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Density and Viscosity of Binary Systems Containing (Linseed or Corn) Oil, (Linseed or Corn) Biodiesel and Diesel Carlos A. Nogueira, Jr.,† Victor M. Nogueira,† Diego F. Santiago,† Filipe A. Machado,† Fabiano A. N. Fernandes,‡ Rílvia S. Santiago-Aguiar,† and Hosiberto B. de Sant’Ana*,† †

Grupo de Pesquisa em Termofluidodinâmica Aplicada, and ‡Núcleo de Análise e Desenvolvimento de Processos, Departamento de Engenharia Química, Centro de Tecnologia, Universidade Federal do Ceará, Campus do Pici, Bloco 709, Fortaleza, CE 60455-760, Brazil ABSTRACT: This work presents density (ρ) and dynamic viscosity (η) data and correlations for binary systems containing (linseed or corn) oil, (linseed or corn) biodiesel and petroleum diesel at T = 293.15 K to 333.15 K in steps of 10 K for the linseed system and T = 293.15 K to 373.15 K in steps of 20 K for the corn system and atmospheric pressure. Density data were adjusted by a proposed function showing a second-order behavior with mole fraction (x) and a linear behavior with temperature. Viscosity data were adjusted to an equation with temperature (T) and mass fraction (w) as independent variables with an exponential dependence of the inverse of temperature and proportional dependence with mass fraction. All correlations presented good agreement to experimental data based on the R2 and chi-square (χ2) statistical analyses. The absolute average error (AAE) was calculated to evaluate the accuracy of predictive models used to estimate density and viscosity for all five pseudopure compounds. Isobaric expansion (αp) and excess Gibbs free energy of activation of viscous flow (ΔGE) were derived by measured properties. A new correlation was proposed for ΔGE as a function of temperature and mole fraction.

1. INTRODUCTION The scarcity of fossil fuels and the increase of environmental problems, such as greenhouse effect and the global climate change, reinforce attention to alternative energy sources. In this context, biodiesel is an excellent alternative for the replacement of petroleum diesel because of some interesting properties, such as nontoxicity, biodegradability, better greasing, complete miscibility in petroleum diesel, and good usage in a diesel engine with no significant modifications of the engine.1 Biodiesel production is usually carried out through a transesterification reaction between vegetable oils and a short chain alcohol (e.g., methanol) using sodium or potassium hydroxide as catalyst.2 The use of biodiesel by a blending process with petrodiesel has been increasing in some countries. However, this process can change the physical and chemical characteristics of the fuel, affecting design and performance of diesel engines. Common mixtures are represented as B5, B7, and B20, which means, respectively 5%, 7%, and 20% (v/v) content of biodiesel in the mixture. Soybean or corn oils are widely used as feedstock to biodiesel production. However, this can also impact the food industry. Linseed oil can also be an important source of biodiesel, but has the additional advantage of nonedibility and high oil content approximately 40%.3 The accurate determination of physical and chemical properties such as density (ρ) and dynamic viscosity (η) is important to the design of diesel engines and to the design and operation of biodiesel plants. © XXXX American Chemical Society

This work deals with the study of thermodynamic and transport properties for the binary blends containing oil, biodiesel, and petroleum diesel. Density and viscosity data were determined in a mass fraction (w) range of 0.100 to 0.900, at atmospheric pressure, for binary systems containing (linseed or corn) oil, (linseed or corn) biodiesel and petroleum diesel at T = 293.15 K to 333.15 K in steps of 10 K for the linseed oil system and T = 293.15 K to 373.15 K in steps of 20 K for the corn oil system.

2. EXPERIMENTAL SECTION 2.1. Materials. Commercial linseed oil was supplied by Campestre Indústria e Comércio de Ó leos Vegetais (São Bernardo do Campo, SP, Brazil) and commercial corn oil was acquired from ́ Cargill Agricola S.A. (Marinque, SP, Brazil). Methanol 99.8% and sodium hydroxide 97% were supplied by Vetec (Duque de Caxias, RJ, Brazil). Diesel S50 was supplied by LUBNOR (Petrobras/LUBNOR, Lubrificantes e Derivados de Petróleo do Nordeste, Fortaleza, Brazil). Table 1 shows specification of the components. 2.2. Transesterification Reaction. Linseed oil was fed with methanol and sodium hydroxide into a glass reactor (500 mL), at a molar ratio of 9:1 (methanol/oil). Sodium hydroxide (with a Received: March 27, 2015 Accepted: September 8, 2015

A

DOI: 10.1021/acs.jced.5b00289 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Specifications of the Components

a

chemical name

supplier

CAS No.

purity (% m/m)

methanol sodium hydroxide linseed oil linseed biodiesel corn oil corn biodiesel diesel

Vetec Vetec Campestre Indústria e Comércio de Ó leos Vegetais

67-56-1 1310-73-2

99.80 97.00 > 99.0 > 99.0 > 99.0 > 99.0 > 99.0

́ Cargill Agricola S.A. Lubnor

molar mass (g mol−1)

chemical formula CH4O NaOH FAMEa

32.04 39.99 878 294 877 294 192

FAME hydrocarbons (C7 to C24)

Fatty acid methyl esters.

mass fraction of w = 0.002) was used as a catalyst for the transesterification reaction. The reaction was carried out at 333.15 K and atmospheric pressure for 90 min. These conditions ensured 99 % conversion of the oil into methyl esters. After transesterification, the reaction mixture was transferred to a separation funnel, where it stayed for 12 h for phase separation. The glycerin and alcohol fraction was removed, and the ester phase was washed three times with distilled water. Moisture was removed from the methyl esters by heating to 110 °C for 15 min. Corn oil, methanol, and sodium hydroxide were fed into another glass reactor (1000 mL). The reaction condition was set with a methanol/oil molar ratio of 6:1 and 0.01 (w/w) of catalyst was used. The remainder of the procedure is the same as presented before. 2.3. Biodiesel Characterization. Methyl ester (linseed/ corn biodiesel) and petroleum diesel content and molecular characterization have been carried out by gas chromatography analysis by using a Thermos apparatus (model Ultra) provided with a flame ionization detector. An OV-1 capillary column with a length of 30 m, 0.25 mm inner diameter, and 0.25 μm film thickness was used. The temperatures in the injector and detector were both set at 523.15 K. The oven temperature started at 323.15 K, and then it was raised up to 503.15 K at a rate of 278.15 K·min−1 and held for 10 min. Table 2 depicts chromatographic profiles for linseed and corn biodiesels and diesel. 2.4. Blends. All binary blends were mixed to give a volumetric fraction ranging between v = 0.1 and 0.9. Mixing was carried out at the temperature range of, approximately, 298.15 K to 303.15 K. The mass fraction was calculated by means of the weights of the components that were obtained using an electronic balance (BEL Engineering 254A) with an accuracy of 0.0001 g. 2.5. Density and Viscosity Measurements. Density (ρ) and viscosity (μ) data were obtained in an Anton Paar SVM 3000 digital oscillation U-tube apparatus. Initially, a calibration procedure was made by using a Cannon mineral oil (CAS No. 68037-01-4) at a temperature range from 293.15 K to 373.15 K. The sample volume of 5 mL was injected into the equipment with a syringe to measure these properties of pure diesel, biodiesel, and oil, and their binary blends. The determination of viscosity was made in a cell containing a tube completely filled with sample rotating at a constant speed. The density was determined by a densimeter using the U-tube principle. Both measurements were done simultaneously. After analyses performed in triplicate, it was observed that the density measurement had an uncertainty of 0.0005 g·cm−3 and the viscosity measurement had an error of 0.35 %. The measurements were made according to the Standard Test Method for Dynamic Viscosity and Density of Liquids by Stabinger Viscometer, following ASTM D7042-04.

