Densities and Viscosities of Ethyl Heptanoate and Ethyl Octanoate at

Article pubs.acs.org/jced

Densities and Viscosities of Ethyl Heptanoate and Ethyl Octanoate at Temperatures from 303 to 353 K and at Pressures up to 15 MPa Xiangyang Liu,† Tianwang Lai,† Xudong Guo,† Maogang He,*,† Wei Dong,‡ Tansu Shang,‡ and Weiping Yang‡ †

Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi Province 710049, P. R. China ‡ State Key Laboratory of Power System of Tractor, Luoyang, Henan Province 471039, P. R. China ABSTRACT: The densities and viscosities of ethyl heptanoate and ethyl octanoate were measured at temperatures ranging from 303 to 353 K and at pressures ranging from 0.1 to 15 MPa. The expanded uncertainties of density and the relative expanded uncertainty of viscosity are better than 5 kg·m−3 and 0.015, respectively. Experimental results show that the densities and viscosities of the two fatty acid ethyl esters increase with the increasing pressure and decrease with the increasing temperature. The density data were correlated using the Tait equation, and the viscosity data were correlated using the Andrade−Tait model. The average absolute relative deviations between the experimental data and the calculated results for the densities and viscosities were less than 0.03% and 0.47%, respectively.

1. INTRODUCTION With the deepening crisis of energy, renewable energy sources are in urgent need of exploration and development. Biodiesel is one such source with the advantages of extensive source and low sulfur content,1 and so forth. The thermophysical properties of biodiesel have an important influence on the performance of the engine.2 The density and viscosity are necessary for optimizing the injection process, which are relevant to the injected mass of biodiesel and the flow frictional resistance in the engine. The major components of biodiesel are different fatty acid alkyl esters. The thermophysical properties of the fatty acid alkyl esters are required for understanding and designing the properties of biodiesels.3 Densities and viscosities of many fatty acid alkyl esters have been studied experimentally or theoretically, but most of these works were conducted at the atmospheric pressure. For example, Knothe et al.4 have measured the densities of fatty acid methyl, ethyl, propyl, and butyl esters (C8 to C24) from 298 to 313 K; Lapuerta et al.5 proposed two equations to convert the densities of fatty acid methyl ester (FAME) and fatty acid ethyl ester (FAEE) to 298 K and predict the density of biodiesel. Pratas et al.6 measured the densities and viscosities of several FAMEs and FAEEs at temperatures from 278 to 363 K and used them to evaluate the GCVOL group contribution method for density and methods of Ceriani−Meirelles and Marreiro−Gani for viscosity. Phankosol et al.7 presented an method to predict the viscosities © 2017 American Chemical Society

of FAMEs and biodiesels at temperatures ranging from 293 to 373 K using the number of carbon atoms and double bonds. Few data for the densities and viscosities of fatty acid alkyl esters at high pressure are available in the literature. To our best knowledge, only the density data of methyl decanoate, methyl dodecanoate, methyl tetradecanoate, methyl oleate, methyl linoleate, ethyl decanoate, and ethyl dodecanoate have been reported by Ndiaye et al.,8,9 Pratas et al.,10 Wang et al.,11 and Outcalt et al.,12 while the viscosity data of methyl decanoate, ethyl decanoate, methyl tetradecanoate, and ethyl tetradecanoate have been reported by Habrioux et al.13,14 at elevated pressure. In addition, Dzida et al.15−17 and Chum-in et al.18,19 have obtained the densities of ethyl octanoate, ethyl decanoate, ethyl dodecanoate, ethyl tetradecanoate, methyl octanoate, methyl decanoate, methyl dodecanoate, methyl tetradecanoate, methyl hexadecanoate, and methyl oleate at pressures up to 100 MPa using theoretical methods. Ethyl heptanoate is the constituent of the grape seed oil,20 while ethyl octanoate is the constituent of coconut oil.21 In this work, the densities and viscosities of ethyl heptanoate and ethyl octanoate at pressures from 0.1 to 15.0 MPa and at temperatures from 303 to 353 K were presented. The Tait Received: April 25, 2017 Accepted: July 5, 2017 Published: July 18, 2017 2454

