.15 to 323.15) K at atmospheric pressure (0.1 MPa).a Component

T/K

g/mPa  s

10
3q/kg  m
3

Exp.

Lit.

Ethyl caprylate

298.15 303.15 308.15 313.15 318.15 323.15

0.86264 0.85834 0.85404 0.84972 0.84539 0.84106

0.8621614 0.8578414 0.8535214 0.8491714 0.8448414 0.8404914

0.863015 0.858715 0.854415 0.850015 0.854715 0.841415

0.8623616 0.8580716 0.8537616 0.8494616 0.8451416 0.8408116

0.8621520 0.8578320 0.8535220 0.8491420 0.8448720 0.8404620

1.428 1.313 1.211 1.121 1.042 0.971

1.41120 1.29820 1.19320 1.09920 1.02720 0.95020

Ethyl caprate

298.15 303.15 308.15 313.15 318.15 323.15

0.86005 0.85599 0.85192 0.84785 0.84377 0.83969

0.8599014 0.8558314 0.8517614 0.8476914 0.8436114 0.8395314

0.860215 0.856215 0.852115 0.848015 0.843915 0.839815

0.8599416 0.8558816 0.8518216 0.8477516 0.8436816 0.839616

0.8598418 0.8555018 0.8516818 0.8480018 0.8435218 0.8397018

2.115 1.919 1.75 1.603 1.474 1.362

2.10315 1.91115 1.74515 1.60015 1.47315 1.36015

Ethyl laurate

298.15 303.15 308.15 313.15 318.15 323.15

0.85819 0.85430 0.85040 0.84650 0.84260 0.83870

0.8582514 0.8543514 0.8504514 0.8465614 0.8426514 0.8387414

0.858515 0.854615 0.850715 0.846815 0.842915 0.839015

0.8582417 0.8543517 0.8504517 0.8465617 0.8426517 0.8387517

3.015 2.704 2.439 2.213 2.016 1.846

3.01515 2.70715 2.44615 2.22015 2.02415 1.85315

298.15 303.15 308.15 313.15 318.15 323.15

0.76992 0.76651 0.76306 0.7596 0.75614 0.75268

0.770222 0.766722 0.763322 0.759822 0.756322 0.752922

0.769823 0.766423 0.762923 0.759423 0.756023 0.752523

0.769924

3.085 2.756 2.477 2.239 2.034 1.857

3.06725 2.75725 2.47825 2.23025 2.01425 1.82925

n-Hexadecane

Exp.

Lit.

0.763624 0.759724

2.12219 1.93719 1.76719 1.61119 1.47119 1.34519 2.69521 2.04521

3.06124 2.72026 2.45824 2.22524 1.82026

Standard uncertainty in the measurement u(T) = 0.01 K and u(p) = 0.002 MPa. The combined expanded uncertainty in density measurement Uc(q) = 0.8 kg  m
3 and in viscosity measurement Uc(g) = 1% with a 0.95 level of confidence.

a

TABLE 3 Densities (q) and excess molar volumes (VE) for the binary mixtures from T = (298.15 to 323.15) K at atmospheric pressure (0.1 MPa).a x1

b

10
3q/kg  m
3

0.0000 0.1000 0.2000 0.3000 0.4000 0.4999 0.6000 0.7000 0.8000 0.9000 1.0000

0.86264 0.84872 0.83620 0.82494 0.81477 0.80552 0.79709 0.78938 0.78233 0.77588 0.76992

0.0000 0.1000 0.2000 0.3000 0.4000 0.4999 0.6000

0.84972 0.83618 0.82400 0.81304 0.80316 0.79416 0.78597

106VE/m3  mol
1 T = 298.15 K 0.0000 0.2173 0.3878 0.5051 0.5636 0.5839 0.5532 0.4852 0.3685 0.2028 0.0000 T = 313.15 K 0.0000 0.2263 0.4023 0.5239 0.5839 0.6061 0.5759