Table 2. Fatty Acid Methyl Esters (FAME) Profile of Linseed and Corn Biodiesel and the Petroleum Diesel Profile mass fraction (w) FAME (Linseed) methyl palmitate methyl stearate methyl oleate methyl linoleate FAME (Corn) methyl palmitate methyl oleate methyl linolate methyl linolenate Diesel (Hydrocarbons) C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24

0.043 0.001 0.420 0.536 0.139 0.367 0.487 0.008 0.030 0.038 0.026 0.028 0.065 0.082 0.100 0.115 0.120 0.112 0.120 0.076 0.023 0.018 0.014 0.010 0.010 0.013

3. MATHEMATICAL PREDICTIVE MODELS 3.1. Density. The group contribution method GCVOL was used to predict the density of all pseudopure liquid compounds with the parameters proposed by Ihmels and Gmehling:4 MW MW ρ= = ∑ niΔvi V (1) where MW is the molecular weight, V is the molar volume of a pure compound (e.g., methyl oleate, n-hexadecane), Δvi and ni are the molar volume contribution of each group and the number of groups i, respectively. The molar volume contribution Δvi was estimated as a function of a second order polynomial of the absolute temperature: Δvi = Ai + Bi T + CiT 2

(2)

where T is the temperature in Kelvin; Ai, Bi, and Ci are the parameters. B



Article

Table 5. Dynamic Viscosity Data, η (mPa·s) and Density Data, ρ (g·cm−3) for the Binary Blends (w1 Linseed Biodiesel + (1 − w1) Diesel) at Temperatures Ranging from 293.15 K to 333.15 K in Steps of 10 Ka

Table 3. Density (ρ) and Viscosity (η) Data for Diesel, Linseed Biodiesel, and Linseed Oil at Temperatures Ranging from 293.15 K to 333.15 K in steps of 10 Ka diesel

linseed biodiesel

linseed oil

T/K

ρ/(g·cm−3)

η/(mPa·s)

293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15

0.8330 0.8259 0.8189 0.8118 0.8047 0.8833 0.8760 0.8687 0.8614 0.8542 0.9195 0.9127 0.9059 0.8992 0.8925

3.1619 2.5066 2.0407 1.6981 1.4390 5.8481 4.5560 3.6502 3.0033 2.5129 71.2891 46.4451 32.0042 23.0573 17.1891

Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.0005 g·cm−3, u(η) = 0.35 % (0.95 level of confidence). a

Table 4. Density (ρ) and Viscosity (η) Data for Corn Biodiesel and Corn Oil at Temperatures Ranging from 293.15 K to 373.15 K in Steps of 20 Ka corn biodiesel

corn oil

T/K

ρ/(g·cm−3)

η/(mPa·s)

293.15 313.15 333.15 353.15 373.15 293.15 313.15 333.15 353.15 373.15

0.8818 0.8673 0.8529 0.8382 0.8237 0.9186 0.9052 0.8920 0.8785 0.8651

6.3288 3.8889 2.6480 1.9820 1.4689 66.244 30.031 16.335 10.048 6.7389

0.107 0.214 0.315 0.414 0.516 0.617 0.712 0.79 0.903

0.073 0.151 0.231 0.316 0.410 0.513 0.617 0.711 0.859

3.3285 3.5335 3.7417 3.9759 4.2551 4.5552 4.8565 5.1607 5.4698

0.107 0.214 0.315 0.414 0.516 0.617 0.712 0.790 0.903

0.073 0.151 0.231 0.316 0.410 0.513 0.617 0.711 0.859

0.8379 0.843 0.8479 0.8527 0.8580 0.8632 0.8683 0.8733 0.8782

T/K = 303.15 η/(mPa·s) 2.6370 2.7911 2.9489 3.1265 3.3437 3.5693 3.7974 4.0329 4.2649 ρ/(g·cm−3) 0.8309 0.8359 0.8408 0.8456 0.8508 0.8560 0.8611 0.8661 0.8709

T/K = 313.15

T/K = 323.15

T/K = 333.15

2.1464 2.2686 2.3941 2.5374 2.7030 2.8811 3.0587 3.2429 3.4285

1.7892 1.8862 1.9895 2.1045 2.2399 2.3824 2.5234 2.6725 2.8239

1.5174 1.5978 1.6842 1.7790 1.8905 2.0091 2.1235 2.2469 2.3721

0.8238 0.8288 0.8336 0.8384 0.8436 0.8488 0.8539 0.8588 0.8637

0.8167 0.8217 0.8265 0.8313 0.8364 0.8416 0.8466 0.8516 0.8564

0.8095 0.8145 0.8193 0.8241 0.8293 0.8344 0.8394 0.8444 0.8492

Table 6. Dynamic Viscosity Data, η (mPa·s) and Density Data, ρ (g·cm−3) for the Binary Blends (w1 Linseed Oil + (1 − w1) Linseed Biodiesel) at Temperatures Ranging from 293.15 K to 333.15 K in Steps of 10 Ka

The molar volume of the pseudopure compounds was calculated using the Key’s mixing rule: (3)

where xj is the mole fraction of each pure compound j; Vj is the molar volume of each pure compound j calculated by the groupcontribution volume (GCVOL) model. 3.2. Viscosity. Values of dynamic viscosity of linseed biodiesel, corn biodiesel, and petroleum diesel were estimated using the group contribution method proposed by Sastri and Rao:5 −N η = ηBPvp

T/K = 293.15

Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.0005 g·cm−3, u(η) = 0.35 % (0.95 level of confidence).


