Measurement and Modeling of Volumetric Properties and Speeds of

Article pubs.acs.org/jced

Measurement and Modeling of Volumetric Properties and Speeds of Sound of Several Mixtures of Alcohol Liquids Containing Butanediol Mohammad Mehdi Alavianmehr,*,† Somayeh Shahsavar,† Hanieh Ghodrati,† and Nahid Hemmati† †

Department of Chemistry, Shiraz University of Technology, Shiraz, 71555-313, Iran S Supporting Information *

ABSTRACT: Densities and speeds of sound for the pure as well as binary mixtures of 1,2-butanediol and benzyl alcohol, 2-phenylethanol, 2-butanol, and 1,3-butanediol were measured over the 0 to 1 composition range and at six different temperatures between 298.150 K and 323.150 K with an interval of 5 K and at atmospheric pressure using a vibrating tube densimeter.The experimental values were used to calculate excess molar volume, VEm, excess isentropic compressibility, KES , excess thermal expansion coefficient, αEp , infinite partial molar E,∞ volumes, V̅ ∞ i and excess partial molar volumes at infinite dilution, V̅ i . The sign and magnitude of mixing quantities have been used to discuss the nature and strength of molecular interactions in binary mixtures. The calculated excess values and deviation quantities were fitted to the Redlich−Kister polynomials equation. Furthermore, it has been checked how the calculated values of densities and excess molar volumes using the Tao−Mason equation of state compare with the experimental ones.

1. INTRODUCTION Thermodynamic properties derived from the measurement of density and speed of sound are useful in many fields of research and give information in many chemical, industrial, and biological processes. The study of pure and binary systems of alcohols with a bifunctional hydroxyl group by the possibility of formation of both inter- and intramolecular hydrogen bonds is very interesting in both practical and theoretical perspectives. Type and extent of the hydrogen bonding in diols depend on the length and degree of branching of the carbon chain and number and positions of the hydroxyl groups. Treatment of this class of solution is a hard test for any theoretical model, and the behavior of their properties is not clear yet. The main difficulty is the overlapping of many effects taking place simultaneously during mixing.1−3 George and Sastry4 measured densities, dynamic viscosities, speed of sound, and relative permittivities for water and alkanediols (propane-1,2- and -1,3-diol and butane-1,2-, -1,3-, -1,4-, and -2,3-diol) at different temperatures. Yeh and Tu5 reported thermophysical properties of the binary mixtures 2-phenylethanol + 2-propanol, 2-phenylethanol + benzyl alcohol, 2-propanol + benzyl alcohol, at T = (298.150, 308.150, and 318.150) K. The present study reports densities (ρ) and speeds of sound (u) for pure and binary mixtures of 1,2-butanediol with benzyl alcohol, 2-phenylethanol, 2-butanol, and 1,3-butanediol at T = 298.150 K, 303.150 K, 308.150 K, 313.150 K, 318.150 K and 323.150 K in the 0 to 1 composition range and atmospheric pressure using a vibrating u-tube densimeter (DSA 5000). The excess molar volume, VEm, excess isentropic compressibility, KES , excess thermal expansion coefficient, αEp , infinite partial molar E,∞ volumes, V̅ ∞ of the i , and excess infinite partial molar volume, V̅ i © XXXX American Chemical Society

components were calculated at infinite dilution by the experimental values of ρ and u. The variation of these parameters with the composition and temperature of the binary mixtures have been discussed in terms of molecular interactions. Finally, the density and excess molar volumes of the studied alcohols (pure and binary mixtures) were evaluated theoretically by using the Tao−Mason (TM) equation of state (EOS) and compared with those obtained from our measurements.

2. EXPERIMENTAL SECTION Materials. The materials used in this study were supplied by Merck and were used without further purification. According to the supplier, the purity of 1,2-butanediol, 2-phenylethanol, benzyl alcohol, and 2-butanol in terms of mass fraction was ≥ 0.99 %, and the purity of 1,3-butanediol was ≥ 0.98 %. The purity of alcohols was checked by comparing the measured values of density and speed of sound with the literature values.3−26 The quality of the substances was further verified with a gas chromatograph (GC) equipped with a flame ionization detector (FID). The GC did not show significant impurities and therefore the resulting purity values for all the substances coincided with those indicated by the manufacturer. The specifications of chemicals used are listed in sample information Table 1. It should be mentioned that the chemicals were kept in dark glass flasks stored in a desiccator wrapped in aluminum foil and stored in a refrigerator. The literature values of the density and speed of sound for pure alcohols as well as those obtained from the Received: October 9, 2014 Accepted: June 10, 2015

A

DOI: 10.1021/je5009334 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Densities and speeds of sound for pure liquids and their binary mixtures were measured with a vibrating u-tube densimeter DSA 5000 (Anton Paar) and sound analyzer, with a certified precision of ± (1·10−6) g·cm−3 and ± 0.01 m·s−1, respectively. This analyzer automatically corrects the influence of viscosity on the measured density. The DSA 5000 simultaneously determines two physically independent properties within one sample in a density cell and a sound velocity cell combining the known oscillating u-tube method with a highly accurate measurement of sound speed. Both cells are temperature-controlled (with a gradation of ± 0.001 K) by a built in Peltier thermostat. These two physical properties and their derived values are used as input for various concentration calculation models that are integrated in DSA 5000M. More details concerning the apparatus and experimental procedure can be found elsewhere.27 The densimeter was checked by using dry air and deionized and degassed (as above) water once a day under atmospheric pressure. Precautions were taken in order to minimize evaporation losses during the storage and preparation of the solutions.

Table 1. Sample Information chemical name

source

initial mole fraction purity

phenylethanol 2-butanol 1,2-butanediol 1,3-butanediol benzyl alcohol

Merck Merck Merck Merck Merck

0.99 0.99 0.99 0.98 0.99

a

purification method none none none none none

final mole fraction analysis purity method GCa GC GC GC GC

0.99 0.99 0.99 0.98 0.99

Gas−liquid chromatography.

