Experimental investigations of density and dynamic viscosity of n-hexadecane with three fatty acid methyl esters

Fuel 166 (2016) 553–559

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Experimental investigations of density and dynamic viscosity of n-hexadecane with three fatty acid methyl esters Xiaojie Wang, Xiaopo Wang ⇑, Jianlin Chen Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an 710049, China

h i g h l i g h t s
Densities and viscosities of binary mixtures of n-hexadecane with three fatty acid methyl esters were reported.
Excess molar volumes and viscosity deviations of the mixtures were calculated.
Excess molar volumes and viscosity deviations of the mixtures were correlated as Redlich–Kister equation.

a r t i c l e

i n f o

Article history: Received 29 July 2015 Received in revised form 21 September 2015 Accepted 3 November 2015 Available online 17 November 2015 Keywords: n-Hexadecane Methyl caprate Methyl laurate Methyl myristate Density Dynamic viscosity

a b s t r a c t The main components of biodiesel are fatty acid methyl esters (FAMEs) or fatty acid ethyl esters (FAEEs). N-hexadecane is commonly used as a reference molecule for modeling diesel fuel thermodynamics properties. In this paper, densities and dynamic viscosities of binary mixtures of n-hexadecane with three fatty acid methyl esters (methyl caprate, methyl laurate, and methyl myristate) were measured at atmospheric pressure from 298.15 to 323.15 K over the entire composition range. Excess molar volumes and viscosity deviations of the mixtures were calculated from the experimental data and correlated using the Redlich–Kister equation. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Due to the rapid growth in fossil fuels demand and environmental degradation, an intensified search for alternatives has become an important issue. The most prominent of alternatives is biodiesel [1], which is a mixture of fatty acid esters (typically methyl or ethyl) and can be produced by transesterification of vegetable oils or animal fats with an alcohol. Fatty acid methyl esters (FAMEs) are obtained using methanol, while fatty acid ethyl esters (FAEEs) are obtained with ethanol. Biodiesel is considered as a renewable and environmental friendly alternative diesel fuel for diesel engine. Investigations show that blending biodiesels with traditional petroleum diesel may improve engine performance and reduce most exhaust emissions significantly [2]. The knowledge of the thermodynamics and transport properties of the mixtures of

⇑ Corresponding author. Tel.: +86 29 82668210; fax: +86 29 82668789. E-mail address: [email protected] (X. Wang). http://dx.doi.org/10.1016/j.fuel.2015.11.008 0016-2361/Ó 2015 Elsevier Ltd. All rights reserved.

biodiesel + diesel oil is essential to optimize the diesel engine. Among these properties, viscosity and density have direct effects on the injection system, atomization quality and combustion quality. A large series of studies on the density and viscosity of biodiesel + diesel oil mixtures have been carried out in the past several years [3–8]. N-hexadecane is commonly used as a reference molecule for modeling diesel oil thermodynamics properties and also as a reference molecule in lumping procedure. Mesquita et al. [9–11] investigated the density and viscosity of n-hexadecane with soybean or coconut biodiesel and obtained the corresponding excess properties. However, to the author’s knowledge, thermodynamics and transport properties of n-hexadecane with pure FAMEs, such as methyl caprate, methyl laurate, and methyl myristrate, are still scarce in the literature. In this work, the density and dynamic viscosity of binary mixtures of n-hexadecane with methyl caprate, methyl laurate, and methyl myristate 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.

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X. Wang et al. / Fuel 166 (2016) 553–559

2. Experimental section 2.1. Samples N-hexadecane (CH3(CH2)14CH3), methyl caprate (CH3(CH2)8 COOCH3), methyl laurate (CH3(CH2)10COOCH3), and methyl myristate (CH3(CH2)12COOCH3) were supplied by Aladdin Chemistry and the mass purity was better than 99%. All samples were used without further purification. The densities and dynamic viscosities of the pure components were measured firstly and compared to the literature data [12–19], the results were presented in Table 1. It shows that the data obtained in this work agree well with the literature values. The preparation of binary mixtures was done by weighing using an analytical balance (model AB204N, MettlerToledo) with an accuracy of ±0.1 mg. The uncertainty in the mole fraction was estimated to be less than 2.0  104. 2.2. Density measurements Densities of the binary mixtures and the corresponding pure substances were measured by an Anton Paar digital vibratingtube densimeter (DMA 5000). The temperature was determined with two integrated Pt100 platinum thermometers, and the temperature in the cell was regulated to ±0.01 K according to ITS-90. The repeatability provided by the manufacturer for the density specified as 1.0  103 kg m3. The combined uncertainty of the density in this work were better than 4  102 kg m3 with a 0.95 level of confidence. Before and after the measurement of each sample, the densimeter was calibrated with deionized water and dry air. 2.3. Viscosity measurements The viscosities of the samples 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 s2 in this work.