∑ xjVj

x1

a

a

V=

w1

(4)

where, Pvp is the vapor pressure in atmospheres and ηB is the viscosity at the normal boiling temperature (Tb) in mPa·s. The vapor pressure (Pvp) was determined by eq 5, which is valid for temperature below the boiling temperature of the component:

w1

x1

T/K = 293.15

0.102 0.201 0.303 0.404 0.499 0.607 0.704 0.803 0.901

0.037 0.078 0.127 0.185 0.25 0.341 0.443 0.577 0.753

7.2947 9.3107 11.4470 14.1141 17.4741 22.5553 28.5472 36.6802 47.6381

0.102 0.201 0.303 0.404 0.499 0.607 0.704 0.803 0.901

0.037 0.078 0.127 0.185 0.250 0.341 0.443 0.577 0.753

0.8868 0.8915 0.8949 0.8985 0.9020 0.9061 0.9098 0.9135 0.9172

T/K = 303.15

T/K = 313.15

η/(mPa·s) 5.6010 4.4411 7.0557 5.5161 8.5847 6.6421 10.4251 7.9697 12.7181 9.6199 16.1400 12.0240 20.0872 14.7681 25.3601 18.3401 32.2891 22.9552 ρ/(g·cm−3) 0.8796 0.8724 0.8844 0.8772 0.8877 0.8807 0.8915 0.8844 0.8949 0.8879 0.8991 0.8921 0.9028 0.8959 0.9065 0.8997 0.9100 0.9031

T/K = 323.15

T/K = 333.15

3.6038 4.4365 5.3165 6.2853 7.5108 9.2666 11.2452 13.7803 16.9621

2.9932 3.6475 4.3058 5.0876 6.0204 7.3483 8.8143 10.667 12.964

0.8652 0.8700 0.8736 0.8773 0.8809 0.8852 0.889 0.8928 0.8964

0.8580 0.8629 0.8665 0.8703 0.8740 0.8783 0.8822 0.8861 0.8901

Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.0005 g·cm−3, u(η) = 0.35 % (0.95 level of confidence). a

ln Pvp = (4.5398 + 1.0309 ln Tb)

The values of ηB and N were calculated according to eqs 6 and 7, respectively:

⎛ ⎞ (3 − 2T /Tb)0.19 × ⎜1 − − 0.38(3 − 2T /Tb) 0.19 ln(T /Tb)⎟ T T / ⎝ ⎠ b (5)

ηB = C

∑ ΔηB + ∑ ΔηBcor

(6) DOI: 10.1021/acs.jced.5b00289 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 7. Dynamic Viscosity Data, η (mPa·s) and Density Data, ρ (g·cm−3) for the Binary Blends (w1 Linseed Oil + (1 − w1) Diesel) at Temperatures Ranging from 293.15 K to 333.15 K in Steps of 10 Ka w1

x1

T/K = 293.15

0.107 0.218 0.319 0.418 0.523 0.615 0.714 0.812 0.902

0.026 0.057 0.093 0.136 0.193 0.259 0.353 0.485 0.668

4.1877 5.6902 7.5922 10.3411 13.8610 18.2060 24.6411 33.6982 45.0751

0.107 0.218 0.319 0.418 0.523 0.615 0.714 0.812 0.902

0.026 0.057 0.093 0.136 0.193 0.259 0.353 0.485 0.668

0.8417 0.8508 0.8595 0.8683 0.8771 0.8853 0.8940 0.9031 0.9119

T/K = 303.15

T/K = 313.15

η/(mPa·s) 3.2663 2.6257 4.3615 3.4522 5.7277 4.4627 7.6679 5.8902 10.1042 7.6311 13.0281 9.7232 17.2931 12.7071 23.2333 16.7872 30.6111 21.7530 ρ/(g·cm−3) 0.8347 0.8276 0.8439 0.8368 0.8525 0.8455 0.8614 0.8544 0.8702 0.8633 0.8784 0.8715 0.8868 0.8801 0.8963 0.8896 0.9051 0.8982

Table 9. Dynamic Viscosity Data, η (mPa·s) and Density Data, ρ (g·cm3) for the Binary Blends of (w1 Corn Oil + (1 − w1) Corn Biodiesel) at Temperatures Ranging from 293.15 K to 373.15 K in Steps of 20 Ka

T/K = 323.15

T/K = 333.15

w1

x1

T/K = 293.15

2.1612 2.8065 3.5847 4.6593 6.0059 7.5095 9.6764 12.5841 16.0682

1.8110 2.3327 2.9482 3.7841 4.7957 5.9698 7.6092 9.7498 12.2631

0.107 0.200 0.306 0.400 0.502 0.612 0.713 0.809 0.905

0.038 0.078 0.129 0.182 0.252 0.346 0.455 0.587 0.761

7.9159 9.6839 12.1850 15.0082 18.9262 24.5383 31.3562 40.1210 51.2550

0.8206 0.8299 0.8386 0.8475 0.8564 0.8647 0.8733 0.8829 0.8915

0.8135 0.8229 0.8316 0.8406 0.8495 0.8578 0.8667 0.8761 0.8847

0.107 0.200 0.306 0.400 0.502 0.612 0.713 0.809 0.905

0.039 0.078 0.129 0.182 0.252 0.346 0.455 0.587 0.761

0.8855 0.8891 0.8928 0.8963 0.9001 0.9041 0.9079 0.9114 0.9149

T/K = 313.15 η/(mPa·s) 4.7420 5.6741 6.9521 8.3422 10.2240 12.8371 15.8750 19.6752 24.2131 ρ/(g·cm−3) 0.8714 0.8750 0.8789 0.8824 0.8862 0.8904 0.8941 0.8978 0.9015

T/K = 333.15

T/K = 353.15

T/K = 373.15

3.1671 3.7236 4.4693 5.2647 6.3143 7.7252 9.3108 11.2420 13.5451

2.2826 2.6654 3.1197 3.6264 4.2806 5.1342 6.0842 7.2075 8.5176

1.7197 1.9869 2.3076 2.6626 3.0933 3.6518 4.2485 5.0100 5.8442

0.8573 0.8608 0.8648 0.8684 0.8724 0.8766 0.8807 0.8844 0.8883

0.8426 0.8465 0.8506 0.8545 0.8585 0.8624 0.8663 0.8703 0.8748

0.8282 0.8321 0.8363 0.8402 0.8443 0.8490 0.8531 0.8568 0.8613

a

Standard uncertainties u are u(T) = 0.0 1 K, u(ρ) = 0.0005 g·cm−3, u(η) = 0.35 % (0.95 level of confidence).