Table 2. Densities, ρ, and Speeds of Sound, u, for the Pure Components Compared with Literature Valuesa ρ/(g·cm−3) T/K

this work

298.150 303.150 308.150 313.150 318.150 323.150

1.016145 1.012384 1.008607 1.004812 1.009260 0.997155

298.150 303.150 308.150 313.150 318.150 323.150

0.803103 0.798891 0.794588 0.790191 0.785692 0.781090

298.150 303.150 308.150 313.150 318.150 323.150

0.998509 0.994759 0.990971 0.987152 0.983297 0.979406

298.150 303.150 308.150 313.150 318.150 323.150

1.001816 0.998418 0.994987 0.991528 0.988035 0.984506

298.150 303.150 308.150 313.150 318.150 323.150

1.041216 1.037352 1.033474 1.029583 1.025674 1.021746

u/(m·s−1) lit

2-Phenylethanol 1.016103 1.012343 1.008563 1.004763 1.000953 0.997113 2-Butanol 0.8027211 0.7989613 0.7941813 0.7901116 0.785406 0.7805514 1,2-Butanediol 0.9987015 0.99465925 0.9909024 0.9873926 0.9834020 0.97928425 1,3-Butanediol 1.0008922 0.9977823 0.9942022 0.9913822 0.9887122 Benzyl Alcohol 1.0412621 1.037510 1.0336412 1.029410 1.025725 1.02217

this work

literature

1526.09 1510.48 1494.66 1479.17 1463.25 1447.73

1526.203 1510.503 1494.753 1479.123 1463.593 1448.083

1212.67 1194.45 1176.20 1157.91 1139.47 1120.99

121218 1194.619 1175.817 1157.617 1139.217 1120.617

1452.61 1437.71 1423.60 1408.55 1394.02 1379.63

1452.621 1436.5225 1423.622] 1407.2425 1395.222

1527.84 1514.06 1500.18 1486.27 1472.34 1458.31

1524.1022 1509.7725 1495.6022 1482.2225 1469.0022

1525.17 1509.34 1493.62 1478.03 1462.63 1447.28

1528.49 1510.89 1496.38

3. RESULTS AND DISCUSSION The measured densities (ρ) and speeds of sound (u) for pure components of the current study and literatures have been summarized in Table 2. It is noticeable that our results agree well with those reported in literature. This agreement gives verification for experimental data that we obtained with our densimeter. After preparing solutions and injecting them into the densimeter, densities and speeds of sound for all binary mixtures of 1,2-butanediol with benzyl alcohol, 2-phenylethanol, 2-butanol, and 1,3-butanediol were measured over the aforementioned composition range at six different temperatures ranging between 298.150 K and 323.150 K. The numerical results are presented in Tables 3 and 4 and Supporting Information Tables S1 and S2. To assess the measured values of mixture densities, in Figure 1 the measured values of 1,2-butanediol + 2-butanol at 303.150 K have been compared with those reported in the literature.28 In general, our measured values of densities are in accord with those given in the literature.28 3.1. Excess Molar Volume. The excess molar volumes, VEm, were calculated from density data according to the following equation: 2

VmE/cm 3·mole−1 =

∑ xiMi(ρ−1 − ρi−1) i=1

(1)

Here, xi, Mi, and ρi are the mole fraction, molar mass, and density of the pure component i, respectively, and ρ is the density of the mixture. The results of the computations have been displayed in Tables 3 and 4 and Supporting Information Tables S1 and S2. Figures 2 to 5 illustrate the excess molar volume, VEm, plotted against mole fraction, x, of 1,2-butanediol for all studied binary mixtures at six different temperatures and at atmospheric pressure. The sign and magnitude of VEm depend on the structure of molecules. Further the estimated reproducibility of the calculated excess molar volumes was found to be about ± 10−3. The results presented in Tables 3 and 4 and Supporting Information Tables S1 and S2 and Figures 2 to 5 reveal that VEm is positive for the binary mixture of 1,2-butanediol with benzyl alcohol and is negative for the remaining three mixtures against the 0 to 1 composition range and at six studied temperatures. Close inspection of the VEm curves shows that for binary mixtures

The expanded uncertainty Uc(T) = ± 0.001, Uc(ρ) = ± 0.00003, Uc(u) = ± 0.06 (0.95 of confidence level).

a

present measurement are tabulated in Table 2. Table 2 demonstrates that the agreement is satisfactory. Methods. The binary solutions were prepared fresh by mass using an analytical balance (SartoriusTE124S). Solutions were stored in special airtight box. Prior to the measurements, two components of four mixtures were partially degassed (20 min) using an ultrasound (MISONIX Ultrasonic Liquid Processors) device. B



Article

Table 3. Densities, ρ, Speeds of Sound, u, Excess Molar Volumes, VEm, Excess Isentropic Compressibilities, KES , and Excess Thermal Expansion Coefficients αEP as Functions of Mole Fraction, x1 of 1,2-Butanediol for {1,2-Butanediol (1) + 2-Phenylethanol (2)} Mixtures at the Temperatures (298.15 to 323.15) K and Pressure (0.1) Mpaa ρ

TM EOS

u

VEm

KES

104·αEP

x1

g·cm−3

AAD %

m·s−1

cm3·mol−1

TPa−1

K−1

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1.016145 1.014518 1.012865 1.011271 1.009624 1.007904 1.006159 1.004331 1.002458 1.000432 0.998509

0.02887

0.000 −0.065 −0.117 −0.164 −0.195 −0.208 −0.206 −0.183 −0.143 −0.072 0.000

0.00 −3.35 −5.74 −7.59 −8.52 −8.78 −8.23 −7.04 −5.44 −2.69 0.00

0.000 0.050 0.067 0.106 0.145 0.156 0.158 0.145 0.097 0.118 0.000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1.012384 1.010725 1.009064 1.007449 1.005786 1.004065 1.002322 1.000504 0.998651 0.996641 0.994759

0.37060

0.000 −0.062 −0.114 −0.159 −0.188 −0.200 −0.198 −0.176 −0.138 −0.068 0.000

0.00 −3.21 −5.63 −7.72 −8.45 −8.78 −8.27 −7.11 −5.70 −2.81 0.00

0.000 0.180 0.065 0.112 0.140 0.143 0.144 0.134 0.094 0.086 0.000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1.008607 1.006917 1.005245 1.003606 1.001929 1.000204 0.998462 0.996652 0.994816 0.992825 0.990971