DOI: 10.1021/acs.jced.7b00386 J. Chem. Eng. Data 2017, 62, 2454−2460

Journal of Chemical & Engineering Data

Article

measured with a Siemens Coriolis flowmeter (Mass 2100 DI 1.5 sensor + Mass 6000 transmitter) with accuracy of 0.1%. The temperature of experimental cell was controlled using a thermostatic bath whose temperature was measured using a Fluke platinum resistant thermometer (5608) with an expanded uncertainty of 0.02 K (k = 2, degree of confidence is 95%). The pressures at the inlet and outlet of the experimental cell were measured with two Rosemount pressure transmitters (3051S, 20 MPa) with expanded uncertainties of 5 kPa (k = 2). The pressure drop of fluid through the capillary tube was measured with a Rosemount differential pressure transmitter (3051S, 60 kPa) with an expanded uncertainty of 0.015 kPa (k = 2). Based on the Poiseuille’s law, the dynamic viscosity η can be calculated by

equation and the Andrade−Tait model were used to correlate the experimental data of density and viscosity, respectively.

2. EXPERIMENTAL SECTION Ethyl heptanoate and ethyl octanoate used in this work were purchased from Sigma-Aldrich. Information about their source, chemical formula, purities, water content, and CAS numbers are listed in Table 1. Table 1. Characteristics of Chemicals Used in This Work

name ethyl heptanoate ethyl octanoate a

chemical formula

source

C9H18O2 C10H20O2

SigmaAldrich SigmaAldrich

mass fraction puritya

water content in mass fractionb

CAS

0.99

0.0008

106-30-9

0.99

0.0007

106-32-1

η=

πR4Δp 8QL

(1)

b

Stated by the supplier. Measured with a KLS701 Karl Fischer titrator provided by Zibo Kulun Analysis Instrument Co., Ltd.

where R and L are the inner radius and length of the capillary tube, respectively; Δp is the pressure drop between the inlet and outlet of the capillary tube; Q is the volume flow rate of fluid through the capillary tube. In consideration of the kinetic energy correction and the change in the geometrical size of the capillary tube, replace Q with the ratio of the mass flow rate of the sample q and the density ρ, eq 1 becomes22

The viscosity was measured using the capillary method as described previously.22 The experimental system is shown in Figure 1. The pressure in the system and the flow rate of fluid

η=

nq πρR4Δp (1 + αΔT )3 − 8qL 8πL(1 + αΔT )

(2)

where α is the linear expansion coefficient of the capillary tube material (304 stainless steel); ΔT is the difference between experimental temperature and room temperature; n is the kinetic energy correction coefficient, which is taken to be 1.12 as recommended in literature.23,24 The length and inner radii of the capillary tube used in this work are 511 mm and 0.189 mm, respectively. The equipment was calibrated with water in the experimental temperature and pressure range. The viscosity data of water are from literature.25 Its accuracy was also tested by comparing the viscosity data of ethyl octanoate at 0.1 MPa with those in literature.26 The relative expanded uncertainty of viscosity can be evaluated by

Figure 1. Schematic diagram of experimental apparatus: 1, sample; 2, filter; 3, plunger-type pump; 4, preheater; 5, pressure transmitter; 6, differential pressure transmitter; 7, condenser; 8, thermostatic bath; 9, capillary tube; 10, experimental cell; 11, thermostatic bath; 12, flow meter; 13, counterbalance valve; 14, needle valve; 15, collecting bottle.

was controlled by a plunger-type pump (Scientific Systems 1500) and a counterbalance valve. The mass flow rate was

2 2 2 2 ⎛ ∂η ⎞2 2 ⎛ ∂η ⎞2 2 ⎛ ∂η ⎞ 2 ⎛ ∂η ⎞2 2 k ⎛ ∂η ⎞ 2 ⎛ ∂η ⎞ 2 ⎛ ∂η ⎞ 2 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ u uR + ⎜ ⎟ uq + ⎜ u + u +⎜ ⎟u +⎜ Ur(η) = ⎟ uΔp + ⎝ ∂L ⎠ L ⎝ ∂n ⎠ n ⎝ ∂ρ ⎠ ρ ⎝ ∂ΔT ⎠ ΔT η ⎝ ∂R ⎠ ⎝ ∂Δp ⎠ ⎝ ∂q ⎠

where uR, uL, uq, uΔp, uΔT, uρ, un are the standard uncertainties of R, L, q, Δp, ΔT, ρ and n, respectively. The density was directly measured using the Siemens Coriolis flow meter in the experimental system for viscosity. The Siemens Coriolis flowmeter can obtained the density of fluid by measuring the oscillation period of the measuring tube inside the flowmeter. The pressure of fluid was controlled by the plunger-type pump and measured using a Rosemount pressure transmitters (3051S, 20 MPa) with expanded uncertainties of 5 kPa (k = 2). The temperature the Mass 2100 DI 1.5 sensor was controlled by a thermostatic bath as shown in Figure 1, and its temperature was measured using a Fluke platinum resistant thermometer (5608) with an expanded uncertainty of 0.02 K (k = 2). When the temperature and

