1-s2.0-S0167732215001798-main

Journal of Molecular Liquids 207 (2015) 145–151
Contents lists available at ScienceDirect
Journal of Molecular Liquids
journal homepage: www.elsevier.com/locate/molliq
Correlations between density, viscosity, surface tension and ultrasonic
velocity of different mono- and di-saccharides
Mircea Oroian ⁎, Sorina Ropciuc, Sonia Amariei, Gheorghe Gutt
Faculty of Food Engineering, Stefan cel Mare University of Suceava, Romania
a r t i c l e
i n f o
Article history:
Received 26 November 2014
Received in revised form 25 February 2015
Accepted 17 March 2015
Available online 20 March 2015
Keywords:
Correlation
Model
Deviation modulus
Master curve
a b s t r a c t
The aim of this study is to correlate the density, viscosity, surface tension and ultrasonic velocity of different concentrations (0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09 and 0.10 mol/L) of mono- (fructose, glucose and galactose) and di- (sucrose, maltose and lactose) saccharide solutions at six different temperatures (298.15, 308.15,
318.15, 328.15, 338.15 and 348.15 K). The correlations between surface tension and viscosity have been investigated using four different models. The suitability of the models was checked using the deviation modulus. The
correlation of ultrasonic velocity, density and surface tension leads to a master curve with a high regression
coefficient (R2 = 0.997).
© 2015 Elsevier B.V. All rights reserved.
1. Introduction
Viscosity and surface tension are two properties of fluids that are different in nature but whose values need to be known for a wide variety of
industrial and physicochemical process (catalysis, adsorption, distillation, extraction, etc.). The surface tension, σ, is a physical property of
matter related to the intermolecular interaction potential energy and
the liquid interfacial microstructure [1–5]. The surface tension can be
measured with high accuracy at low and moderate temperatures and
pressures, while at high temperatures and pressures, the values are determined using computer simulations [6,7]. The fluid viscosity, η, is
measured with high precision, and the resulting data and its temperature dependence are used as essential properties for the accurate determination of molecular information such as the pair interaction potential
function [8].
Density, as the other parameters, is the basic physical parameter frequently used in chemical engineering, and also the indispensable thermodynamic data for chemical researches and computations involving
fluid flow, heat transfer and mass transfer [9].
Pelofsky proposed in 1966 [10] an empirical relationship between
natural logarithm of surface tension and the inverse of viscosity (usually
termed the fluidity). Pelofsky's empirical expression (which we shall
denote here as the P correlation) can be applied to both the organic
and inorganic phases of pure and mixed components [10]. Two adjustable coefficients are needed, whose values may depend in the temperature range being considered. The P correlation was later modified by
Schonhorn [11] who introduced a correction into the second term of
⁎ Corresponding author.
E-mail address: m.oroian@fia.usv.ro (M. Oroian).
http://dx.doi.org/10.1016/j.molliq.2015.03.033
0167-7322/© 2015 Elsevier B.V. All rights reserved.
the right-hand side of the expression to fulfill the requirement that, at
the critical point, the surface tension goes to zero while the viscosity
tends to a small constant value. This modification introduces new coefficients, and has not subsequently been used [12].
Ghatee et al. [13] applied the Pelofsky model (modified Pelofsky
model) to correlate the surface tension and viscosity of some ionic liquids. It was observed that it was necessary to modify it slightly by introducing an exponent into the viscosity term. They initially treated this
exponent as an adjustable coefficient but then they found that its
value could be fixed at 0.3 without any significant loss of accuracy for
the fluids considered. The same observations were observed by Oroian
[14] in the case of honeys.
The two model accuracy (Pelofsky and Ghatee), according to Zheng
et al. [12], are very limited in terms of performance and accuracy for the
calculation of surface tension for selected fluids in a different temperature range. The use of equations with greater number of coefficients
can improve the performance of the model for the correlation of surface
tension and viscosity [12].
In the case of the physical properties of mono- and di-saccharide solutions, some studies related to hydration behavior at different temperatures [15], the measuring of density, viscosity and ultrasonic velocity at
different temperatures [16], and heat capacity in solid state [17] have
been reported. To the authors' knowledge no other studies related to
the correlation of different physical properties of mono- and di-saccharide solution have been reported.