0.72489

0.000 −0.060 −0.111 −0.154 −0.182 −0.194 −0.192 −0.170 −0.133 −0.065 0.000

0.00 3.13 −5.50 −7.58 −8.26 −8.55 −7.99 −6.82 −5.43 −2.46 0.00

0.000 0.040 0.063 0.118 0.136 0.129 0.130 0.122 0.092 0.053 0.000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1.004812 1.003089 1.001390 0.999730 0.998053 0.996320 0.994579 0.992775 0.990951 0.988976 0.987152

1.08602

0.000 −0.063 −0.112 −0.153 −0.181 −0.192 −0.190 −0.169 −0.134 −0.067 0.000

0.00 −3.08 −5.49 −7.38 −8.32 −8.66 −8.18 −7.04 −5.72 −2.78 0.00

0.000 0.035 0.061 0.125 0.131 0.116 0.116 0.111 0.090 0.020 0.000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000

1.000926 0.999245 0.997515 0.995794 0.994121 0.992412 0.990674 0.988872

1.45249

0.000 −0.062 −0.109 −0.144 −0.173 −0.187 −0.185 −0.165

0.00 −3.19 −5.48 −7.13 −8.40 −8.57 −8.11 −6.99

0.000 0.085 0.107 0.172 0.161 0.129 0.124 0.115

T = 298.150 1526.09 1521.28 1515.59 1509.66 1502.88 1495.67 1487.76 1479.44 1471.08 1461.56 1452.61 T = 303.150 1510.48 1505.34 1499.66 1494.14 1487.06 1480.03 1472.28 1464.14 1456.21 1446.66 1438.19 T = 308.150 1494.66 1489.47 1483.82 1478.39 1471.40 1464.48 1456.86 1448.92 1441.23 1431.83 1423.60 T = 313.150 1479.17 1473.77 1468.12 1462.34 1455.79 1448.98 1441.55 1433.75 1426.25 1417.07 1408.55 T = 318.150 1463.25 1458.14 1452.44 1446.44 1440.50 1433.54 1426.28 1418.67 C

K

K

K

K

K



Article

Table 3. continued ρ x1

a

g·cm

0.8000 0.9000 1.0000

0.987058 0.985093 0.983297

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.997155 0.995386 0.993644 0.991945 0.990215 0.988495 0.986752 0.984949 0.983126 0.981261 0.979406

AAD %

1.82195

VEm

u

TM EOS −3

m·s

−1

cm ·mol 3

T = 318.150 K 1411.32 1402.30 1394.58 T = 323.150 K 1447.73 1442.82 1437.07 1431.31 1425.24 1418.63 1411.35 1403.79 1396.03 1388.18 1379.93

KES −1

TPa

−1

104·αEP K−1

−0.130 −0.064 0.000

−5.68 −2.74 0.00

0.098 −0.008 0.000

0.000 −0.063 −0.109 −0.147 −0.171 −0.183 −0.182 −0.161 −0.124 −0.070 0.000

0.00 −3.39 −5.66 −7.47 −8.60 −8.92 −8.35 −7.13 −5.37 −3.15 0.00

0.000 0.025 0.057 0.138 0.122 0.088 0.088 0.088 0.085 −0.047 0.000

The expanded uncertainty Uc(T) = ± 0.001, Uc(x) = ± 0.0001, Uc(ρ) = ± 0.00003, Uc(u) = ± 0.06 (0.95 of confidence level).

where κ*s,i is the isentropic compressibilities of the pure component i and φi is the volume fraction of component i:

of 1,2-butanediol with 2-phenylethanol and 2-butanol a minimum occurs at x1 = 0.5. As for 1,2-butanediol with 1,3-butanediol, the minimum occurs at x1 = 0.4 and x1 = 0.6 and a shift is in the plot at x1 = 0.5. In the case of the 1,2-butanediol and benzyl alcohol mixture the maximum occurs from x1 = 0.6 to x1 = 0.7. This behavior may be related to the difference in size and shape of the mixture partners. Moreover, Figure 6 shows the excess molar volume increases in the sequence as 1,2-butanediol + 2-butanol < 1,2-butanediol + 1-phenylethanol < 1,2-butanediol + 1,3-butanediol < 1,2butanediol + benzyl alcohol suggesting that the strength of interaction between unlike molecules in the 1,2-butanediol + 2-butanol system is greater than that of three other systems. Further inspection of the Tables 3 and S1 and Figures 2 and 4 indicates that as the temperature increases from 298.150 K to 323.150 K, the values of VEm for binary systems of 1,2-butanediol with 2-phenylethanol and 1,3-butanediol increase (become less negative). On the contrary, rising temperature from 298.150 K to 323.150 K for 1,2-butanediol with 2-butanol leads to an increase of VEm values as indicated in Figure 3. As for 1,2-butanediol and benzyl alcohol, VEm values become more positive when the temperature goes up as shown in Figure 5. 3.2. Speed of Sound and Excess Isentropic Compressibility. The isentropic (adiabatic) compressibility, κs, was calculated using the Newton−Laplace equation: κs/Pa−1 =

1 ρu 2

ϕi =

(5)

where V*i is the molar volume of the pure component i. The superscript (∗) stands for the pure state. Other properties in eq 4 are obtained from eqs 6 to 8: * αPid = φ1αP,*1 + φ2αP,2

(6)

id * + x 2C P,2 * C P,m = x1C P,1

(7)

Vmid = x1V1* + x 2V 2*

(8)

αP is the isobaric thermal expansion coefficient. The necessary isobaric heat capacities (Cp) for pure components 1,2-butandiol and 1,3-butandiol, as well as 2-butanol, benzyl alcohol, and 2-phenyl ethanol, were taken from refs 31, 32, 33, and 34, respectively. The results of excess isentropic compressibility, KES , for all binary systems are shownin Tables 3 and 4 and Supporting Information Tables S1 and S2. The changes of this property for all systems with mole fraction of 1,2-butanediol have been shown in Figures 7 to 10. It is evident from the above-mentioned tables and figures that KES values are negative for the whole mole fractions of four mixtures. According to Figures 7 to 10 and Tables 3 and 4 and Supporting Information Tables S1 and S2, the calculated KES values decrease with increasing temperature for 1,2-butanediol with 2-phenylethanol, 1,3-butanediol, and benzyl alcohol, whereas for the mixture of 1,2-butanediol with 2-butanol KES values become more negative. The negative values of KES indicate that the binary mixtures are less compressible than the pure components, that is, there is a greater resistance to compression (enhanced rigidity). Interpretation of the KES data is generally not simple because the KES values are affected by both the molecular packing and the patterns of molecular aggregation induced by the molecular interactions. It should be added that the estimated reproducibility of the calculated excess isentropic compressibility was found to be about ± 10−2.