10
3q/kg  m
3

106VE/m3  mol
1

n-Hexadecane(1) + ethyl caprylate (2) T = 303.15 K 0.85834 0.0000 0.84455 0.2211 0.83214 0.3946 0.82097 0.5149 0.81090 0.5753 0.80174 0.5968 0.79339 0.5678 0.78575 0.5010 0.77876 0.3860 0.77236 0.2221 0.76651 0.0000 T = 318.15 K 0.84539 0.0000 0.83198 0.2283 0.81992 0.4059 0.80906 0.5281 0.79927 0.5887 0.79037 0.6102 0.78225 0.5794

10
3q/kg  m
3

0.85404 0.84037 0.82807 0.81701 0.80703 0.79795 0.78968 0.78211 0.77518 0.76884 0.76306 0.84106 0.82777 0.81583 0.80508 0.79539 0.78656 0.77853

106VE/m3  mol
1 T = 308.15 K 0.0000 0.2236 0.3989 0.5197 0.5805 0.6028 0.5732 0.5060 0.3908 0.2263 0.0000 T = 323.15 K 0.0000 0.2314 0.4105 0.5343 0.5947 0.6163 0.5844

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X. Wang et al. / J. Chem. Thermodynamics 97 (2016) 127–134 TABLE 3 (continued) x1

b

0.7000 0.8000 0.9000 1.0000

10
3q/kg  m
3

106VE/m3  mol
1

10
3q/kg  m
3

106VE/m3  mol
1

10
3q/kg  m
3

106VE/m3  mol
1

0.77847 0.77161 0.76533 0.75960

0.5074 0.3913 0.2252 0.0000

0.77483 0.76804 0.76181 0.75614

0.5107 0.3928 0.2262 0.0000

0.77118 0.76446 0.75830 0.75268

0.5147 0.3954 0.2271 0.0000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.86005 0.84840 0.83744 0.82717 0.81750 0.80841 0.79981 0.79169 0.78398 0.77678 0.76992

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.84785 0.83643 0.82569 0.81562 0.80615 0.79724 0.78882 0.78086 0.77331 0.76626 0.75960

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.7999 0.9000 1.0000

0.85819 0.84820 0.83849 0.82903 0.81983 0.81088 0.80218 0.79376 0.78559 0.77765 0.76992

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.7999 0.9000 1.0000

0.84650 0.83663 0.82707 0.81775 0.80868 0.79987 0.79130 0.78301 0.77496 0.76714 0.75960

T = 298.15 K 0.0000 0.1570 0.2869 0.3744 0.4278 0.4399 0.4215 0.3747 0.3001 0.1608 0.0000 T = 313.15 K 0.0000 0.1647 0.2993 0.3907 0.4479 0.4626 0.4457 0.3990 0.3240 0.1842 0.0000

n-Hexadecane(1) + ethyl caprate (2) T = 303.15 K 0.85599 0.0000 0.84441 0.1604 0.83353 0.2937 0.82332 0.3832 0.81371 0.4393 0.80469 0.4532 0.79615 0.4363 0.78808 0.3912 0.78042 0.3185 0.77327 0.1800 0.76651 0.0000 T = 318.15 K 0.84377 0.0000 0.83243 0.1669 0.82176 0.3030 0.81177 0.3951 0.80235 0.4528 0.79351 0.4666 0.78515 0.4499 0.77725 0.4016 0.76976 0.3263 0.76274 0.1866 0.75614 0.0000