(3)

pressure of fluid in the Mass 2100 DI 1.5 sensor were stable, the density of fluid was shown by the Mass 6000 transmitter. The equipment was factory calibrated with water, and its accuracy was verified by the comparing the densities of acethyl heptanoate and ethyl octanoate at 0.1 MPa with those in literature.6,15,27−33 Taking into account the uncertainties from the temperature, the pressure, the sample purity, the calibrated error, and the random error, the overall expanded uncertainty of density was estimated to be within 5 kg·m−3, while the overall relative expanded uncertainty of viscosity is less than 0.015 (k = 2).34 2455



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3. RESULTS AND DISCUSSION Density. The densities of ethyl heptanoate and ethyl octanoate were measured at temperatures from 303 to 353 K and at pressures from 0.1 to 15 MPa, which are listed in Table 2 Table 2. Experimental Density Data of Ethyl Heptanoate and Ethyl Octanoatea ethyl heptanoate

ethyl octanoate −3

T/K

p/MPa

ρ/(kg·m )

T/K

p/MPa

ρ/(kg·m−3)

303.20 303.20 303.10 303.20 303.21 303.19 312.96 313.06 313.13 313.17 313.18 313.17 323.09 323.11 323.14 323.10 323.13 323.09 333.05 333.14 333.18 333.14 333.14 333.20 343.02 343.06 343.23 343.20 343.22 343.19 352.85 352.95 353.11 353.06 353.14 353.23

0.10 3.02 6.00 9.01 11.95 14.98 0.10 3.06 6.09 9.07 12.00 15.01 0.10 3.10 6.11 9.10 12.06 15.15 0.10 3.01 6.08 9.02 12.01 15.07 0.10 3.01 6.05 9.00 12.10 15.00 0.10 3.09 6.07 9.09 12.07 15.01

860.8 864.5 867.7 871.2 874.5 877.5 851.2 854.7 858.1 861.4 864.7 867.9 841.6 845.2 848.8 852.5 855.8 859.2 832.1 835.6 839.7 843.2 846.8 850.5 823.0 827.1 831.0 834.8 838.5 842.1 815.1 819.4 823.2 827.5 831.2 835.1

303.25 303.32 303.30 303.32 303.26 303.33 313.05 313.12 313.08 313.10 313.10 313.11 323.00 323.09 323.10 323.13 323.14 323.16 333.00 333.14 333.18 333.18 333.20 333.21 343.11 343.11 343.14 343.16 343.10 343.17 353.10 353.21 353.27 353.16 353.25 353.24

0.10 3.12 6.08 9.13 12.08 15.08 0.10 3.14 6.15 9.15 12.10 15.11 0.10 3.13 6.15 9.11 12.14 15.05 0.10 3.10 6.08 9.09 12.10 15.10 0.10 3.12 6.10 9.07 12.15 15.00 0.10 3.15 6.15 9.13 12.14 15.07

858.1 861.3 864.4 867.8 871.0 874.1 849.5 853.0 856.1 859.6 862.7 865.9 841.1 844.7 848.1 851.4 854.8 858.1 832.2 836.2 839.7 843.3 846.9 850.3 823.6 827.8 831.7 835.0 838.8 842.1 814.5 819.0 823.0 826.8 830.7 834.4

Figure 2. Densities of ethyl heptanoate: □, 0.1 MPa; △, 3 MPa; ◆, 6 MPa; ■, 9 MPa; ▲, 12 MPa; ●, 15 MPa; +, Vidal et al.27 (0.1 MPa); ○, Lieben et al.28 (0.1 MPa); ◇, Perkin29,30 (0.1 MPa); ×, Vogel31 (0.1 MPa); , Gartenmeister32 (0.1 MPa). The line is the calculated results from the Tait equation.