(2)

By employing the experimental values of ρ and u, the excess isentropic compressibility, kEs , was obtained from the equation: κsE = κs − κsid

*

xiV i 2 ∑i = 1 xiV i*

(3)

where κs is obtained from eq 2 and κids can be calculated from the following expression:29,30 ⎡ φ V *(α * )2 id id 2 ⎤ φ V *(α * )2 * + φ κs,2 * + T ⎢ 1 1 P,1 + 2 2 P,2 − Vm (αP ) ⎥ κsid = φ1κs,1 2 id * * ⎢⎣ C P,1 C P,2 C P,m ⎥⎦

(4) D



Article

Table 4. Densities, ρ, Speeds of Sound, u, Excess Molar Volumes, VEm, Excess Isentropic Compressibilities KES , and Excess Thermal Expansion Coefficients αEP as Functions of Mole Fraction, x1 of 1,2-Butanediol for {1,2-Butanediol (1) + 2-Butanol (2)} Mixtures at the Temperatures (298.15 to 323.15) K and Ambient Pressureand Pressure (0.1) Mpa ρ

TM EOS

u

VEm

KES

104·αEP

x1

g·cm−3

AAD %

m·s−1

cm3·mol−1

TPa−1

K−1

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.803103 0.821980 0.841211 0.860512 0.879912 0.899493 0.919721 0.939207 0.959168 0.978763 0.998509

0.04760

0.000 −0.725 −1.291 −1.669 −1.875 −1.926 −1.876 −1.598 −1.216 −0.666 0.000

0.00 −7.30 −14.10 −17.74 −19.58 −20.49 −20.29 −17.21 −13.36 −8.14 0.00

0.000 0.248 0.247 0.196 0.145 0.114 0.057 0.044 0.025 0.009 0.000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.798891 0.817802 0.837068 0.856416 0.875848 0.895477 0.915764 0.935294 0.955308 0.974958 0.994759

0.42856

0.000 −0.735 −1.309 −1.693 −1.901 −1.953 −1.902 −1.619 −1.232 −0.675 0.000

0.00 −8.18 −15.36 −19.16 −21.27 −22.33 −22.44 −18.77 −14.58 −8.86 0.00

0.000 −0.665 −0.364 −0.352 −0.340 −0.300 −0.271 −0.213 −0.150 −0.078 0.000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.794588 0.813551 0.832862 0.852256 0.871737 0.891419 0.911761 0.931345 0.951414 0.971120 0.990971

0.85596

0.000 −0.748 −1.330 −1.720 −1.930 −1.983 −1.931 −1.644 −1.251 −0.686 0.000

0.00 −9.17 −17.06 −21.27 −23.59 −24.82 −24.79 −20.79 −16.07 −9.69 0.00

0.000 0.325 −0.348 −0.198 −0.222 −0.209 −0.193 −0.166 −0.122 −0.063 0.000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.790191 0.809205 0.828579 0.848033 0.867576 0.887316 0.907718 0.927356 0.947483 0.967241 0.987152

1.29417

0.000 −0.761 −1.353 −1.750 −1.964 −2.018 −1.964 −1.672 −1.272 −0.696 0.000

0.00 −9.95 −18.41 −23.61 −26.22 −27.61 −27.43 −22.99 −17.74 −10.62 0.00

0.000 0.315 −0.368 −0.050 −0.102 −0.117 −0.115 −0.118 −0.094 −0.048 0.000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000

0.785692 0.804796 0.824244 0.843762 0.863365 0.883169 0.903630 0.923329

1.74266

0.000 −0.779 −1.383 −1.786 −2.003 −2.057 −2.000 −1.702

0.00 −11.22 −20.57 −26.38 −29.30 −30.85 −30.45 −25.56

0.000 −0.598 0.194 −0.787 −0.587 −0.531 −0.443 −0.376

T = 298.150 1212.67 1230.96 1250.62 1270.88 1292.22 1315.45 1340.24 1365.68 1393.30 1423.14 1452.61 T = 303.150 1194.45 1213.13 1233.47 1253.83 1275.51 1299.11 1324.62 1350.05 1378.07 1408.33 1438.19 T = 308.150 1176.20 1195.33 1216.05 1236.79 1258.83 1282.90 1308.73 1334.54 1362.85 1393.41 1423.60 T = 313.150 1157.91 1177.29 1198.22 1219.72 1242.18 1266.71 1292.87 1319.01 1347.68 1378.54 1408.55 T = 318.150 1139.47 1159.33 1180.68 1202.63 1225.52 1250.53 1277.02 1303.55 E

K

K

K

K

K



Article

Table 4. continued ρ x1

g·cm

0.8000 0.9000 1.0000

0.943516 0.963332 0.983297

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.781090 0.800305 0.819834 0.839427 0.859100 0.878969 0.899488 0.919266 0.939516 0.959384 0.979406

AAD %

2.20261

VEm

u

TM EOS −3

m·s

−1

KES −1

cm ·mol 3

T = 318.150 K 1332.55 1363.64 1394.58 T = 323.150 K 1120.99 1141.45 1163.13 1185.55 1208.89 1234.34 1260.79 1288.38 1317.60 1348.70 1379.93

TPa

−1

104·αEP K−1

−1.295 −0.709 0.000

−19.66 −11.63 0.00

−0.270 −0.135 0.000

0.000 −0.799 −1.416 −1.827 −2.047 −2.100 −2.040 −1.737 −1.321 −0.723 0.000

0.00 −13.12 −23.53 −30.21 −33.58 −35.29 −34.19 −29.44 −22.53 −13.07 0.00

0.000 −0.613 −0.222 −0.828 −0.475 −0.449 −0.374 −0.337 −0.248 −0.123 0.000

The expanded uncertainty Uc(T) = ± 0.001, Uc(x) = ± 0.0001, Uc(ρ) = ± 0.00003, Uc(u) = ± 0.06 (0.95 of confidence level).