T = 298.15 K 0.0000 0.1062 0.1917 0.2621 0.3112 0.3376 0.3359 0.2974 0.2295 0.1275 0.0000 T = 313.15 K 0.0000 0.1183 0.2061 0.2804 0.3324 0.3607 0.3605 0.3225 0.2539 0.1522 0.0000

n-Hexadecane(1) + ethyl laurate (2) T = 303.15 K 0.85430 0.0000 0.84434 0.1139 0.83469 0.2009 0.82527 0.2732 0.81611 0.3244 0.80721 0.3520 0.79855 0.3524 0.79018 0.3152 0.78204 0.2480 0.77414 0.1473 0.76651 0.0000 T = 318.15 K 0.84260 0.0000 0.83277 0.1210 0.82326 0.2092 0.81399 0.2840 0.80497 0.3364 0.79619 0.3644 0.78768 0.3637 0.77943 0.3260 0.77142 0.2559 0.76364 0.1532 0.75614 0.0000

T = 308.15 K 0.0000 0.1623 0.2973 0.3875 0.4447 0.4588 0.4425 0.3970 0.3240 0.1846 0.0000 T = 323.15 K 0.0000 0.1693 0.3074 0.4007 0.4587 0.4718 0.4547 0.4058 0.3292 0.1862 0.0000

0.85192 0.84042 0.82961 0.81948 0.80993 0.80096 0.79249 0.78447 0.77687 0.76976 0.76306 0.83969 0.82842 0.81783 0.80790 0.79856 0.78978 0.78148 0.77364 0.76620 0.75924 0.75268

T = 308.15 K 0.0000 0.1165 0.2042 0.2777 0.3292 0.3576 0.3585 0.3207 0.2535 0.1522 0.0000 T = 323.15 K 0.0000 0.1238 0.2133 0.2888 0.3406 0.3688 0.3681 0.3292 0.2589 0.1549 0.0000

0.85040 0.84049 0.83088 0.82151 0.81240 0.80354 0.79493 0.78659 0.77850 0.77064 0.76306 0.83870 0.82891 0.81945 0.81022 0.80125 0.79252 0.78405 0.77584 0.76788 0.76014 0.75268

The standard uncertainties u are u(x1) = 2.0  10
4, u(p) = 0.002 MPa, and u(T) = 0.01 K, the combined expanded uncertainties Uc are Uc(q) = 0.8 kg  m
3 and Uc(V E ) = 0.002  10
6 m3  mol
1, with a 0.95 level of confidence. b x1 is the mole fraction of n-hexadecane. a

TABLE 4 Viscosities (g) and viscosity deviations (Dg) for the binary mixtures from T = (298.15 to 323.15) K at atmospheric pressure (0.1 MPa).a x1b

g

Dg (mPa  s)

(mPa  s) T = 298.15 K 0.0000 0.1000 0.2000 0.3000 0.4000 0.4999 0.6000

1.428 1.539 1.651 1.776 1.916 2.065 2.229

0.000
0.055
0.108
0.149
0.175
0.191
0.193

g (mPa  s) n-Hexadecane(1) + ethyl caprylate (2) T = 303.15 K 1.313 1.407 1.513 1.623 1.744 1.875 2.019

Dg (mPa  s)

(mPa  s)

g

0.000
0.050
0.088
0.123
0.145
0.159
0.160

1.211 1.296 1.387 1.490 1.596 1.712 1.837

Dg (mPa  s) T = 308.15 K 0.000
0.042
0.077
0.101
0.121
0.132
0.134 (continued on next page)

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X. Wang et al. / J. Chem. Thermodynamics 97 (2016) 127–134

TABLE 4 (continued) (mPa  s)

Dg (mPa  s)

(mPa  s)

Dg (mPa  s)

(mPa  s)

Dg (mPa  s)