The viscometer was kept in a water thermostat bath and the uncertainty of the temperature measurement was within 0.01 K. The flow-time of the samples was measured using an electronic stopwatch with a precision of 0.01 s. An average of five sets of flow-time was taken and each measurement was done successively with an interval of 5 K. The dynamic viscosity of the samples was obtained by multiplying the characteristic constant of the viscometer with the flowing time and corresponding density. The combined uncertainty of the dynamic viscosity was estimated to be less than 1% with a 0.95 level of confidence.

3. Results and discussion The experimental density and dynamic viscosity results of the binary mixtures n-hexadecane with methyl caprate, methyl laurate, and methyl myristate over the temperature range from 298.15 to 323.15 K at atmospheric pressure are given in Tables 2 and 3, respectively. The excess molar volume VE was calculated from density values according to the following equation:

VE ¼

x1 M 1 þ x2 M 2

q




x1 M 1

q1

þ

x2 M 2



ð1Þ

q2

where x1, M1, and q1 are the mole fraction, molar mass, and density, respectively, of n-hexadecane; x2, M2, and q2 are the mole fraction, molar mass, and density, respectively, of the three FAMEs (methyl caprate, methyl laurate, or methyl myristate); q is the density of the binary mixtures. The VE values of the binary mixtures are also presented in Table 2. The combined expanded uncertainty in the excess molar volume was estimated to be less than 0.002  106 m3 mol1 (with a 95% level of confidence). The viscosity deviations were calculated from the dynamic viscosity data,

Dg ¼ g 

2 X xi g i

ð2Þ

i¼1

Table 1 Comparison of experimental densities and viscosities of pure components with literature values at different temperatures. Component

T (K)

g (mPa s)

103  q (kg m3) This work

Literature

This work

Literature

298.15 303.15 308.15 313.15 318.15 323.15

0.76992 0.76651 0.76306 0.75960 0.75614 0.75268

0.7702 0.7699 0.7637 0.7598 0.7563

[12] [13] [14] [12] [12]

0.7707 [14] 0.76698 [15] 0.7636 [13] 0.7597 [13] 0.7568 [14]

3.056 2.727 2.451 2.217 2.013 1.837

3.065 2.706 2.458 2.219 2.017

Methyl caprate

298.15 303.15 308.15 313.15 318.15 323.15

0.86805 0.86402 0.85994 0.85583 0.85171 0.84759

0.8682 0.8641 0.8600 0.8560 0.8519 0.8478

[17] [17] [17] [17] [17] [17]

0.8682 0.8641 0.8599 0.8558 0.8517 0.8475

[18] [18] [18] [18] [18] [18]

1.915 1.739 1.589 1.458 1.341 1.240

1.9335 1.7601 1.6091 1.4773 1.3613 1.2589

[17] [17] [17] [17] [17] [17]

1.9067 1.7316 1.5755 1.4429 1.3341 1.2307

[18] [18] [18] [18] [18] [18]

Methyl laurate

298.15 303.15 308.15 313.15 318.15 323.15

0.86527 0.86133 0.85740 0.85347 0.84954 0.84560

0.8658 0.8618 0.8579 0.8539 0.8500 0.8461

[17] [17] [17] [17] [17] [17]

0.8649 0.8611 0.8570 0.8533 0.8494 0.8452

[18] [18] [18] [18] [18] [18]

2.780 2.495 2.250 2.041 1.862 1.705

2.8237 2.5356 2.2893 2.0776 1.8944 1.7347

[17] [17] [17] [17] [17] [17]

2.7895 2.4907 2.2437 2.0346 1.8624 1.7023

[18] [18] [18] [18] [18] [18]

Methyl myristate

298.15 303.15 308.15 313.15 318.15 323.15

0.86325 0.85943 0.85562 0.85181 0.84801 0.84420

0.8637 0.8599 0.8560 0.8522 0.8484 0.8446

[17] [17] [17] [17] [17] [17]