Figure 3. Plots of excess molar volumes, VmE, against mole fraction, x1, for {1,2-butanediol (1) + 2-butanol (2)} at T = 298.150 K, ◆; 303.150 K, ■; 308.150 K, ▲; 313.150 K, ●; 318.150 K, ◊; and 323.150 K, □.

Figure 1. Comparison of the measured values of densities of 1,2butanediol + 2-butanol at 303.150 K with those reported in ref 28. x is mole fraction of 1,2-butanediol.

Figure 2. Plot of excess molar volumes, VEm, against mole fraction, x1, for {1,2-butanediol (1) + 2-phenylethanol (2)} at T = 298.150 K, ◆; 303.150 K, ■; 308.150 K, ▲; 313.150 K, ●; 318.150 K, ◊; and 323.150 K, □.

Figure 4. Plots of excess molar volumes, VmE, against mole fraction, x1, for {1,2-butanediol (1) + 1,3-butanediol (2) at T = 298.150 K, ◆; 303.150 K, ■; 308.150 K, ▲; 313.150 K, ●; 318.150 K, ◊; and 323.150 K, □. F



Article

Figure 5. Plots of excess molar volumes, VmE, against mole fraction, x1, for {1,2-butanediol (1) + benzyl alcohol (2)} at T = 298.150 K, ◆; 303.150 K, ■; 308.150 K, ▲; 313.150 K, ●; 318.150 K, ◊; and 323.150 K, □.

Figure 8. Plots of excessis entropic compressibility, KES , against mole fraction x1 for {1,2-butanediol (1) + 2-butanol (2)} at the temperatures 298.150 K, ◆; 303.150 K, ■; 308.150 K, ▲; 313.150 K, ●; 318.150 K, ◊; and 323.150 K, □.

Figure 6. Excess molar volumes of mixtures 1,2-butanediol (1) + 2-phenylethanol (2), ◆; 1,2-butanediol (1) + 2-butanol (2), ■; 1,2butanediol (1) + 1,3-butanediol (2), ▲; 1,2-butanediol (1) + benzyl alcohol (2), ●, versus mole fraction of 1,2-butanediol at temperature 298.15 K.

Figure 9. Plots of excess isentropic compressibility, KES , against mole fraction x1 for {1,2-butanediol (1) + 1,3-butanediol (2)} at the temperatures 298.150 K, ◆; 303.150 K, ■; 308.150 K, ▲; 313.150 K, ●; 318.150 K, ◊; and 323.150 K, □.

Figure 7. Plots of excess isentropic compressibility, KES , against mole fraction x1 for {1,2-butanediol (1) + 2-phenylethanol (2)} at the temperatures 298.150 K, ◆; 303.150 K, ■; 308.150 K, ▲; 313.150 K, ●; 318.150 K, ◊; and 323.150 K, □.

Figure 10. Plots of excess isentropic compressibility, KES , against mole fraction x1 for {1,2-butanediol (1) + benzyl alcohol (2)} at the temperatures 298.150 K, ◆; 303.150 K, ■; 308.150 K, ▲; 313.150 K, ●; 318.150 K, ◊; and 323.150 K, □.

3.3. Excess Thermal Expansion Coefficient. The excess thermal expansion coefficient, αEP, was determined using the following equation:

Here αP and αP,i are thermal expansion coefficients of the binary mixture and pure component i, respectively; ϕi represents the volume fraction of component i obtained through the relation

2

αPE

= αP −

∑ φα i P, i i=1

φi =

(9) G

*

xiV i 2 ∑i = 1 xiV i*

(10) DOI: 10.1021/je5009334 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 5. Coefficients, Ai from eq 13 for VEm, KES , αEP and Standard Deviations σ for Binary Mixture of 1,2-Butanediol + Four Alcohols Mixtures at Temperatures from 298.150 K to 323.150 K T/K

A0

A1

A2

A3

1,2-Butanediol + 2-Phenylethanol (2) VEm/cm3·mol−1 298.15 −0.838 −0.146 0.089 0.108 303.15 −0.809 −0.137 0.092 0.113 308.15 −0.783 −0.128 0.089 0.111 313.15 −0.776 −0.127 0.051 0.123 318.15 −0.748 −0.160 0.046 0.205 323.15 −0.733 −0.102 0.000 0.069 KES /TPa−1 298.15 −35.070 2.230 1.390 2.050 303.15 −35.140 2.230 0.750 −1.530 308.15 −34.280 2.720 2.380 0.190 313.15 −34.580 0.900 1.080 −0.434 318.15 −34.270 0.220 0.670 1.790 323.15 −35.250 2.210 0.610 −1.20 104·αEP/K−1 298.15 0.599 0.088 0.125 0.474 303.15 0.515 0.396 0.701 −1.317 308.15 0.550 0.006 −0.080 0.220 313.15 0.527 −0.031 −0.180 0.081 318.15 0.585 −0.008 −0.046 −0.660 323.15 0.477 −0.117 −0.393 −0.179 1,2-Butanediol + 2-Butanol (2) VEm/cm3·mol−1 298.15 −7.780 −0.273 −0.046 −0.281 303.15 −7.880 −0.279 −0.049 −0.288 308.15 −8.010 −0.287 −0.058 −0.300 313.15 −8.140 −0.302 −0.050 −0.296 318.15 −8.300 −0.331 −0.071 −0.311 323.15 −8.470 −0.365 −0.102 −0.332 KES /TPa−1 298.15 −82.450 −3.060 −7.030 7.860 303.15 −89.960 −0.451 −7.970 1.200 308.15 −99.800 −64.800 −8.420 −0.580 313.15 −110.920 −1.150 −4.920 2.810 318.15 −123.710 −1.940 −14.710 1.310 323.15 −140.960 −2.560 −7.560 −0.840 104·αEP/K−1 298.15 0.378 0.703 1.430 1.400 303.15 −1.030 0.323 −3.070 −5.930 308.15 −1.027 −1.576 1.310 4.900 313.15 −0.576 −0.996 0.535 3.405 318.15 −2.151 −1.018 −0.999 −1.215 323.15 −1.841 −1.222 −1.864 −1.323