0.7000 0.8000 0.9000 1.0000

2.408 2.608 2.840 3.085


0.180
0.146
0.079 0.000

2.175 2.348 2.543 2.756


0.148
0.119
0.069 0.000

1.974 2.124 2.291 2.478


0.124
0.100
0.060 0.000

0.0000 0.1000 0.2000 0.3000 0.4000 0.4999 0.6000 0.7000 0.8000 0.9000 1.0000

1.121 1.197 1.279 1.371 1.467 1.570 1.680 1.801 1.933 2.083 2.239

0.000
0.036
0.066
0.086
0.101
0.110
0.112
0.103
0.083
0.044 0.000

1.042 1.110 1.185 1.267 1.351 1.444 1.543 1.650 1.766 1.897 2.034

0.000
0.031
0.055
0.073
0.088
0.094
0.094
0.086
0.070
0.038 0.000

0.971 1.034 1.101 1.172 1.251 1.334 1.422 1.517 1.620 1.736 1.857

0.000
0.036
0.068
0.091
0.109
0.118
0.118
0.109
0.088
0.054 0.000

1.750 1.790 1.837 1.890 1.948 2.013 2.086 2.167 2.257 2.358 2.478

0.000
0.025
0.043
0.057
0.068
0.074
0.073
0.067
0.054
0.032 0.000

1.362 1.390 1.423 1.460 1.501 1.546 1.595 1.651 1.712 1.779 1.857

0.000
0.036
0.065
0.088
0.101
0.107
0.106
0.096
0.077
0.045 0.000

2.439 2.412 2.392 2.377 2.368 2.367 2.372 2.384 2.403 2.433 2.478

0.000
0.022
0.042
0.056
0.064
0.068
0.068
0.062
0.050
0.029 0.000

1.846 1.832 1.813 1.801 1.795 1.793 1.795 1.800 1.813 1.833 1.857

x1b

g

g

T = 313.15 K

T = 318.15 K

T = 298.15 K 0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

2.115 2.169 2.230 2.298 2.374 2.460 2.556 2.664 2.785 2.923 3.085

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1.603 1.639 1.680 1.726 1.777 1.835 1.899 1.970 2.049 2.137 2.239

0.000
0.043
0.079
0.107
0.129
0.140
0.140
0.130
0.106
0.065 0.000 T = 313.15 K 0.000
0.028
0.050
0.068
0.081
0.086
0.085
0.078
0.063
0.038 0.000 T = 298.15 K

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.7999 0.9000 1.0000

3.015 2.977 2.954 2.935 2.925 2.923 2.933 2.952 2.980 3.024 3.085

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.7999 0.9000 1.0000

2.213 2.188 2.169 2.155 2.149 2.146 2.150 2.160 2.179 2.203 2.239

g

0.000
0.046
0.075
0.102
0.118
0.127
0.124
0.112
0.091
0.054 0.000 T = 313.15 K 0.000
0.027
0.049
0.065
0.075
0.079
0.079
0.071
0.055
0.034 0.000

n-Hexadecane(1) + ethyl caprate (2) T = 303.15 K 1.919 1.966 2.019 2.079 2.144 2.219 2.303 2.396 2.501 2.618 2.756 T = 318.15 K 1.474 1.506 1.544 1.585 1.630 1.680 1.737 1.799 1.869 1.947 2.034 n-Hexadecane(1) + ethyl laurate (2) T = 303.15 K 2.704 2.673 2.650 2.632 2.624 2.623 2.629 2.645 2.668 2.706 2.756 T = 318.15 K 2.016 1.996 1.978 1.966 1.959 1.957 1.959 1.967 1.981 2.003 2.034

T = 323.15 K 0.000
0.026
0.048
0.064
0.074
0.080
0.080
0.074
0.059
0.032 0.000 T = 308.15 K 0.000
0.032
0.058
0.078
0.092
0.100
0.100
0.092
0.075
0.047 0.000 T = 323.15 K 0.000
0.022
0.038
0.050
0.059
0.064
0.064
0.058
0.046
0.028 0.000 T = 308.15 K 0.000
0.031
0.055
0.074
0.086
0.092
0.090
0.082
0.067
0.041 0.000 T = 323.15 K 0.000
0.016
0.035
0.048
0.055
0.058
0.058
0.054
0.042
0.023 0.000