Figure 3. Densities of ethyl octanoate: □, 0.1 MPa; △, 3 MPa; ○, 6 MPa; ■, 9 MPa; ▲, 12 MPa; ●, 15 MPa; ◇: Pratas et al.6 (0.1 MPa); +, Dzida et al.15 (0.1 MPa); ◆, Vogel 31 (0.1 MPa); , Gartenmeister32 (0.1 MPa); ×, Liew et al.33 (0.1 MPa). The line is the calculated results from the Tait equation.

a

Expanded uncertainties U are U(T) = 0.02 K, U(p) = 5 kPa, U(ρ) = 5 kg·m−3. The level of confidence is 0.95 (k = 2).

and shown in Figures 2 and 3. Figures 2 and 3 also show that, at a fixed temperature, the densities of ethyl heptanoate and ethyl octanoate increase as the pressure rises while they decrease as the temperature rises at a fixed pressure. Figure 4 compares the densities of ethyl heptanoate and ethyl octanoate at 303 and 313 K as a function of pressure. It shows that the densities of ethyl heptanoate are larger than those of ethyl octanoate and the difference between the densities of ethyl heptanoate and ethyl octanoate at 313 K is smaller than that at 303 K. The density data of saturated FAMEs and FAEEs reported by Pratas et al.6 also show that the density difference of two saturated FAMEs or FAEEs at 0.1 MPa decrease when the temperature increases and no significant difference can be found when temperature is up to a certain value. Moreover, a pressure

increment of 15 MPa results a very small change in the density difference of ethyl heptanoate and ethyl octanoate as shown in Figure 4. The density data of ethyl heptanoate and ethyl octanoate in this work were correlated by the Tait equation:35 ρ(T , p) = ρ0 (T , p0 ) /[1 − A ln((p + B(T ))/(p0 + B(T )))] 2

B(T ) = B1 + B2 (T /100) + B3(T /100)

(4) (5)

where ρ0 is the density at p0 = 0.1 MPa; A, B1, B2, and B3 are adjustable coefficients. As shown in Figures 2−3, the densities 2456



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Figure 4. Densities of ethyl heptanoate and ethyl octanoate at 303 and 313 K: ▲, ethyl heptanoate at 303 K; △, ethyl heptanoate at 313 K; ●, ethyl octanoate at 303 K; ○, ethyl octanoate at 313 K.

Figure 5. Deviations of the Tait equation from the experimental data for the densities of ethyl heptanoate and ethyl octanoate: △, ethyl heptanoate (this work); ●, ethyl heptanoate (Vidal et al.27); , ethyl heptanoate (Lieben et al.28); ∗, ethyl heptanoate (Perkin29,30); ■, ethyl heptanoate (Vogel31); ◇, ethyl heptanoate (Gartenmeister32);○, ethyl octanoate (this work); ▲, ethyl octanoate (Pratas et al.6); □, ethyl octanoate (Dzida et al.15); +, ethyl octanoate (Vogel31); ×, ethyl octanoate (Gartenmeister32); ◆, ethyl octanoate (Liew et al.33). The line is the calculated results from the Tait equation.

of ethyl heptanoate and ethyl octanoate at 0.1 MPa can be expressed as a linear function of temperature

ρ0 = a + bT

(6)

where a and b are adjustable coefficients. Therefore, eq 4 becomes ρ(T , p) = (a + bT ) /[1 − A ln((p + B(T ))/(p0 + B(T )))]