σ

T/K

1 ⎛ ∂ρ ⎞ ⎜ ⎟ ρ ⎝ ∂T ⎠ P

0.002 0.003 0.003 0.003 0.002 0.003 0.101 0.168 0.204 0.160 0.175 0.104 0.019 0.039 0.007 0.015 0.021 0.034

0.013 0.014 0.014 0.014 0.014 0.014 0.375 0.465 0.482 0.458 0.461 0.295 0.012 0.091 0.146 0.166 0.173 0.179

(11)

A3

σ

0.0031 0.0030 0.0029 0.0030 0.0032 0.0031 0.250 0.232 0.235 0.238 0.257 0.312 0.397 0.360 0.355 0.346 0.358 0.333

0.0002 0.0001 0.0002 0.0004 0.0005 0.0002 0.043 0.098 0.092 0.091 0.055 0.167 0.0054 0.0035 0.0018 0.0011 0.0026 0.0045

3

2

Y E = x1x 2 ∑ Ai (1 − 2x1)i

i

∑ ai(T /K) i=0

A2

Tables 3 and 4 and Supporting Information Tables S1 and S2. These data show that for the the binary mixture of 1,2-butanediol with 2-butanol αEP values are negative at high temperatures and positive at 298.150 K. As for other three mixtures αEP values are positive indicating weak interactions between unlike molecules. In this studyVEm, KES , and αEP of all binary mixtures were fitted to a isothermal Redlich−Kister-type polynomial equation:35

The measured densities for all components were fitted with temperature by the following simple polynomial equation: ρ=

A1

1,2-Butanediol +1,3-Butanediol VEm/cm3·mol−1 298.15 −0.406 −0.018 0.118 0.033 303.15 −0.401 −0.012 0.102 0.055 308.15 −0.380 −0.019 0.125 0.021 313.15 −0.365 −0.019 0.127 0.017 318.15 −0.351 −0.018 0.136 0.005 323.15 −0.341 −0.006 0.218 −0.125 KES /TPa−1 298.15 −28.220 2.250 6.140 0.374 303.15 −27.880 2.300 6.770 −1.040 308.15 −27.980 2.210 7.710 −0.570 313.15 −27.820 2.040 7.900 −0.280 318.15 −27.800 2.310 9.810 −0.315 323.15 −28.250 −1.000 14.640 15.620 104·αEP/K−1 298.15 37.500 −0.070 −9.890 −0.091 303.15 34.300 −0.062 −13.100 1.300 308.15 32.900 −0.361 −14.300 0.060 313.15 31.200 −0.045 −14.200 0.206 318.15 29.600 −0.420 −16.60 −0.990 323.15 29.300 −0.794 −11.000 −6.850 1,2-Butanediol + Benzyl Alcohol VEm/cm3·mol−1 298.15 0.043 −0.046 0.090 −0.327 303.15 0.078 −0.046 0.100 −0.042 308.15 0.117 −0.058 0.095 −0.022 313.15 0.150 −0.058 0.103 −0.016 318.15 0.188 −0.067 0.099 0.001 323.15 0.221 −0.066 0.100 0.008 KES /TPa−1 298.15 −26.850 3.460 1.290 −0.731 303.15 −28.900 2.712 5.014 2.328 308.15 −26.530 2.629 3.918 −0.294 313.15 −25.940 2.855 4.283 −0.785 318.15 −25.050 2.346 2.575 −1.159 323.15 −29.040 0.544 −6.442 −13.892 104·αEP/K−1 298.15 0.760 −0.073 0.111 0.203 303.15 0.750 −0.062 0.079 0.215 308.15 0.730 −0.050 0.046 0.228 313.15 0.710 −0.038 0.013 0.241 318.15 0.700 −0.027 −0.020 0.254 323.15 0.680 −0.014 −0.054 0.267

Also, here Vi* is the molar volume of the pure component i. The thermal expansion coefficient, αP, was calculated from αP /K−1 = −

A0

i=0

(12)

(13)

where YE denotes VEm, KES and αEP. Ai is the polynomial coefficient, and x is the mole fraction. The coefficient Ai in eq 13 was allowed to vary using a nonlinear least-squares method, and the values are

where ai refers to the fitting coefficients. The numerical values of αEP were calculated by eqs 9 to 12 for the selected binary mixtures.The results are listed in H



Article

∞ E,∞ E,∞ Table 6. Values of V̅ 1*, V̅ 2*, V̅ ∞ for 1,2-Butanediol with 2-Phenylethanol, 2-Butanol, 1,3-Butanediol, and Benzyl 1 , V̅ 2 , V̅ 1 , and V̅ 2 Alcohol at Temperatures from 298.150 K to 323.150 K