The standard uncertainties u are u(x1) = 2.0  10
4, u(p) = 0.002 MPa, and u(T) = 0.01 K, the combined expanded uncertainties Uc are Uc(g) = 1% and Uc(4g) = 0.05 mPa  s, with a 0.95 level of confidence. b x1 is the mole fraction of n-hexadecane. a

131

X. Wang et al. / J. Chem. Thermodynamics 97 (2016) 127–134 TABLE 5 Redlich
Kister coefficients (Ai) at different temperatures for the excess molar volumes (VE) and viscosity deviations (Dg) and standard deviations (r). YE

T/K

A0

A1

VE/(cm3  mol
1)

298.15 303.15 308.15 313.15 318.15 323.15 298.15 303.15 308.15 313.15 318.15 323.15

2.32596 2.37938 2.40206 2.41495 2.43205 2.45570
0.76170
0.63539
0.52878
0.43924
0.37629
0.31930

n-Hexadecane (1) + ethyl caprylate (2) 0.11573 0.22773
0.02776 0.10359 0.23895
0.16702 0.10528 0.24048
0.18604 0.11376 0.24353
0.15967 0.12365 0.24460
0.16328 0.13423 0.24534
0.15811 0.17210
0.20406 0.13131 0.13652
0.04872 0.15561 0.14727
0.05751
0.10977 0.11909
0.11071
0.09244 0.06575
0.04632 0.12519 0.05330
0.08031 0.06116


0.33596
0.17485
0.13974
0.15476
0.15988
0.16429 0.34970 0.02472
0.00256 0.15451 0.05690 0.11488

298.15 303.15 308.15 313.15 318.15 323.15 298.15 303.15 308.15 313.15 318.15 323.15

1.75423 1.80798 1.83106 1.84625 1.86415 1.88530
0.55983
0.47285
0.39996
0.34451
0.29533
0.25575

n-Hexadecane (1) + ethyl caprate (2) 0.10073 0.34972
0.81048 0.06219 0.36529
0.81661 0.05346 0.37158
0.80638 0.05492 0.33710
0.77888 0.06312 0.32836
0.76247 0.07651 0.35471
0.80835 0.12273
0.03212 0.06064 0.10261
0.01402
0.00901 0.08164
0.01767 0.00330 0.04855
0.00506 0.08138 0.05699 0.00212 0.02675 0.05038
0.00096
0.04622


0.48790
0.33748
0.31533
0.27521
0.24322
0.30817
0.04094
0.05157
0.06731
0.04257
0.04508
0.05172

298.15 303.15 308.15 313.15 318.15 323.15 298.15 303.15 308.15 313.15 318.15 323.15

1.35176 1.41207 1.43465 1.44670 1.46195 1.47942
0.50542
0.42869
0.36636
0.31854
0.27357
0.23276

n-Hexadecane (1) + ethyl laurate (2)
0.24512
0.12556 0.14878
0.26873
0.11881 0.06321
0.27575
0.12059 0.05006
0.26982
0.13920 0.05831
0.26919
0.13570 0.07364
0.26467
0.12481 0.07898 0.04717
0.00187 0.18614 0.03663
0.05666 0.11319 0.03830
0.02711 0.06856 0.04453
0.01782
0.08479 0.03878
0.05859
0.02217 0.03422
0.08978
0.03481

0.06646 0.27465 0.32289 0.34578 0.35092 0.35353
0.11711 0.04140
0.03629
0.01769 0.06883 0.19008

Dg/(mPa  s)

VE/(cm3  mol
1)

Dg/(mPa  s)

VE/(cm3  mol
1)

Dg/(mPa  s)

±0.1 mg. The uncertainty in the mole fraction was estimated to be less than 2.0  10
4.

2.2. Density measurements Densities of the binary mixtures were measured by an Anton Paar digital vibrating-tube densimeter (DMA 5000). The temperature in the cell was regulated to T = ±0.01 K according to ITS-90. The repeatability provided by the manufacturer for the density specified as 1.0  10
3 kg  m
3. The combined uncertainty of the density in this work were better than 0.8 kg  m
3 with a 0.95 level of confidence. Additional details regarding the procedure were given elsewhere [27,28].