0.8594 [19] 0.8557 [19] 0.8517 [19] 0.848 [19] 0.8444 [19]

3.919 3.484 3.101 2.784 2.516 2.311

3.9821 [17] 3.543 [17] 3.1651 [17] 2.8447 [17] 2.5709 [17] 2.3343 [17]

n-Hexadecane

[12] [16] [13] [12] [12]

3.061 [13]

2.225 [13]

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X. Wang et al. / Fuel 166 (2016) 553–559 Table 2 Densities (q) and excess molar volumes (VE) for the binary mixtures from 298.15 to 323.15 K. x1a

103  q (kg m3)

106  VE (m3 mol1)

n-Hexadecane(1) + methyl caprate(2) 298.15 K 0.0000 0.1000 0.2000 0.2999 0.4000 0.5001 0.6001 0.7000 0.7999 0.8999 1.0000

0.86805 0.85459 0.84203 0.83049 0.81978 0.80988 0.80068 0.79212 0.78424 0.77689 0.76992

0.85583 0.84253 0.83020 0.81888 0.80839 0.79867 0.78965 0.78128 0.77355 0.76636 0.75960

0.86527 0.85379 0.84279 0.83219 0.82209 0.81245 0.80319 0.79434 0.78581 0.77776 0.76992

0.85347 0.84216 0.83129 0.82085 0.81090 0.80140 0.79228 0.78357 0.77517 0.76724 0.75960

0.0000 0.1134 0.2072 0.2903 0.3409 0.3578 0.3483 0.3148 0.2465 0.1217 0.0000

0.86325 0.85326 0.84340 0.83369 0.82412 0.81470 0.80543 0.79632 0.78737 0.77855 0.76992

0.85181 0.84194 0.83217 0.82256

0.84954 0.83827 0.82746 0.81707 0.80717 0.79772 0.78865 0.77998 0.77163 0.76374 0.75614

0.85943 0.84949 0.83965 0.82998 0.82045 0.81106 0.80183 0.79275 0.78385 0.77507 0.76651

0.0000 0.1131 0.2161 0.3027 0.3559 0.3744 0.3662 0.3351 0.2678 0.1436 0.0000

0.84801 0.83816 0.82843 0.81886

0.0000 0.1550 0.3001 0.3959 0.4605 0.4863 0.4791 0.4350 0.3278 0.1772 0.0000

0.84759 0.83446 0.82229 0.81113 0.80078 0.79119 0.78230 0.77405 0.76643 0.75934 0.75268

0.0000 0.1650 0.3169 0.4145 0.4820 0.5096 0.4978 0.4503 0.3374 0.1817 0.0000

0.85740 0.84604 0.83512 0.82462 0.81463 0.80508 0.79592 0.78716 0.77872 0.77074 0.76306

0.0000 0.1150 0.2205 0.3086 0.3629 0.3820 0.3735 0.3424 0.2742 0.1491 0.0000

323.15 K 0.0000 0.1221 0.2274 0.3173 0.3728 0.3916 0.3828 0.3500 0.2782 0.1501 0.0000

0.84560 0.83439 0.82363 0.81329 0.80344 0.79403 0.78501 0.77639 0.76808 0.76024 0.75268

0.0000 0.1232 0.2320 0.3228 0.3785 0.3979 0.3885 0.3546 0.2835 0.1517 0.0000

308.15 K 0.0000 0.0811 0.1680 0.2290 0.2737 0.2982 0.2973 0.2739 0.2132 0.1321 0.0000

318.15 K 0.0000 0.0862 0.1745 0.2369

0.85994 0.84655 0.83415 0.82275 0.81219 0.80241 0.79333 0.78489 0.77711 0.76987 0.76306

308.15 K

303.15 K 0.0000 0.0845 0.1629 0.2206 0.2636 0.2856 0.2832 0.2576 0.1994 0.1186 0.0000

313.15 K 0.0000 0.1000 0.2000 0.3000

0.86133 0.84992 0.83895 0.82840 0.81836 0.80876 0.79955 0.79075 0.78226 0.77424 0.76651