Table 8. Dynamic Viscosity Data, η (mPa·s) and Density Data, ρ (g·cm3) for the Binary Blends of (w1 Corn Biodiesel + (1 − w1) Diesel) at Temperatures Ranging from 293.15 K to 373.15 K in Steps of 20 Ka

Table 10. Dynamic Viscosity Data, η (mPa·s) and Density Data, ρ (g·cm3) for the Binary Blends of (w1 Corn Oil + (1 − w1) Diesel) at Temperatures Ranging from 293.15 K to 373.15 K in Steps of 20 Ka

w1

x1

T/K = 293.15

0.100 0.210 0.308 0.417 0.516 0.610 0.707 0.812 0.907

0.068 0.148 0.225 0.318 0.410 0.505 0.611 0.738 0.864

3.3830 3.6041 3.8732 4.1541 4.4360 4.7492 5.0913 5.5064 5.9102

0.100 0.210 0.308 0.417 0.516 0.610 0.707 0.812 0.907

0.068 0.148 0.225 0.318 0.410 0.505 0.611 0.738 0.864

0.8384 0.8434 0.8480 0.8531 0.8576 0.8620 0.8668 0.8721 0.8771

T/K = 313.15 η/(mPa·s) 2.1754 2.3011 2.4614 2.6259 2.7940 2.9738 3.1749 3.4164 3.6917 ρ/(g·cm−3) 0.8245 0.8294 0.8339 0.8389 0.8436 0.8479 0.8526 0.8579 0.8627

a

T/K = 333.15

T/K = 353.15

T/K = 373.15

w1

x1

T/K = 293.15

1.5363 1.6134 1.7221 1.8286 1.9394 2.0544 2.1864 2.3416 2.5104

1.1485 1.2012 1.2784 1.3556 1.4347 1.5149 1.6078 1.7173 1.8431

0.8897 0.9275 0.988 1.0444 1.1042 1.1644 1.2332 1.3141 1.4060

0.110 0.214 0.317 0.423 0.530 0.626 0.719 0.818 0.909

0.026 0.056 0.092 0.138 0.197 0.267 0.359 0.495 0.686

4.2956 5.7540 7.7407 10.5811 14.5842 19.5781 26.2520 36.3951 49.4613

0.8103 0.8151 0.8197 0.8247 0.8293 0.8338 0.8385 0.8436 0.8483

0.7961 0.8004 0.8051 0.8102 0.8148 0.8190 0.8238 0.8290 0.8338

0.7814 0.7864 0.7907 0.7956 0.8001 0.8047 0.8094 0.8145 0.8192

0.110 0.214 0.317 0.423 0.529 0.626 0.719 0.818 0.909

0.026 0.056 0.092 0.138 0.197 0.267 0.359 0.495 0.686

0.8428 0.8511 0.8593 0.8681 0.8772 0.8853 0.8935 0.9017 0.9100


∑ ΔN + ∑ ΔNcor

η/(mPa·s) 2.6849 3.4783 4.5373 5.9656 7.9360 10.2800 13.2961 17.8052 23.3033 ρ/(g·cm−3) 0.8288 0.8372 0.8456 0.8544 0.8635 0.8717 0.8799 0.8885 0.8965

T/K = 333.15

T/K = 353.15

T/K = 373.15

1.8679 2.3462 2.9885 3.7976 4.9516 6.2506 7.8773 10.2272 13.0031

1.3922 1.7001 2.1416 2.6370 3.3973 4.1834 5.1987 6.5915 8.1989

1.0548 1.2911 1.6083 1.9553 2.4636 2.9909 3.6670 4.6088 5.6528

0.8148 0.8233 0.8317 0.8408 0.8498 0.8583 0.8665 0.8749 0.8830

0.8006 0.8093 0.8178 0.8264 0.8360 0.8442 0.8527 0.8612 0.8691

0.7863 0.7949 0.8035 0.8126 0.8223 0.8307 0.8390 0.8477 0.8551


a

N = 0.2 +

T/K = 313.15

a

(7)

Values of Tb of all pure compounds were predicted by the group contribution method based on the UNIFAC groups proposed by Constantinou and Gani.5

where Δη B , Δη Bcor, ΔN, and ΔNcor are the functional groups. D



Article

Figure 2. Temperature and mole fraction effect on density (ρ) for blends of (a) corn biodiesel (1) + diesel (2); (b) corn oil (1) + corn biodiesel (2); (c) corn oil (1) + diesel (2); temperature ranging from 293.15 K to 373.15 K in steps of 20 K.

Figure 1. Temperature and mole fraction effect on density (ρ) for blends of (a) linseed biodiesel (1) + diesel (2); (b) linseed oil (1) + linseed biodiesel (2); (c) linseed oil (1) + diesel (2); temperature ranging from 293.15 K to 333.15 K in steps of 10 K.

For linseed oil and corn oil the values of viscosity were calculated according to the Vogel equation with parameters calculated from a correlation proposed by Rabelo et al.:6

The group contribution method proposed by Sastri Rao should be used for estimation of low-temperature liquid viscosity and is limited to reduced temperatures less than about 0.75.

ln η = A +

B T+C

(8)

where A, B, and C are the parameters. E



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Figure 3. Temperature and mass fraction effect on dynamic viscosity (η) for blends of (a) linseed biodiesel (1) + diesel (2); (b) linseed oil (1) + linseed biodiesel (2); (c) linseed oil (1) + diesel (2); temperature ranging from 293.15 K to 333.15 K in steps of 10 K.

Figure 4. Temperature and mass fraction effect on dynamic viscosity (η) for blends of (a) corn biodiesel (1) + diesel (2); (b) corn oil (1) + corn biodiesel (2); (c) corn oil (1) + diesel (2); temperature ranging from 293.15 K to 373.15 K in steps of 20 K.

The Grunberg-Nissan5 mixing rule was used to calculate the dynamic viscosity of all pseudopure compounds, neglecting the

interaction parameter (Gij) of the equation by considering the pseudopure compounds as ideal mixtures of pure compounds F



Article

Table 11. Density and Isobaric Expansion Regression Constants A

systems

B

D

R2

χ2

RMSD

−7.20·10−04 −7.00·10−04 −6.90·10−04

0.99977 0.99520 0.98241

8.22·10−08 1.18·10−06 1.54·10−05

0.000276 0.001045 0.003782

7.10·10−07 6.20·10−07 6.40·10−07

0.99952 0.99909 0.99846

1.70·10−13 1.70·10−13 1.10·10−12

4.02·10−07 4.00·10−07 1.02·10−06

−7.18·10−04 −6.96·10−04 −6.90·10−04

0.99990 0.99747 0.98602

6.71·10−08 1.47·10−06 1.69·10−05

0.000249 0.001169 0.003958

7.52·10−07 6.38·10−07 6.64·10−07

0.99887 0.99915 0.99828

8.46·10−13 4.10·10−13 1.87·10−12

8.86·10−07 6.17·10−07 1.32·10−06

C −3

linseed biodiesel (1) + diesel (2) linseed oil (1) + linseed biodiesel (2) linseed oil (1) + diesel (2)

1.04363 1.08978 1.04144

0.06816 0.07700 0.19649

linseed biodiesel (1) + diesel (2) linseed oil (1) + linseed biodiesel (2) linseed oil (1) + diesel (2)