shown in Figures 2−3, while the deviations of the Tait equation obtained based on our data from the experimental data in literature6,15,27−33 are shown in Figure 5. They show that our data are in good agreement with those in the literature. The absolute relative deviations of the Tait equation from the experimental density data reported by Pratas et al.,6 Dzida et al.,15 Vidal et al.,27 Lieben et al.,28 Perkin,29,30 and Liew et al.33 are less than 0.1%. Most of the experimental density data reported by Vogel31 and Gartenmeister32 are larger than our data and those in other literature,6,15,27−30,33 especially at high temperature. The absolute relative deviations of the Tait equation from their data are between 0.1% and 0.5%. Viscosity. The experimental viscosity data of ethyl heptanoate and ethyl octanoate in this work are listed in Table 4 and shown in Figures 6−7. The same as the densities, the viscosities of ethyl heptanoate and ethyl octanoate increase with the increasing pressure at a fixed temperature while at a fixed pressure, they decrease with the increasing temperature. Figure 8 compares the viscosities of ethyl heptanoate and ethyl octanoate at 323 and 353 K as a function of pressure. Obviously, ethyl heptanoate is less viscous than ethyl octanoate, and the difference between their viscosities at 353 K is smaller than that at 323 K. From the viscosity data reported by Pratas et al.,6 we can get the same conclusion for other saturated FAMEs and FAEEs at 0.1 MPa. In addition, Figure 8 also shows that the pressure has a small influence on the difference between the viscosities of ethyl heptanoate and ethyl octanoate under 15 MPa. The Andrade−Tait (AT) model is a classical model which can accurately predict the viscosity of liquid using temperature and pressure.36,37 The AT model is given by

(7)

The coefficients in the Tait equation for ethyl heptanoate and ethyl octanoate are listed in Table 3. The calculated results Table 3. Coefficients and Deviations of the Tait Equation coefficient

ethyl heptanoate

ethyl octanoate

a b A B1 B2 B3 MARD (%) AARD (%)

1141 −0.9272 0.1047 −1143 773.4 −123.0 0.10 0.03

1121 −0.8659 0.1293 412.0 −150.2 15.54 0.05 0.02

from the Tait equation are shown in Figures 2−3. The deviations of the Tait equation from the experimental density data in our work for ethyl heptanoate and ethyl octanoate are plotted as a function of temperature in Figure 5. They show that the Tait equation gives very good predictions for the densities of ethyl heptanoate and ethyl octanoate. The maximum absolute relative deviation (MARD) and the average absolute relative deviation (AARD) between the experimental data in our work and the calculated values from the Tait equation are less than 0.10% and 0.03%, respectively, as shown in Table 3. To verify the accuracy of our data, the densities of ethyl heptanoate and ethyl octanoate at 0.1 MPa reported by Pratas et al.,6 Dzida et al.,15 Vidal et al.,27 Lieben et al.,28 Perkin,29,30 Vogel,31 Gartenmeister,32 and Liew et al.33 are 2457



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Table 4. Experimental Viscosity Data of Ethyl Heptanoate and Ethyl Octanoatea ethyl heptanoate

ethyl octanoate

T/K

p/MPa

η/(mPa·s)

T/K

p/MPa

η/(mPa·s)

312.73 312.80 312.77 312.72 313.10 313.17 322.62 322.71 322.78 322.85 322.91 322.76 333.45 333.57 333.63 333.60 333.50 333.42 343.16 343.27 343.38 343.22 343.22 343.27 352.71 352.83 352.86 352.90 352.95 353.04

0.10 3.10 6.10 9.12 12.18 15.17 0.10 3.12 6.13 9.09 12.08 15.11 0.10 3.07 6.13 9.16 12.10 15.07 0.10 3.07 6.08 9.07 12.05 15.12 0.10 3.04 6.10 9.03 12.08 15.04

0.9036 0.9452 0.9702 1.0060 1.0328 1.0604 0.7963 0.8252 0.8471 0.8702 0.9036 0.9293 0.7016 0.7229 0.7431 0.7629 0.7844 0.8106 0.6217 0.6412 0.6593 0.6801 0.6996 0.7191 0.5547 0.5733 0.5898 0.6068 0.6227 0.6414

312.87 312.96 313.03 313.08 313.12 313.14 323.07 323.16 323.17 323.17 323.17 323.19 333.14 333.29 333.30 333.30 333.31 333.30 342.78 343.41 343.07 343.16 343.22 343.27 353.21 353.32 353.35 353.38 353.35 353.36

0.10 3.12 6.06 9.09 12.07 15.24 0.10 3.15 6.11 9.08 12.07 15.06 0.10 3.11 6.06 9.13 12.04 15.09 0.10 3.12 6.13 9.09 12.10 15.05 0.10 3.12 6.09 9.07 12.08 15.06

1.0825 1.1334 1.1892 1.2112 1.2450 1.2839 0.9464 0.9842 1.0158 1.0430 1.0637 1.0979 0.8143 0.8536 0.8851 0.9101 0.9301 0.9551 0.7310 0.7572 0.7776 0.7968 0.8165 0.8446 0.6393 0.6742 0.6910 0.7070 0.7292 0.7479

Figure 7. Viscosities of ethyl octanoate: ■, 313 K; ▲, 323 K; ●, 333 K; □, 343 K; △, 353 K. The line is the calculated results from the AT model.

a

Expanded uncertainties U are U(T) = 0.02 K, U(p) = 5 kPa; relative expanded uncertainty Ur is Ur(η) = 0.015. The level of confidence is 0.95 (k = 2).