106  VE (m3 mol1)

323.15 K 0.0000 0.1610 0.3106 0.4073 0.4737 0.5011 0.4901 0.4437 0.3330 0.1792 0.0000

318.15 K 0.0000 0.1175 0.2238 0.3127 0.3679 0.3858 0.3774 0.3459 0.2755 0.1491 0.0000

n-Hexadecane(1) + methyl myristate(2) 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

0.85171 0.83849 0.82624 0.81500 0.80459 0.79493 0.78598 0.77766 0.76999 0.76285 0.75614

103  q (kg m3) 308.15 K

0.0000 0.1481 0.2918 0.3861 0.4498 0.4757 0.4687 0.4258 0.3193 0.1705 0.0000

303.15 K

313.15 K 0.0000 0.0998 0.1998 0.3000 0.4000 0.4999 0.6000 0.6997 0.8002 0.9000 1.0000

0.86402 0.85058 0.83809 0.82662 0.81599 0.80614 0.79700 0.78851 0.78067 0.77338 0.76651 318.15 K

0.0000 0.1578 0.3052 0.4011 0.4666 0.4933 0.4845 0.4388 0.3299 0.1774 0.0000

n-Hexadecane(1) + methyl laurate(2) 298.15 K 0.0000 0.0998 0.1998 0.3000 0.4000 0.4999 0.6000 0.6997 0.8002 0.9000 1.0000

106  VE (m3 mol1)

303.15 K 0.0000 0.1269 0.2677 0.3604 0.4295 0.4498 0.4424 0.4002 0.2951 0.1475 0.0000

313.15 K 0.0000 0.1000 0.2000 0.2999 0.4000 0.5001 0.6001 0.7000 0.7999 0.8999 1.0000

103  q (kg m3)

0.85562 0.84571 0.83591 0.82627 0.81678 0.80742 0.79822 0.78918 0.78031 0.77157 0.76306

0.0000 0.0835 0.1712 0.2335 0.2788 0.3040 0.3034 0.2798 0.2191 0.1379 0.0000

323.15 K 0.0000 0.0875 0.1762 0.2410

0.84420 0.83439 0.82469 0.81515

0.0000 0.0897 0.1790 0.2443 (continued on next page)

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X. Wang et al. / Fuel 166 (2016) 553–559

Table 2 (continued)

a

x1a

103  q (kg m3)

106  VE (m3 mol1)

103  q (kg m3)

106  VE (m3 mol1)

103  q (kg m3)

106  VE (m3 mol1)

0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.81311 0.80379 0.79462 0.78562 0.77678 0.76808 0.75960

0.2823 0.3070 0.3064 0.2818 0.2208 0.1371 0.0000

0.80944 0.80016 0.79102 0.78206 0.77325 0.76458 0.75614

0.2857 0.3098 0.3109 0.2847 0.2232 0.1380 0.0000

0.80577 0.79652 0.78743 0.77849 0.76973 0.76109 0.75268

0.2897 0.3143 0.3137 0.2877 0.2254 0.1401 0.0000

x1 is the mole fraction of n-hexadecane.

Table 3 Viscosities (g) and viscosity deviations (Dg) for the binary mixtures from 298.15 to 323.15 K. x1a

g (mPa s)

Dg (mPa s)

n-Hexadecane(1) + methyl caprate(2) 298.15 K 0.0000 0.1000 0.2000 0.3000 0.4000 0.5001 0.6001 0.7000 0.7999 0.8999 1.0000