6.50·10−04 6.10·10−04 6.30·10−04

−7.00·10−05 −6.90·10−05 −1.80·10−04

corn biodiesel (1) + diesel (2) corn oil (1) + corn biodiesel (2) corn oil (1) + diesel (2)

1.04509 1.08663 1.04235

0.06345 0.07537 0.18882

corn biodiesel (1) + diesel (2) corn oil (1) + corn biodiesel (2) corn oil (1) + diesel (2)

6.41·10−04 6.02·10−04 6.29·10−04

−6.90·10−05 −6.99·10−05 −1.84·10−04

ρ/(g·cm ) −0.01823 −0.04245 −0.11874 αp/(K−1) 2.00·10−05 3.90·10−05 1.10·10−04 ρ/(g·cm−3) −0.01664 −0.03916 −0.11246 αp/(K−1) 2.01·10−05 3.69·10−05 1.12·10−04

Table 12. Viscosity Regression Constants systems

A

B

C

R2

χ2

RMSD

linseed biodiesel(1) + diesel (2) linseed oil (1) + linseed biodiesel (2) linseed oil (1) + diesel (2) corn biodiesel(1) + diesel (2) corn oil (1) + linseed biodiesel (2) corn oil (1) + diesel (2)

−5.793 −9.484 −10.398 −5.642 −8.845 −9.726

2031.233 3253.483 3315.549 0.630 2.342 3.057

0.614 2.562 3.284 2000.431 3123.424 3175.992

0.998 0.987 0.991 0.994 0.994 0.995

0.002 2.267 1.569 0.011 0.911 0.680

0.041 1.464 1.218 0.104 0.928 0.802

Table 13. Redlich−Kister Parameters for Excess Gibbs Free Energy of Linseed Systems T/K = 293.15 A0 A1 A2 R2 RMSD

668.194 126.727 −138.981 0.982 7.140

A0 A1 A2 R2 RMSD

5537.610 −3792.330 1787.720 0.996 32.316

A0 A1 A2 R2 RMSD

10159.800 −7269.331 6470.591 0.999 50.104

T/K = 303.15

T/K = 313.15

Linseed Biodiesel(1) + Diesel (2) 665.187 682.811 123.361 110.201 −131.165 −89.174 0.979 0.983 7.8233 7.144 Linseed Oil (1) + Linseed Biodiesel (2) 5529.370 5529.940 −3669.260 −3589.300 1859.731 1861.450 0.996 0.996 31.585 30.595 Linseed Oil (1) + Diesel (2) 10084.300 10034.600 −7032.351 −6911.091 6535.831 6470.670 0.999 0.999 51.241 51.290

ln ηm =

∑ xi ln ηi + i=1

1 2

n

n

∑ ∑ i = 1 j = 1, j ≠ i

T/K = 333.15

695.176 78.122 −57.484 0.983 7.284

725.076 77.472 −6.114 0.985 7.228

5526.170 −3535.070 1839.910 0.996 30.720

3175.440 −6560.151 −645.684 0.988 44.227

9999.060 −6872.141 6497.032 0.999 50.592

7620.950 −9471.600 4752.400 0.998 39.909

and its binary blends were obtained at temperatures ranging between 293.15 K and 333.15 K with 10 K steps for the linseed system and T = 293.15 K to 373.15 K in steps of 20 K for the corn system (Tables 3 and 4). Tables 5 to 10 present experimental data of density and viscosity of six combinations of blends (linseed/ corn biodiesel + diesel; linseed/corn oil + linseed/corn biodiesel; linseed/corn oil + diesel). Figures 1 to 4 depict density and viscosity as functions of temperature and mole or mass fractions. Density (ρ) was correlated to mole fraction and temperature. For all blends, it showed a second-order behavior with mole fraction and a linear behavior with temperature. A new correlation

with similar chain and intermolecular behavior: n

T/K = 323.15

xixjGij (9)

where ηm is the liquid pseudopure viscosity (mPa·s), ηi is the viscosity of the ith component (mPa·s), xi and xj are the mole fractions of the ith and jth components.

4. RESULTS AND DISCUSSION The experimental data of density (ρ) and dynamic viscosity (η) of pure (linseed or corn) oil, (linseed or corn) biodiesel, diesel, G



Article

Table 14. Redlich−Kister Parameters for Excess Gibbs Free Energy of Corn Systems T/K = 293.15 A0 A1 A2 R2 RMSD

1104.780 552.023 828.677 0.986 12.481

A0 A1 A2 R2 RMSD

20380.388 8110.858 27302.944 0.982 277.851

A0 A1 A2 R2 RMSD

24438.267 2639.828 3459.941 0.989 250.042

T/K = 313.15

T/K = 333.15

Corn Biodiesel (1) + Diesel (2) −908.551 −2454.458 519.759 392.340 −3991.258 −7920.273 0.813 0.880 59.903 103.625 Corn Oil (1) + Linseed Biodiesel (2) 17474.376 15262.121 7133.414 6389.271 20646.660 15701.015 0.990 0.995 178.298 104.214 Corn Oil (1) + Diesel (2) 20882.925 18283.078 3493.669 4227.824 1754.660 470.810 0.991 0.986 177.457 209.585

T/K = 353.15

T/K = 373.15

−3740.617 363.328 −11131.904 0.895 141.737

−4881.663 379.452 −14143.283 0.901 177.992

13581.493 5796.552 11832.001 0.998 56.002

12261.125 5486.600 8731.525 0.999 42.310

16360.439 4885.656 −547.656 0.975 276.383

15350.363 3971.371 −5961.481 0.952 354.951

Table 15. ΔGE Regression Constants systems

A0

A1

A2

B0

B1

B2

R2

X2

RMSD

linseed biodiesel (1) + diesel (2) linseed oil (1) + linseed biodiesel (2) linseed oil (1) + diesel (2) corn biodiesel (1) + diesel (2) corn oil (1) + corn biodiesel (2) corn oil (1) + diesel (2)

678.039 5477.427 10010.450 −1966.809 15455.754 19264.190

109.595 −3641.760 −7036.380 429.362 6617.330 5353.007

−103.700 1671.453 6244.941 −6737.701 15815.059 6260.555

719.949 15.945 3029.205 13774.773 20813.887 20348.468

−4.934 0.281 −18.427 −66.925 −104.980 −104.415

0.008 −0.001 0.028 0.076 0.128 0.127

0.983 0.996 0.999 0.811 0.960 0.967

66.575 1093.671 1277.949 64945.887 105856.149 117631.818

6.785 27.489 29.716 240.543 307.097 323.727

Table 16. AE and AAE for Density and Viscosity Prediction for Pseudopure Compounds of Linseed System and Diesel AE/% compound