2.3. Viscosity Measurements The viscosities of the mixtures were measured using an Ubbelohde capillary viscometer (model EGV 700) with a diameter of 0.47 mm provided by Lauda (Lauda Co., Germany), the characteristic constant of the viscometer is 0.0033549 mm2  s
2. The viscometer was kept in a water thermostat bath and the uncertainty of the temperature measurement was within 0.01 K. The combined uncertainty of the viscosity was estimated to be less than 1% with a 0.95 level of confidence. Details about the experimental procedure can be found in our previous work [29].

A2

A3

A4

A5

r


0.23954
0.12053

0.0018 0.0018 0.0019 0.0020 0.0019 0.0021 0.0010 0.0006 0.0007 0.0008 0.0007 0.0004

0.95435 0.79202 0.75129 0.75092 0.70174 0.78827
0.02199 0.06395 0.04527
0.06456
0.06833 0.05806

0.0031 0.0030 0.0031 0.0028 0.0028 0.0029 0.0004 0.0004 0.0003 0.0003 0.0002 0.0002


0.26456
0.11756
0.03429 0.13557 0.05857 0.09014

0.0009 0.0011 0.0013 0.0012 0.0011 0.0015 0.0007 0.0003 0.0003 0.0004 0.0001 0.0002


0.20625
0.25240 0.10978

3. Results and discussion The experimental density and viscosity results of the binary mixtures n-hexadecane with ethyl caprylate, ethyl caprate, and ethyl laurate over the temperature range from 298.15 to 323.15 K at atmospheric pressure are listed in tables 3 and 4, respectively. The excess molar volume VE can be obtained from experimental density data according to the following equation:

VE ¼

  2 X 1 1 xi M i


q

i¼1

qi

ð1Þ

where xi, Mi, and qi are the mole fraction, molar mass, and density of the pure component i, respectively. q is the density of mixtures. The VE values are also presented in table 3. The combined expanded uncertainty in the excess molar volume was estimated to be less than 0.002  10
6 m3  mol
1 (with a 95% level of confidence). The viscosity deviations Dg were calculated as follows,

Dg ¼ g


2 X xi g i

ð2Þ

i¼1

where xi and gi are the mole fraction and viscosity of pure component i, respectively. g is the measured viscosity data of the binary mixtures. The calculated values of the viscosity deviation are shown

132

X. Wang et al. / J. Chem. Thermodynamics 97 (2016) 127–134

0.6

0.7

(a)

0.6 0.5

-1

10 V /m ·mol

0.4

3

0.3

0.3

6

E

6

E

3

10 V /m ·mol

-1

0.5 0.4

0.2

0.2

0.1

0.0 0.0

0.1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.0 0.0

1.0

x1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x1 FIGURE 2. Excess molar volumes as functions of the n-hexadecane mole fraction for the binary mixtures at T = 308.15 K: j, ethyl caprylate; h, ethyl caprate; d, ethyl laurate. Solid lines show results calculated using equation (3).

0.5

(b) 0.4

ð3Þ

i¼0

3

10 V /m ·mol

-1

n X Y E ¼ x1 ð1
x1 Þ Ai ð1
2x1 Þi

0.3

6

E

where YE is either VE or Dg, Ai are adjustable parameters, and n is the number of coefficients in the equation, which was determined based on the standard deviation (r). The standard deviation can be calculated using the following equation:

0.2

0.1

0.0 0.0

r¼ 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.6

0.7

0.8

0.9

1.0

x1

0.35

(c)