V̅ 1*

V̅ ∞ 1

V̅ 2*

V̅ ∞ 2

V̅ E,∞ 1

V̅ E,∞ 2

−0.887 −0.741 −0.711 −0.729 −0.657 −0.766

−0.611 −0.611 −0.611 −0.721 −0.747 −0.700

−8.380 −8.496 −8.655 −8.788 −9.013 −9.269

−7.272 −7.272 −7.481 −7.592 −7.729 −12.146

−0.273 −0.256 −0.252 −0.241 −0.228 −0.254

−0.303 −0.342 −0.257 −0.235 −0.201 −0.190

0.045 0.090 0.131 0.179 0.221 0.262

0.221 0.266 0.292 0.327 0.352 0.378

−1

(cm · mol ) 3

T/K 298.150 303.150 308.150 313.150 318.150 323.150

90.256 90.596 90.942 91.294 91.652 92.016

298.150 303.150 308.150 313.150 318.150 323.150

90.256 90.596 90.942 91.294 91.652 92.016

298.150 303.150 308.150 313.150 318.150 323.150

90.256 90.596 90.942 91.294 91.652 92.016

298.150 303.150 308.150 313.150 318.150 323.150

90.256 90.596 90.942 91.294 91.652 92.016

1,2-Butanediol (1) + 2-Phenylethanol (2) 120.229 89.368 119.617 120.676 89.855 120.064 121.127 90.231 120.516 121.585 90.565 120.864 121.049 90.995 120.302 122.519 91.250 121.819 1,2-Butanediol (1) + 2-Butanol (2) 92.292 81.875 85.020 92.779 82.100 85.506 93.281 82.287 85.800 93.800 82.506 86.208 94.337 82.639 86.608 94.893 82.747 87.018 1,2-Butanediol (1) + 1,3-Butanediol (2) 89.958 89.983 89.654 90.264 90.339 89.922 90.575 90.690 90.318 90.891 91.053 90.656 91.212 91.424 91.012 91.539 91.762 91.548 1,2-Butanediol (1) + Benzyl Alcohol (2) 103.859 90.477 103.904 104.246 90.862 104.336 104.637 91.234 104.769 105.033 91.622 105.212 105.433 92.004 105.654 105.838 92.395 106.101

listed in Table 5. To ascertain the validity of the polynomial coefficients, the standard deviations σ(YE) are also calculated from the following expression and are included in Table 5. ⎡ n (Y − Y (calc))2 ⎤1/2 i ⎥ σ (Y ) = ⎢∑ i ⎢⎣ i = 1 ⎥⎦ n−p

Partial molar volumes at infinite dilution were calculated by using eqs 16 and 17. Excess partial molar volumes, V̅ E,∞ and V̅ E,∞ 1 1 of each component at infinite dilution were calculated using eqs 18 and 19.

E

(14)

Here n is the number of experimental data and p is the number of parameters. 3.4. Partial Molar Volume. The partial molar volume V̅ i of each component was calculated by using the following relations: ⎛ ∂V E ⎞ Vi̅ = VmE + V i* + (1 − xi)⎜ m ⎟ ⎝ ∂xi ⎠T , P

(15)

3

V1̅ = V1* + x 22 ∑ Ai (1 − 2x1)i − 2x1x 22 ∑ Ai (i)(1 − 2x1)i − 1 i=0

i=0

(16) 3

3

V2̅ = V 2* + x12 ∑ Ai (1 − 2x1)i − 2x12x 2 ∑ Ai (i)(1 − 2x1)i − 1 i=0

(18)

V2̅ E , ∞ = V2̅ ∞ − V 2*

(19)

∞ E,∞ E,∞ The values of V1*, V2*, V̅ ∞ for all binary 1 , V̅ 2 , V̅ 1 , and V̅ 2 systems at different temperatures are listed in Table 6. As seen in Table 6 the partial molar volumes of 1,2-butanediol at infinite dilution V̅ ∞ 1 , in 2-phenylethanol, 2-butanol, and 1,3butanediol, and the partial molar volumes of 2-phenylethanol, 2-butanol, and 1,3-butanediol, at infinite dilution V̅ ∞ 2 in 1,2butanediol are smaller than the corresponding molar volumes V1* and V2* of 1,2-butanediol and the four mentioned alcohols, respectively. This observation is consistent with the idea that the molar volume of pure components is a result of the sum of the actual molar volume plus the free or empty volume that arises from the intermolecular self-association of pure molecules. Thus, negative V̅ E,∞ and V̅ E,∞ values of 1,2-butanediol + alkanol and 1 2 alkanediol suggest the contraction in volume of the mixtures on mixing, which may be attributed to the presence of significant interactions between 1,2-butanediol + alkanol and alkanediol and 2-phenylethanol molecules. Conversely, as can be noticed from Table 6 that the partial molar volume of 1,2-butanediol at infinite dilution V̅ ∞ 1 in benzyl alcohol is more than the corresponding molar volumes V̅ 2* resulting in a positive value of V̅ E,∞ 1 . Since these values are indicative of the interactions between solute and

Here V̅ *i is the molar volume of pure component i. By differentiating eq 13 and employing eq 15, V̅ 1 and V̅ 2 were computed according to the following equations: 3

V1̅ E , ∞ = V1̅ ∞ − V1*

i=0

(17) I



Article

For a pure system, we have I1 = (α − B) ξ(T) Φ(bp). Tao and Mason proposed Φ(bp) and ξ(T) as follows:

solvent interactions, it reveals the fact that at infinite dilution of benzyl alcohol the interactions between benzyl alcohol and 1,2-butanediol are weak leading to positive value of V̅ E,∞ which 1 supports our earlier results of excess molar volumes, VEm. 3.5. Modeling with Equation of State. The volumetric properties of the present mixtures are modeled with the Tao− Mason (TM) EOS.36 The TM EOS reads as

ρ ∑k xkbk

Φmix ≈

1 + 1.8ρ 4 (∑k xkbk4)

ξmix ≈ 0.143[exp(k mixTcmix /T ) − A 2mix ]

α ̅ (T )ρ P = 1 + (B(T ) − α̅(T ))ρ + 1 − ρb(T )λ ρkT

k mix =

(e kTc / T − A 2 ) + A1(α̅(T ) − B(T ))b(T )ρ 1 + 1.8(ρb(T ))4

∑ xk k k

kk = 1.093 + 0.26[(ω + 0.002)1/2 + 4.50(ω + 0.002)] (30)

where P,B(T), b(T) and ρ, are the pressure, second virial coefficient, effective van der Waals covolume and number density, respectively.kT is the molecular thermal energy, Tc is the critical temperature and α (T) is the scaling factor. λ is an adjustable parameter. The parameter lambda that appears in eq 20 was found empirically from the experimental PVT data of pure alcohols. We were able to obtain λ using TM equation of state along with PVT data. This procedure is an iterative method that converges very rapidly. This method for determining λ makes the whole procedure self-correcting. Once the value of the constant λ is determined, the entire volumetric behavior of the given fluid is established. The parameter λ for five pure alcohols 1,2-butanediol, 1,3-butanediol, 2-phenylethanol,2butanol and benzyl alcohol are found to be 0.716, 0.709, 0.737, 0.823 and 0.7277, respectively. Other parameters A1 and A2 in eq 20 are defined as A1 = 0.143