293.15 K

303.15 K

313.15 K

323.15 K

333.15 K

AAE/%

0.7493 1.4031 9.2188

0.9951 1.1111 9.2714

1.2518 0.8155 9.3092

0.7516 1.3923 9.1997

8.651 14.337 4.2281

10.437 14.651 3.6338

11.669 15.073 2.4149

7.4156 14.832 3.3358

ρ/(g·cm−3) linseed biodiesel (GCVOL) linseed oil (GCVOL) diesel (GCVOL)

0.2584 1.9522 9.0584

0.5036 1.6799 9.1405

linseed biodiesel (Sastri-Rao) linseed oil (Rabelo et al) diesel (Sastri-Rao)

0.8929 15.575 2.4568

5.4278 14.523 3.9454

η/(mPa·s)

Table 17. AE and AAE for Density and Viscosity Prediction for Pseudopure Compounds of Corn System AE/% compound

293.15 K

313.15 K

333.15 K

353.15 K

373.15 K

AAE/%

1.1523 0.8602

1.6110 0.2700

2.0912 0.3321

1.1424 0.9901

4.7001 7.9101

3.3610 11.0912

6.7110 14.1512

4.7121 8.6821

−3

ρ/(g·cm ) corn biodiesel (GCVOL) corn oil (GCVOL)

0.1701 2.0200

0.6513 1.4600

corn biodiesel (Sastri-Rao) corn oil (Rabelo et al.)

8.1510 4.9111

0.6201 5.3220

η/(mPa·s)

directly dependent to the mass fraction, as evaluated in previous works:7

was proposed according to eq 10: ρ = A + Bx1 + Cx12 + DT

(10)

ln η = A +

where ρ is density; x1 is the mole fraction of compound 1; T is the absolute temperature; A, B, C, and D are the adjusted parameters. Viscosity (η) data showed good agreement with eq 11. Viscosity was dependent to the inverse of temperature and

B + Cw1 T

(11)

where η is the dynamic viscosity; T is the temperature, and w1 is the mass fraction of compound 1; A, B, and C are the adjusted parameters. H



Article

Table 18. Calculated Excess Properties for the Binary Blends (x1 Linseed Biodiesel + (1 − x1) Diesel) at Temperatures Ranging from 293.15 K to 333.15 K in Steps of 10 K x1

T/K = 293.15

T/K = 303.15

0.073 0.151 0.231 0.316 0.410 0.513 0.617 0.711 0.859

0.042 0.078 0.106 0.126 0.138 0.139 0.128 0.109 0.062

0.073 0.151 0.231 0.316 0.410 0.513 0.617 0.711 0.859

44.533 94.202 130.323 163.340 193.039 206.265 198.178 192.693 87.803

0.073 0.151 0.231 0.316 0.410 0.513 0.617 0.711 0.859

32.204 71.224 99.157 126.261 152.492 165.439 160.533 160.622 69.498

T/K = 313.15

ΔSE/(J·mol−1·K−1) 0.187 0.468 0.339 0.821 0.449 1.056 0.521 1.195 0.556 1.243 0.546 1.193 0.492 1.054 0.411 0.867 0.228 0.471 ΔHE/(J·mol−1) 91.786 185.393 174.467 333.272 234.292 434.797 282.259 507.719 322.561 547.231 330.138 542.928 307.933 491.922 286.116 435.918 137.563 220.902 ΔGE/(J·mol−1) 35.078 38.906 71.591 76.106 98.225 104.190 124.282 133.660 154.070 158.047 164.607 169.270 158.773 162.011 161.412 164.459 68.295 73.397

T/K = 323.15

Table 19. Calculated Excess Properties for the Binary Blends (x1 Linseed Oil + (1 − x1) Linseed Biodiesel) at Temperatures Ranging from 293.15 K to 333.15 K in Steps of 10 K

T/K = 333.15

1 ⎛ ∂ρ ⎞ ⎜ ⎟ ρ ⎝ ∂T ⎠ P , x

1.586 2.564 3.097 3.329 3.312 3.059 2.615 2.101 1.106

0.037 0.078 0.127 0.185 0.250 0.341 0.443 0.577 0.753

0.230 0.447 0.659 0.849 0.999 1.113 1.135 1.028 0.707

344.657 583.572 737.553 829.442 866.631 833.702 735.958 630.330 322.768

580.982 941.093 1150.397 1255.399 1274.902 1201.449 1040.789 872.272 450.209

0.037 0.078 0.127 0.185 0.250 0.341 0.443 0.577 0.753

453.042 921.748 1249.375 1518.490 1729.785 1865.446 1827.957 1560.605 937.779

46.905 80.669 110.592 138.298 164.255 173.143 162.862 164.961 74.301

52.586 86.860 118.653 146.182 171.570 182.327 169.521 172.378 81.718

0.037 0.078 0.127 0.185 0.250 0.341 0.443 0.577 0.753

385.646 790.706 1056.189 1269.604 1437.075 1539.174 1495.212 1259.165 730.381

T/K = 303.15


n

(12.2)

i=0

i=1

(13)

where R is the universal gas constant; T is the absolute temperature; V and Vi are the molar volumes of the binary blends and pseudopure compounds, respectively. For the calculation of excess Gibbs free energy all blends have been considered as binary mixtures. Excess Gibbs free energy values were correlated by using the Redlich−Kister polynomial series:10 n

ME = x1x 2 ∑ Ai (x1 − x 2)i i=0

T/K = 333.15

8.987 12.412 14.234 15.049 15.112 14.382 12.897 10.340 6.341

15.734 19.623 21.349 21.835 21.435 19.992 17.665 13.979 8.476

3270.394 4777.245 5650.462 6107.949 6298.717 6166.391 5652.583 4605.230 2806.022

5567.471 7212.472 7997.812 8309.463 8269.606 7790.155 6861.477 5258.686 2718.723

366.224 766.242 1050.874 1244.952 1415.179 1518.893 1484.806 1263.988 756.786

325.620 675.045 885.469 1035.153 1128.679 1129.739 976.328 601.600 −105.081

∑ BiT j=0

(15)

These correlations were adjusted to all experimental data and showed good agreement according to each equation previously shown. The chi-square (χ2) statistical analysis and the root mean standard deviation (RMSD) were used to evaluate the accuracy of the proposed correlations. The highest values of chi-square (χ2) were 1.69·10−5 and 2.27 for density and viscosity, respectively. Regressed parameters for density (ρ) and isobaric expansion (αp) adjusted to eq 10 are shown in Table 11. The parameters of eq 11 for viscosity are shown in Table 12. Parameters adjusted by the Redlich−Kister series are shown in Tables 13 and 14. Parameters obtained for eq 15 of each system are shown in Table 15. The results of predicted density (ρ) and dynamic viscosity (η) were compared with experimental data by means of absolute error (AE) and average absolute error (AAE):

2

∑ xi ln(ηiVi )]