1.915 1.987 2.063 2.145 2.235 2.338 2.449 2.572 2.709 2.874 3.056

1.458 1.505 1.559 1.615 1.677 1.745 1.820 1.903 1.997 2.099 2.217

2.780 2.762 2.745 2.745 2.757 2.776 2.803 2.842 2.896 2.968 3.056

0.0000 0.0998 0.1998 0.3000 0.4000 0.4999 0.6000 0.6997 0.8002 0.9000 1.0000

2.041 2.028 2.026 2.027 2.031 2.042 2.059 2.084 2.120 2.161 2.217

0.000 0.038 0.066 0.096 0.116 0.121 0.120 0.114 0.096 0.058 0.000

1.589 1.640 1.703 1.765 1.836 1.915 2.001 2.092 2.196 2.317 2.451

1.341 1.385 1.432 1.483 1.538 1.599 1.667 1.739 1.820 1.911 2.013

0.000 0.024 0.044 0.059 0.072 0.078 0.077 0.072 0.058 0.035 0.000

1.240 1.280 1.321 1.367 1.419 1.472 1.531 1.596 1.667 1.751 1.837

2.495 2.479 2.473 2.472 2.480 2.494 2.517 2.551 2.595 2.653 2.727

0.000 0.030 0.050 0.067 0.080 0.088 0.088 0.080 0.062 0.039 0.000

1.862 1.850 1.847 1.847 1.853 1.864 1.879 1.900 1.927 1.966 2.013

0.000 0.020 0.038 0.053 0.060 0.067 0.067 0.062 0.050 0.026 0.000

308.15 K 0.000 0.039 0.068 0.093 0.108 0.117 0.117 0.107 0.086 0.050 0.000

2.250 2.235 2.231 2.232 2.240 2.253 2.274 2.303 2.342 2.386 2.451

0.000 0.027 0.045 0.060 0.070 0.074 0.074 0.068 0.055 0.032 0.000

1.705 1.695 1.690 1.692 1.697 1.706 1.718 1.736 1.764 1.797 1.837

0.000 0.056

3.101 2.989

0.000 0.036 0.060 0.079 0.091 0.098 0.097 0.088 0.070 0.045 0.000

323.15 K

303.15 K 3.484 3.352

0.000 0.035 0.059 0.082 0.098 0.105 0.106 0.101 0.083 0.048 0.000

323.15 K

318.15 K

0.000 0.067

Dg (mPa s)

308.15 K

303.15 K

n-Hexadecane(1) + methyl myristate(2) 298.15 K 3.919 3.766

1.739 1.800 1.871 1.940 2.019 2.113 2.212 2.317 2.433 2.570 2.727

0.000 0.045 0.091 0.117 0.134 0.142 0.142 0.131 0.105 0.060 0.000

313.15 K

0.0000 0.1001

g (mPa s)

318.15 K 0.000 0.024 0.044 0.059 0.072 0.078 0.077 0.072 0.058 0.035 0.000

n-Hexadecane(1) + methyl laurate(2) 298.15 K 0.0000 0.0998 0.1998 0.3000 0.4000 0.4999 0.6000 0.6997 0.8002 0.9000 1.0000

Dg (mPa s)

303.15 K 0.000 0.042 0.080 0.113 0.136 0.148 0.151 0.142 0.119 0.068 0.000

313.15 K 0.0000 0.1000 0.2000 0.3000 0.4000 0.5001 0.6001 0.7000 0.7999 0.8999 1.0000

g (mPa s)

0.000 0.024 0.041 0.052 0.061 0.065 0.066 0.061 0.047 0.027 0.000

308.15 K 0.000 0.047

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X. Wang et al. / Fuel 166 (2016) 553–559 Table 3 (continued) x1a

g (mPa s)

Dg (mPa s)

g (mPa s)

Dg (mPa s)

g (mPa s)

Dg (mPa s)

0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9001 1.0000

3.640 3.521 3.413 3.321 3.242 3.178 3.121 3.070 3.056

0.106 0.139 0.160 0.166 0.159 0.137 0.108 0.072 0.000

3.240 3.136 3.043 2.958 2.888 2.834 2.788 2.742 2.727

0.093 0.121 0.138 0.147 0.142 0.120 0.090 0.061 0.000

2.893 2.804 2.724 2.652 2.592 2.545 2.504 2.466 2.451

0.079 0.103 0.117 0.125 0.119 0.101 0.078 0.050 0.000

0.0000 0.1001 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9001 1.0000

2.784 2.689 2.604 2.528 2.457 2.396 2.343 2.304 2.266 2.232 2.217

0.000 0.039 0.067 0.086 0.100 0.105 0.101 0.083 0.065 0.042 0.000

2.516 2.432 2.358 2.293 2.231 2.176 2.131 2.095 2.059 2.027 2.013

0.000 0.034 0.057 0.072 0.084 0.088 0.083 0.069 0.055 0.036 0.000

2.311 2.234 2.166 2.107 2.049 1.999 1.954 1.919 1.884 1.852 1.837

313.15 K

a

318.15 K

323.15 K 0.000 0.030 0.050 0.062 0.073 0.075 0.072 0.060 0.048 0.033 0.000

x1 is the mole fraction of n-hexadecane.