A 2mix = 1.64 + 2.65[exp(k mix − 1.093) − 1]

where Tcmix is the traditional pseudocritical temperature. Besides, we used three correlations for B, α, and b proposed by Sheikh et al., which have already been obtained based on speed of sound data.39 These correlations are ⎛ ΔH vap ⎞2 ⎛ ΔH vap ⎞4 Bρnb = 0.1 − 0.054⎜ ⎟ − 0.00028⎜ ⎟ ⎝ RT ⎠ ⎝ RT ⎠

(33)

⎧ ⎡ ⎛ ⎤⎫ ⎪ RT ⎞⎟⎥⎪ αρnb = a1⎨exp⎢ −d1⎜⎜ ⎟ ⎬ ⎪ ⎪ ⎩ ⎢⎣ ⎝ ΔH vap ⎠⎥⎦⎭ ⎧ ⎡ ⎛ ΔH vap ⎞1/4 ⎤⎫ ⎪ ⎪ + a 2⎨1 − exp⎢ −d 2⎜ ⎟ ⎥⎬ ⎢ ⎪ ⎝ RT ⎠ ⎥⎦⎪ ⎣ ⎩ ⎭

Here

(34)

⎡ ⎡ ⎛ ⎛ RT ⎞⎤ ⎞⎤ ⎟⎟⎥ exp⎢ − d1⎜⎜ RT ⎟⎟⎥ bρnb = a1⎢1 − d1⎜⎜ ⎢⎣ ⎢⎣ ⎝ ΔΗ vap ⎠⎥⎦ ⎝ ΔΗ vap ⎠⎥⎦

κ = 1.093 + 0.26[(ω + 0.002)1/2 + 4.50(ω + 0.002)] (23)

⎧ ⎡ ⎛ ΔΗ vap ⎞1/4 ⎤ ⎪ + a 2⎨1 − ⎢1 + 0.25d 2⎜ ⎟ ⎥ ⎢ ⎪ RT ⎝ ⎠ ⎥⎦ ⎣ ⎩

In eq 23,ω is the Pitzer acentric factor. The mixture version of the TM EOS which was already developed by Yousefi et al.37,38 is given by P = 1 + ρ ∑ xixj(Bij − αij) + ρ ∑ xixjαijGij + ρ ∑ xixj(I )ij ρkT ij ij ij

⎡ ⎛ ΔΗ vap ⎞1/4 ⎤⎫ ⎪ ⎢ exp −d 2⎜ ⎟ ⎥⎬ ⎢ ⎥ ⎝ RT ⎠ ⎦⎪ ⎣ ⎭

(24)

where ρ is the total molecular number density, P is the pressure, xi and xj are mole fractions,and the double summation runs over all components. The interaction parameters Bij, αij and bij for i ≠ j correspond to a hypothetical single substance whose molecules interact according to a pairwise ij potential. For i = j, the parameters are those for the pure substance i. The problem is now how to estimate the parameters Gij and (I)ij appeared in eq 24. The Gij, the pair distribution function at contact for real mixtures, is defined by

(

(31)

(32)

k

(22)

⎛ bibj ⎞1/3 ρ ∑k xkbk2/3 λk − 1 1 4 + ⎜⎜ ⎟⎟ Gij = ∑ 1−η b (1 )(1 x b − η − ρ λ) ⎝ ij ⎠ k k k k

∑ xkTck

Tcmix =

(21)

− 1]

(29)

k

(20)

A 2 = 1.64 + 2.65[e

(28)

where

2

(κ− 1.093)

(27)

(35)

Where ρnb is the normal boiling density. The coefficients in the above equations are a1 = −0.1162, a2 = 2.22572, d1 = 6.58566, and d2 = 0.71472. After that, we performed a comprehensive comparison of the calculated values of the densities (ρ) and excess molar volumes (VEm) for the studied binary mixtures as well as pure ones at temperatures 298.150 K, 303.150 K, 308.150 K, 313.150 K, 318.150 K, and 323.150 K and atmospheric pressure with our experimental results.The absolute average percentage deviation (AAD) was calculated to evaluate the fitting goodness as shown in eq 36.

)

(25)

N

Where η is the packing fraction for the mixture, given by ρ η = ∑ xkbk 4 k (26)

AAD =

∑i = 1 |(ρi,exp − ρi ,calc )/ρi,exp | × 100 N

(36)

where N stands for the number of data points. AAD of the calculated densities from the measured values have been listed in J



Article

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Figure 11. Excess molar volume of 1,2-butanediol and 2-phenylethanol in terms of mole fraction at temperatures 298.150 K, ◆; 308.150K, ■; and 313.150 K, ●. The solid line and markers represent the calculated and experimental values, respectively.

Tables 3 and 4 and Supporting Information Tables S1 and S2. The maximum observed deviations of the calculated density is 2.20261. Figure 11 compares the experimental and calculated excess molar volumes for the typical mixture of 1,2-butanediol + 2-phenylethanol. Therefore, it is noticeable that the agreement between TM model and experimental data are quite well.

4. CONCLUSION This article reported the densities and speeds of sound of four binary systems of 1,2-butanediol with benzyl alcohol, 1,3-butanediol, 2-phenylethanol, and 2-butanol, at six different temperatures (298.150 K to 323.150 K) at atmospheric pressures over the entire range of mole fractions using a vibrating tube densimeter. As it has been outlined earlier, all systems under study showed nonideal behavior. This nonideality can be explained by two factors: intermolecular forces in the mixture and enhanced rigidity. The TM EOS demonstrates good performance in predicting the densities and excess molar volumes of mixtures of studied alcohols.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental results. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ je5009334.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax/Tel.: +98-713-735-4520. Funding

The authors are grateful to Shiraz University of Technology for supporting this project. Notes

The authors declare no competing financial interest.

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REFERENCES

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Measurement and Modeling of Volumetric Properties and Speeds of

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