T/K = 323.15

m

ΔGE = x1x 2 ∑ Ai (x1 − x 2)i +

where the partial differential was taken from eq 10. Isobaric expansion showed behavior similar to density. Density (ρ) and viscosity (η) experimental data were used to derive the excess Gibbs free energy of activation of viscous flow (ΔGE) according to eq 13 based on the theory of reaction rates:9 ΔGE = RT[ln(ηV ) −

T/K = 313.15

where ME is any excess property and Ai are the adjusted polynomial parameters. A new correlation was proposed for excess Gibbs free energy as a function of mole fraction and absolute temperature by combining the Redlich−Kister equation and a temperaturedependent term:

(12.1)

⎛ ∂ρ ⎞ ⎜ ⎟ =D ⎝ ∂T ⎠ P , x

T/K = 293.15

0.921 1.556 1.940 2.139 2.174 2.044 1.773 1.440 0.769

Isobaric expansion (αp) values were calculated from density data, according to eq 12:8 αP = −

x1

AE = 100 (14) I

Mexp − Mcalc Mexp

(16.1) DOI: 10.1021/acs.jced.5b00289 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 20. Calculated Excess Properties for the Binary Blends (x1 Linseed Oil + (1 − x1) Diesel) at Temperatures Ranging from 293.15 K to 333.15 K in Steps of 10 K x1

T/K = 293.15

0.026 0.057 0.093 0.136 0.193 0.259 0.353 0.485 0.668

0.340 0.702 1.033 1.352 1.665 1.893 2.038 1.970 1.514

0.026 0.057 0.093 0.136 0.193 0.259 0.353 0.485 0.668

692.950 1409.682 2036.783 2650.307 3111.032 3412.167 3519.523 3235.420 2291.050

0.026 0.057 0.093 0.136 0.193 0.259 0.353 0.485 0.668

593.167 1203.896 1733.861 2254.083 2622.938 2857.200 2922.185 2658.020 1847.222

T/K = 303.15

T/K = 313.15


AAE/% = 100 ∑ n

T/K = 323.15

Table 21. Calculated Excess Properties for the Binary Blends (x1 Corn Biodiesel + (1 − x1) Diesel) at Temperatures Ranging from 293.15 K to 373.15 K in Steps of 20 K

T/K = 333.15

x1

16.562 21.235 23.377 24.414 24.574 23.871 21.972 18.338 12.356

27.291 32.006 33.866 34.469 33.997 32.549 29.562 24.382 16.261

0.068 0.148 0.225 0.318 0.410 0.505 0.611 0.738 0.864

0.041 0.079 0.107 0.130 0.142 0.143 0.133 0.105 0.062

5933.216 8037.127 9244.398 10084.780 10516.490 10503.710 9958.781 8537.783 5836.162

9638.841 11773.210 12865.820 13517.990 13658.830 13332.960 12301.740 10174.790 6489.341

0.068 0.148 0.225 0.318 0.410 0.505 0.611 0.738 0.864

88.005 145.321 222.477 267.442 298.438 323.241 328.356 313.639 272.314

581.313 1175.148 1690.014 2195.422 2575.272 2789.880 2858.434 2611.832 1843.404

546.744 1110.304 1583.226 2034.611 2332.861 2489.218 2453.156 2052.059 1071.889

0.068 0.148 0.225 0.318 0.410 0.505 0.611 0.738 0.864

76.113 122.074 191.017 229.237 256.840 281.254 289.444 282.884 254.118

Mexp, n − Mcalc, n Mexp, n

T/K = 293.15

T/K = 313.15

ΔSE/(J·mol−1·K−1) 0.181 0.454 0.344 0.833 0.454 1.069 0.537 1.227 0.570 1.273 0.562 1.228 0.509 1.089 0.392 0.821 0.227 0.466 ΔHE/(J·mol−1) −382.011 −681.890 −296.722 −535.415 −197.127 −390.453 −139.996 −313.500 −106.041 −278.067 −93.222 −286.502 −106.977 −334.103 −158.214 −445.963 −217.058 −587.840 ΔGE/(J·mol−1) −438.681 −833.002 −404.416 −812.837 −339.318 −746.654 −308.012 −722.409 −284.570 −702.209 −269.262 −695.706 −266.318 −696.823 −280.962 −719.432 −288.028 −743.068

ΔS E = −R ∑ xi ln i

(16.2)

T/K = 333.15

T/K = 353.15

T/K = 373.15

0.895 1.578 1.966 2.192 2.222 2.102 1.831 1.356 0.758

1.546 2.601 3.140 3.405 3.382 3.145 2.698 1.970 1.089

−852.871 −598.222 −397.746 −293.693 −264.921 −305.727 −408.105 −603.958 −833.149

−904.427 −506.297 −230.700 −111.810 −100.930 −189.551 −365.542 −669.143 −1021.360

−1169.029 −1155.443 −1091.896 −1067.735 −1049.724 −1048.217 −1054.547 −1082.783 −1101.003

−1481.290 −1476.844 −1402.531 −1382.459 −1362.852 −1363.265 −1372.136 −1404.064 −1427.748

ϕi xi

(17)

where ϕi is the apparent volume fraction. The excess molar enthalpy (ΔHE) was obtained from the definition of molar Gibbs free energy in terms of excess properties, as shown by eq 18:

where M is any property. Absolute error and average absolute error for density and viscosity prediction for all pseudopure compounds were presented in Tables 16 and 17. For density, the values predicted by the GCVOL model showed good agreement with experimental data, with a maximum value of AE of 9.41 % for pure diesel at 373.15 K. The calculation of viscosity using the group contribution method of Sastri-Rao showed good agreement to viscosity data of pure diesel with a maximum AE of 4.23 %. For linseed biodiesel, the Sastri-Rao model showed higher absolute errors as temperature increased, reaching a maximum AE of 11.67 %, while for corn biodiesel the higher absolute error was 8.15 % at 293.15 K. For linseed and corn oil, the equations of Rabelo et al.10 that were used to predict the parameters of the Vogel equation had not resulted in a good agreement between the calculated and the experimental data for viscosity, with a maximum value of AE of 15.57 % for linseed oil and 14.15 % for corn oil. The main excess properties (ΔHE, ΔGE, and ΔSE) can show several combinations of signs. The trend shown by these properties reflects the observation of the intermolecular behavior.11 The Flory−Huggins equation was used to evaluate the excess molar entropy (ΔSE), according to eq 17:

ΔGE ≡ ΔHE − T ΔS E

(18)

where T is the absolute temperature. Calculated excess properties for all binary blends are shown in Tables 18 to 23. The structural contributions to ΔSE are important features to describe the relative strengths of the competing intermolecular bonds. Since all ΔSE values are positive, the structure breaking is prevalent in comparison to structure making when the compounds are mixed; that is, the molecular aggregates gathered by dipole−dipole interaction are broken up by the mixing effect. For the blends containing species with approximate size, such as the mixtures of linseed biodiesel + diesel, the enthalpic contribution to ΔGE is dominant.11 In this case, the ΔHE values are positive, that is, the mixing of the species is endothermic. Thus, the dispersion forces between like species are stronger than the dispersion forces between unlike species.12 For the blends containing species with a very different size, such as the mixtures of linseed oil + (linseed biodiesel or diesel), the positive size/shape contributions lead to ΔSE values greater than J



Article

Table 22. Calculated Excess Properties for the Binary Blends (x1 Corn Oil + (1 − x1) Corn Biodiesel) at Temperatures Ranging from 293.15 K to 373.15 K in Steps of 20 K x1

T/K= 293.15

0.038 0.078 0.129 0.182 0.252 0.346 0.455 0.587 0.761

0.239 0.443 0.661 0.836 0.996 1.109 1.124 1.009 0.685

0.038 0.078 0.129 0.182 0.252 0.346 0.455 0.587 0.761

2185.073 2738.727 3351.894 3884.279 4441.329 5004.671 5452.803 5794.154 5948.016

0.038 0.078 0.129 0.182 0.252 0.346 0.455 0.587 0.761

2115.035 2608.752 3158.246 3639.084 4149.280 4679.427 5123.165 5498.231 5747.120

T/K = 313.15

T/K = 333.15


T/K = 353.15

Table 23. Calculated excess properties for the binary blends (x1 corn oil + (1-x1) diesel) at temperature ranging from 293.15 to 373.15 K in steps of 20 K

T/K = 373.15

T/K = 293.15

x1

9.104 12.280 14.143 14.907 14.986 14.216 12.614 10.069 6.113

15.822 19.419 21.187 21.651 21.238 19.739 17.249 13.598 8.164

0.026 0.056 0.092 0.138 0.197 0.267 0.359 0.495 0.686

0.352 0.692 1.031 1.371 1.687 1.919 2.045 1.959 1.453

4012.725 5596.103 6708.340 7392.790 7849.245 7999.569 7760.603 7102.668 5795.998

6408.843 8207.494 9324.499 9914.718 10166.242 10004.735 9367.245 8251.445 6285.755

0.026 0.056 0.092 0.138 0.197 0.267 0.359 0.495 0.686

910.564 1774.629 2639.241 3527.324 4399.577 5142.270 5785.619 6316.221 6462.885

797.792 1259.449 1713.788 2128.358 2556.950 2979.215 3305.931 3546.892 3637.345

505.027 961.243 1418.715 1835.726 2241.440 2639.093 2930.619 3177.325 3239.399

0.026 0.056 0.092 0.138 0.197 0.267 0.359 0.495 0.686

807.342 1571.709 2337.012 3125.278 3905.110 4579.689 5186.226 5742.005 6036.922

T/K = 313.15

T/K = 333.15

ΔSE/(J·mol−1·K−1) 2.337 7.774 4.060 11.300 5.422 13.450 6.507 14.803 7.262 15.431 7.595 15.324 7.471 14.423 6.582 12.182 4.513 8.052 ΔHE/(J·mol−1) 998.406 2463.063 2268.354 4329.335 3432.653 5765.870 4514.799 6912.646 5494.505 7859.472 6229.007 8424.608 6747.905 8649.484 6977.675 8364.024 6556.044 7156.701 ΔGE/((J·mol−1)) 266.692 −126.898 996.874 564.815 1734.800 1285.067 2477.275 1981.173 3220.258 2718.571 3850.483 3319.292 4408.296 3844.547 4916.435 4305.716 5142.748 4474.209

T/K = 353.15

T/K = 373.15

16.747 21.112 23.333 24.424 24.532 23.711 21.817 18.039 11.707

27.454 31.855 33.794 34.420 33.879 32.261 29.316 23.953 15.386

5483.198 7674.967 9190.528 10223.956 11007.976 11284.635 11133.070 10221.963 8106.856

9470.527 11808.146 13270.122 14148.428 14666.843 14619.580 14029.364 12452.531 9349.069

−431.063 219.189 950.414 1598.593 2344.379 2911.227 3428.440 3851.618 3972.583

−774.008 −78.666 659.770 1304.570 2024.960 2581.484 3090.097 3514.313 3607.728

comprising linseed oil and petroleum diesel. The dynamic viscosity data was adjusted according to eq 11 resulting in a minimum R2 of 0.987 for the system comprising linseed oil and linseed biodiesel. The GCVOL model is able to predict density for all pseudopure compounds, showing low deviation between the calculated and experimental data, with maximum AAE of 9.20 % for petroleum diesel. The Sastri−Rao model showed good agreement between the experimental and the calculated values of dynamic viscosity for diesel. For linseed biodiesel, this model presented low deviations at 293.15 K and 303.15 K, but it was not accurate at higher absolute temperatures, resulting in an overall AAE of 7.42 %. For corn biodiesel the Sastri−Rao model showed good accuracy with an AAE of 4.71 %. The viscosity parameters calculated by means of the equation proposed by Rabelo et al.10 showed high deviations with an AAE of 14.83 %.

for the mixtures of linseed biodiesel + diesel; that is, the entropic contribution to ΔGE is more evident, which implies a higher level of disorder for these systems. The ΔSE values calculated from Flory−Huggins equation, ΔHE values, and ΔGE values are presented in Tables 12 to 14. Furthermore, it is consistent to say that the viscosity (η) not only reflects the intermolecular behavior, but also is a reflection of molecular ordering;13 that is, the greater is the difference in viscosity between different substances, the greater is the entropic character of the mixtures presented in this work, mainly due to the sterically hindered feature of the triglycerides present in the linseed oil. Also, the higher is the dynamic viscosity, the stronger are the intermolecular bonds, thus, the lower is the deformation of the fluid.13,14

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5. CONCLUSIONS Density (ρ) and dynamic viscosity (η) data for pseudopure and binary systems of linseed or corn oil, linseed or corn biodiesel, and petroleum diesel have been measured in this work, at a temperature range from 293.15 K to 333.15 K for linseed systems and 293.15 K to 373.15 for corn systems. Density shows proportional linear behavior against temperature. Although dynamic viscosity presents a Newtonian behavior (an exponential behavior), inversely proportional against temperature. All systems showed good agreement to eq 10, which was proposed to adjust density, and have resulted in a minimum R2 of 0.982 for the system

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +55 85 3366-9611. Funding

The authors thank CNPq (Conselho Nacional de Desenvolvimento ́ Cientifico e Tecnológico, Brazil) and CAPES (Coordenaçaõ de ́ Superior) for the financial Aperfeiçoamento de Pessoal de Nivel support. Notes

The authors declare no competing financial interest. K



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Article

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