Table 4 Redlich–Kister coefficients (Ai) at different temperatures for the excess molar volumes (VE) and viscosity deviations (Dg) and standard deviations (r). YE

T (K)

n-Hexadecane(1) + methyl caprate(2) VE (cm3 mol1) 298.15 303.15 308.15 313.15 318.15 323.15

Dg (mPa s)

298.15 303.15 308.15 313.15 318.15 323.15

n-Hexadecane(1) + methyl laurate(2) VE (cm3 mol1) 298.15 303.15 308.15 313.15 318.15 323.15

Dg (mPa s)

298.15 303.15 308.15 313.15 318.15 323.15

n-Hexadecane(1) + methyl myristate(2) VE (cm3 mol1) 298.15 303.15 308.15 313.15 318.15 323.15 Dg (mPa s) 298.15 303.15 308.15 313.15 318.15 323.15

A5

r

A0

A1

A2

A3

A4

1.80354 1.90272 1.94606 1.97182 2.0005 2.03426

0.20943 0.22569 0.22266 0.21677 0.2057 0.20122

0.24865 0.31781 0.31574 0.29572 0.27613 0.26793

0.12109 0.14326 0.13891 0.16053 0.15934 0.16928

1.06819 0.82539 0.74434 0.73168 0.7009 0.68226

0.59193 0.48656 0.42177 0.31077 0.31077 0.26451

0.13696 0.02637 0.06947 0.05725 0.05725 0.06318

0.12609 0.06433 0.08061 0.02084 0.02084 0.08405

0.32456 0.61385 0.31648 0.09733 0.09733 0.01157

0.14752 0.00222 0.04299 0.00878 0.00878 0.1488

0.4141 0.68754 0.45145 0.10323 0.10323 0.06729

0.0006 0.0009 0.0005 0.0007 0.0007 0.0009

1.43029 1.49634 1.52635 1.54376 1.56677 1.5897

0.02509 0.06578 0.07169 0.06537 0.06495 0.05892

0.15961 0.22974 0.23221 0.23456 0.20574 0.24014

1.04847 0.99343 0.99061 0.99284 1.00901 1.03716

0.54674 0.52385 0.50031 0.51631 0.45346 0.51847

1.55673 1.19748 1.1478 1.17919 1.26334 1.28204

0.0008 0.0004 0.0004 0.0002 0.0001 0.0007

0.56604 0.46624 0.39203 0.35131 0.29585 0.26238

0.0962 0.08035 0.0609 0.08867 0.0388 0.06642

0.22559 0.04202 0.01399 0.04909 0.05415 0.05529

0.13992 0.07107 0.07483 0.1103 0.08936 0.13542

0.30305 0.01046 0.15803 0.15887 0.00596 0.03873

0.22777 0.11662 0.12671 0.10244 0.15131 0.11183

0.0007 0.0006 0.0007 0.0006 0.0003 0.0005

1.14142 1.19070 1.21427 1.22663 1.24089 1.25720 0.66915 0.59044 0.49855 0.42228 0.35143 0.30246

0.23504 0.29328 0.30116 0.29293 0.29310 0.28410 0.02078 0.04623 0.01578 0.00520 0.01336 0.00113

0.02607 0.03511 0.02865 0.04234 0.05639 0.03589 0.17140 0.19819 0.14418 0.14075 0.11602 0.08858

0.24046 0.41852 0.41238 0.38870 0.38802 0.35642 0.06186 0.35980 0.16889 0.16164 0.05542 0.09137

0.00798 0.07343 0.01167 0.03549 0.06711 0.01526 0.51408 0.44459 0.32671 0.29356 0.28265 0.25385

0.37593 0.79499 0.82430 0.74935 0.74602 0.71537 0.04523 0.53252 0.28912 0.30473 0.16129 0.19008

0.0013 0.0020 0.0019 0.0016 0.0012 0.0014 0.0011 0.0010 0.0006 0.0010 0.0007 0.0010

0.0038 0.0028 0.0027 0.0028 0.0033 0.0033

558

X. Wang et al. / Fuel 166 (2016) 553–559

0.5

0.00

(a)

0.4 -1

-0.04 -0.06

Δη/mPa.s

0.3

E

3

10 V /m ·mol

(a)