0.25 0.20

6

E

3

10 V /m ·mol

-1

0.30

0.15 0.10 0.05 0.00 0.0

0.1

0.2

0.3

0.4

0.5

x1 FIGURE 1. Excess molar volumes for n-hexadecane with ethyl caprylate (a), ethyl caprate (b), and ethyl laurate (c) as functions of the n-hexadecane mole fraction at various temperatures: j, 298.15 K; h, 303.15 K; d, 308.15 K; s, 313.15 K; ▲, 318.15 K; 4, 323.15 K. Solid lines show results calculated using equation (3).

in table 4 with the combined expanded uncertainty of 0.05 mPa  s (with a 95% level of confidence). For each binary mixture, Redlich–Kister equation [30] was used to represent the composition dependence of the excess molar volume and the viscosity deviation,

hX

2

ðY E
Y Ecal Þ =ðNexp
pÞ

i1=2

ð4Þ

where Y Ecal is the calculated results from equation 1 or 2, p is the number of the fitted parameters, Nexp is the number of experimental points. At each temperature, the values of coefficients Ai and the corresponding standard deviations are given in table 5. Figure 1 displays the dependence of excess molar volume (VE) on molar fraction (x1) of n-hexadecane. The solid lines represent calculated results from equation (3). The results shown in figure 1 indicate that VE values are positive over the whole range of compositions for all temperatures and systems studied in this work. However, the growing trends of VE do not change significantly with temperature. The positive values can be attributed to the weak interactions between unlike molecules. In addition, the magnitude of VE for the three systems follows the order ethyl caprylate > ethyl caprate > ethyl laurate, as shown in figure 2. And the maximum value occurs at approximately x1 = 0.5. Figure 3 shows that values of viscosity deviation are slightly negative in the entire composition range and decrease with increasing temperature. The negative values of the viscosity deviations indicate that attractive forces among molecules are stronger than the repulsion forces. Figure 4 shows a comparison of the viscosity deviation of the studied mixtures as a function of the mole fraction of n-hexadecane at T = 308.15 K. It indicates that the values of Dg become more negative with increasing alkyl ester chain length. 4. Viscosity correlation In this work, the rough hard-sphere theory, proposed by Chandler [31], was used to correlate the viscosity of the studied binary mixtures. The rough hard sphere expressions for the reduced viscosity (g ) as functions of the reduced molar volume V r ¼ V=V 0 are as follows [32–34]:

133

X. Wang et al. / J. Chem. Thermodynamics 97 (2016) 127–134 0.00

0.00

(a) -0.02 -0.04

-0.05

Δη/mPa·s

Δη/mPa·s

-0.06

-0.10

-0.08 -0.10 -0.12

-0.15

-0.14

-0.20 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

-0.16 0.0

0.1

0.2

0.3

0.4

x1

(b)

Δη/mPa·s

0.8

0.9

1.0

TABLE 6 Rough hard sphere coefficients.

-0.06

Substance

A0

B0  104/ m3  mol
1

B1  103/ m3  K  mol
1

AARD

MD

n-Hexadecane Ethyl caprylate Ethyl caprate Ethyl laurate

0.9964 0.5193 0.7295 0.9897

2.0291 1.5304 1.6922 1.8443

7.7159 0.0636 3.0903 6.4379

0.23 0.26 0.25 0.22

0.33 0.38 0.35 0.34

-0.08 -0.10 -0.12

The reduced viscosity is defined as

-0.14 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x1

g ¼ 6:035  108



1 MRT

1=2

gV 2=3

ð6Þ

where M is the molar mass, R is the gas constant, T is the temperature, g is the viscosity, V is the molar volume. The coupling parameters Rg and the characteristic volume V0 can be expressed [35,36]

0.00

(c)

Δη/mPa·s

0.7

FIGURE 4. Viscosity deviations as functions of the n-hexadecane mole fraction for the binary mixtures at T = 308.15 K: j, ethyl caprylate; h, ethyl caprate; d, ethyl laurate. Solid lines show results calculated using equation (3).