Figure 8. Viscosities of ethyl heptanoate and ethyl octanoate at 323 and 353 K: ▲, ethyl heptanoate at 323 K; △, ethyl heptanoate at 353 K ; ●, ethyl octanoate at 323 K; ○, ethyl octanoate at 353 K.

η = C1 exp[C2/(T − C3)] exp[C4 ln((p + D)/(p0 + D))] (8)

D = D1 + D2T + D3T 2

(9)

where C1, C2, C3, C4, D1, D2, and D3 are adjustable coefficients, which were obtained using experimental viscosity data. The coefficients for ethyl heptanoate and ethyl octanoate are listed in Table 5 along with the MARD and AARD between the experimental data and the calculated values from the AT model. The calculated results from the AT model for the viscosities of ethyl heptanoate and ethyl octanoate are shown in Figures 6 and 7. The relative deviations of the AT model from experimental viscosity data in our work for ethyl heptanoate and ethyl octanoate are shown in Figure 9. We can easily find that the AT model agrees very well with experimental data with the deviations ranging from −0.69% to 0.66% for ethyl

Figure 6. Viscosities of ethyl heptanoate: ■, 313 K; ▲, 323 K; ●, 333 K; □, 343 K; △, 353 K. The line is the calculated results from the AT model.

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octanoate in our work and in literature26 as a function of temperature at 0.1 MPa while the relative deviations of the AT model obtained based on our data from the experimental data in literature26 for ethyl octanoate are shown in Figure 10. It can be found that our data and those in literature are in good agreement. The absolute relative deviations of the AT model from the experimental data in literature28 are less than 0.9%.

Table 5. Coefficients and Deviations of the AT Model component

ethyl heptanoate

ethyl octanoate

C1 C2 C3 C4 D1 D2 D3 MARD/% AARD/%

0.0004303 4490 −273.9 0.7740 −995.8 6.197 −0.008981 0.69 0.22

0.03680 745.4 93.61 0.3190 −66.57 0.4848 −0.0006226 1.81 0.47

4. CONCLUSIONS New density and viscosity data of ethyl heptanoate and ethyl octanoate at temperatures from 313 to 353 K under pressures up to 15 MPa were presented and well-correlated by the Tait equation and Andrade−Tait model, respectively. The density and viscosity data in our work at 0.1 MPa agree well with those reported in literature. The experimental data show that high pressure and low temperature result in high densities and viscosities of ethyl heptanoate and ethyl octanoate. When the temperature is high enough, there is no significant difference between the densities of ethyl heptanoate and ethyl octanoate while a temperature increment will reduce the difference between the viscosities of ethyl heptanoate and ethyl octanoate. In the studied pressure range, the effect of pressure on the density and viscosity differences of ethyl heptanoate and ethyl octanoate is small.

■

AUTHOR INFORMATION

Corresponding Author

*Phone: 86-29-82663863, e-mail: [email protected]. ORCID

Maogang He: 0000-0002-2364-2140 Funding

The support provided by the National Science Fund for Distinguished Young Scholars of China (no. 51525604), the National Basic Research Program of China (no. 2015CB251502), and 111 Project (no. B16038) for the completion of the present work is gratefully acknowledged.

Figure 9. Deviations of the AT model from experimental data for the viscosities of ethyl heptanoate and ethyl octanoate: ○, ethyl heptanoate (this work). ●, ethyl octanoate (this work); △, ethyl octanoate (Sheu et al.26).

heptanoate and from −0.92% to 1.81% for ethyl octanoate. Figure 10 compares the experimental viscosity data for ethyl

Notes

The authors declare no competing financial interest.

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REFERENCES

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Figure 10. Viscosities of ethyl octanoate at 0.1 MPa: ◆, our experimental data; △, Sheu et al.26 The line is the calculated results from the AT model. 2459



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Densities and Viscosities of Ethyl Heptanoate and Ethyl Octanoate at

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