-0.02

6

0.2

-0.08 -0.10 -0.12

0.1

-0.14 0.0 0.0

0.4

0.2

0.4

x1

0.6

0.8

-0.16 0.0

1.0

0.2

0.4

0.8

1.0

0.6

0.8

1.0

0.6

0.8

1.0

(b)

-0.04

-1

0.3

Δη/mPa.s

-0.06 0.2

6

E

3

0.6

0.00

(b)

-0.02

10 V /m ·mol

x1

-0.08 -0.10

0.1

-0.12 -0.14

0.0 0.0

0.2

0.4

x1

0.6

0.8

1.0

0.0

0.2

0.4

x1

0.00 0.30

(c)

-0.04 -0.06

0.20

0.15

-0.08 -0.10

6

E

3

Δη/mPa.s

-1

0.25

10 V /m ·mol

(c)

-0.02

-0.12

0.10

-0.14

0.05

-0.16 0.00 0.0

0.2

0.4

x1

0.6

0.8

1.0

0.0

0.2

0.4

x1

Fig. 1. Excess molar volumes for (a) n-hexadecane(1) + methyl caprate(2), (b) n-hexadecane(1) + methyl laurate(2), and (c) n-hexadecane(1) + methyl myristate(2) as function of the mole fraction of n-hexadecane at various temperatures. j, 298.15 K; h, 303.15 K; d, 308.15 K; s, 313.15 K; N, 318.15 K; 4, 323.15 K. Solid lines show results calculated from Redlich–Kister equation.

Fig. 2. Viscosity deviations for (a) n-hexadecane(1) + methyl caprate(2), (b) n-hexadecane(1) + methyl laurate(2), and (c) n-hexadecane(1) + methyl myristate(2) as function of the mole fraction of n-hexadecane at various temperatures: j, 298.15 K; h, 303.15 K; d, 308.15 K; s, 313.15 K; N, 318.15 K; 4, 323.15 K. Solid lines show results calculated using the Redlich–Kister equation.

where xi and gi are the mole fraction and dynamic viscosity of pure component i, respectively. g is the measured dynamic viscosity data of the binary mixture. The calculated values of the viscosity deviation are shown in Table 3. The combined expanded uncertainty in

the viscosity deviations is 0.05 mPa s (with a 95% level of confidence). For each binary mixture, we have represented the composition dependence of the excess molar volume and the viscosity deviation using Redlich–Kister equation [20]:

X. Wang et al. / Fuel 166 (2016) 553–559

Y E ¼ x1 ð1  x1 Þ

n X Ai ð1  2x1 Þi

ð3Þ

i¼0

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 was calculated using the following equation:

r¼

X  1=2 2  ðNexp  pÞ Y E  Y Ecal

ð4Þ

where Y Ecal is the calculated results from Eqs. (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 4. For the studied binary mixtures in this work, the dependence of VE on concentration at different temperatures is shown in Fig. 1. The solid lines represent calculated results from Eq. (3). The VE values of all the systems (n-hexadecane + methyl caprate, methyl laurate, and methyl myristate) are positive over the whole range of compositions and increase slightly with temperature. Positive VE values can be attributed to the weak interactions between different molecules. The maximum value of VE occurs at approximately x1 = 0.5. Comparison of (a), (b), (c) in Fig. 1, it clearly indicates that the VE values for the mixtures decrease with methyl ester chain length at constant temperature. This shows that as R1 in R1COOCH3 increases in chain length, the polarity of the ester decreases, allowing greater accommodation of the n-hexadecane molecules. Fig. 2 depicts the behavior of viscosity deviations as function of mole fraction for all the temperatures. It can be found that all of the systems present negative viscosity deviations over entire composition range. The sign of the viscosity deviations was strongly related to the predominance of the dispersion forces [21]. The negative viscosity deviations confirm that dispersion forces are dominant in these systems due to different molecular size and shapes. The absolute value of Dg decreases for all of the systems while the temperature decreases. 4. Conclusion New experimental data for densities and dynamic viscosities of binary mixtures of n-hexadecane with methyl caprate, methyl laurate, and methyl myristate were reported at temperatures ranging from 298.15 to 323.15 K and at atmospheric pressure. Excess molar volumes and viscosity deviations were calculated from experimental data and fitted using the Redlich–Kister equation. In all the 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. Acknowledgement The authors are grateful to acknowledge financial support for the work by National Natural Science Foundation of China (Grant No. 51476129).

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