-0.04

0.0

0.6

x1

0.00 -0.02

0.5

-0.02

Rg ¼ A0

ð7Þ

-0.04

V 0 ¼ B0 þ B1 =T

ð8Þ

-0.10

The coefficients A0, B0, and B1 were obtained by fitting the experimental viscosity data of pure substances studied in this work. table 6 contains the coefficients as well as the average absolute relative deviation (AARD) and maximum absolute relative deviation (MD) between the experimental data and calculated results. The AARD and MD are defined:

-0.12

AARD=% ¼

-0.06

-0.08

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x1

 N  exp cal  100 X qi
qi  exp   N i¼1 qi

 exp   q
qcal  MD=% ¼ max 100 i exp i  q

ð9Þ

ð10Þ

i

FIGURE 3. Viscosity deviations for n-hexadecane with ethyl caprylate (a), ethyl caprate (b), and ethyl laurate (c) as functions of the n-hexadecane mole fraction at various temperatures: j, 298.15 K; h, 303.15 K; d, 308.15 K; s, 313.15 K; ▲, 318.15 K; 4, 323.15 K. Solid lines show results calculated using equation (3).


2 logðg =Rg Þ ¼ 1:0945
9:2632V
1 r þ 71:0385V r

V 0;mix ¼ x21 V 0;1 þ 2x1 x2 V 0;12 þ x22 V 0;2 V 0;12 ¼


4
5
301:9012V
3 r þ 797:69V r
1221:977V r
7 þ 987:5574V
6 r
319:4636V r

Equation (5) can be extended to mixtures using mole fraction averaged mixture parameters [37]:

ð5Þ

1=3 ðV 0;1 þ V 1=3 0;2 Þ 8

Rg;mix ¼ x21 Rg1 þ 2x1 x2 Rg12 þ x22 Rg2

ð11Þ ð12Þ ð13Þ

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X. Wang et al. / J. Chem. Thermodynamics 97 (2016) 127–134

TABLE 7 Rough hard sphere correlations for the binary mixtures.

References

Substance

Kg

AARD

MD

n-Hexadecane + ethyl caprylate


0.21 0
0.06 0 0.02 0

0.26 5.84 0.30 1.62 0.24 0.65

0.71 10.04 0.63 3.08 0.77 1.22

n-Hexadecane + ethyl caprate n-Hexadecane + ethyl laurate

Rg12 ¼ ðRg1 Rg12 Þ1=2 ð1
K g Þ

ð14Þ

where Kg is adjustable parameter. In this work, equations (5)–(8) and (11)–(14) were used to correlate or predict the viscosity of the binary mixtures. Table 7 lists the optimized Kg values and the AARD and MD between the experimental data and calculated results. The calculated AARD and MD are within the experimental uncertainty for all three mixtures. Table 7 also shows the AARD and MD when Kg = 0. From table 7, we can see that, for n-hexadecane + ethyl laurate and n-hexadecane + ethyl caprate mixtures, the viscosity data could be correlated reasonably well without any adjustable parameters (Kg = 0). However, for n-hexadecane + ethyl caprylate mixtures, the adjustable parameters are required in order to obtain good results. This may be caused by the significant difference in polarities between those two compounds. 5. Conclusion New experimental data for densities and viscosities of binary mixtures of n-hexadecane with ethyl caprylate, ethyl caprate, and ethyl laurate were reported at temperatures ranging from 298.15 to 323.15 K at atmospheric pressure. Results show that, for the studied systems, the excess molar volumes are positive for all the compositions at different temperatures. However, the deviations in viscosity are negative and show larger negative values with decreased temperature in every case. In addition, the experimental viscosity data of the mixtures were correlated using a rough hard-sphere model. The calculated AARD and MD are within the experimental uncertainty for all three mixtures.

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Acknowledgment The authors are grateful to acknowledge financial support for the work by National Natural Science Foundation of China (Grant No. 51476129).

JCT 15-780