The aim of this study is to investigate the correlation between surface tension and viscosity of different concentrations (0.01, 0.02, 0.03,
0.04, 0.05, 0.06, 0.07, 0.08, 0.09 and 0.10 m) of mono- (fructose, glucose
and galactose) and di- (sucrose, maltose and lactose) saccharide solutions at six different temperatures (298.15, 308.15, 318.15, 328.15,
146
M. Oroian et al. / Journal of Molecular Liquids 207 (2015) 145–151
338.15 and 348.15 K) using four models, and the correlation between
surface tension, density and ultrasonic velocity in the same conditions.
where n is the total number of data. Subscripts exp. and cal. denote experimental and calculated values, respectively. X represents viscosity, η,
or surface tension, σ.
2. Materials and methods
3. Results and discussions
2.1. Materials
For this study, six different mono- and di-saccharides: fructose,
glucose, galactose, maltose, lactose and sucrose at different molar
concentrations (0.01 to 0.10 mol/L) were analyzed. All the mono- and
di-saccharides were purchased from Sigma Aldrich (Germany). The solutions were prepared using double deionized water. Double deionized
water (18 MΩ cm resistivity) produced by a water purification system
(Thermofisher, Germany) was used in all solutions.
2.2. Density measurements
Density (ρ) of the samples was measured using a pycnometer with
an accuracy 10−4 kg/m3. The calibration of a pycnometer was made
with ultrapure water. Temperature was kept constant within ±0.01 K
using a PID controller and circulating water using a thermostatic-fluid
bath. The density of the samples was measured at 298.15, 308.15,
318.15, 328.15, 338.15 and 348.15 K. The values of parameters were
expressed as the mean ± standard deviation to a confidence interval
for mean of 95%.
The ultrasonic velocity measurement was carried out using a flow
detector USM 35X (GE Measurement and Control, USA) with a dualelement (TR) probe working at 4 MHz. The measurements were carried
out at 298.15, 308.15, 318.15, 328.15, 338.15 and 348.15 K. The values of
parameters were expressed as the mean ± standard deviation to a
confidence interval for mean of 95 %.
2.4. Viscosity measurement
Viscosity measurements were carried out on the samples at different
temperatures (298.15, 308.15, 318.15, 328.15, 338.15 and 348.15 K),
with an Ubbelohde viscometer and a temperature controlled water
bath (uncertainty 0.26%). The sample was allowed to reach the desired
temperature for 20 min. Each measurement was taken in duplicate. The
values of parameters were expressed as the mean ± standard deviation
to a confidence interval for mean of 95%.
2.5. Surface tension determination
The surface tension was computed using Auerbach's equation: [18]
u¼
σ
6:33 10−10 ρ
2=3
ð1Þ
where u is the ultrasonic velocity (m/s), σ is the surface tension in N/m
and ρ is the density in kg/m3. Therefore, for the calculation of the surface
tension, first we measured the ultrasonic velocity and density and later
on by using the Auerbach equation we were able to compute the surface
tension.
2.6. Prediction accuracy
The mean relative deviation modulus, D, was used to verify the suitability of model for experimental data:
100 Xn X exp;i −Xcal;i D% ¼
i¼1
n
X exp;i
3.1. Influence of temperature and concentration on the viscosity
The saccharide solution viscosity has been measured using the
Ubbelohde viscometer at different temperatures (298.15, 308.15,
318.15, 328.15, 338.15 and 348.15 K). It can be observed in Fig. 1 that
the solution viscosity is influenced positively by the concentration and
negatively by the temperature.
Correlations were made to allow the prediction of viscosity of the
honey samples. The correlations of viscosity were as a function of
temperature or honey concentration using polynomial fitting by
means of the experimental data. The following expressions were used
for the regression equations of the experimental data:
η¼aþbT þ f T
2.3. Ultrasonic velocity measurement
The physical parameters (ultrasonic velocity, density, viscosity and
surface tension) have been analyzed at different temperatures
(298.15, 308.15, 318.15, 328.15, 338.15 and 348.15 K, with a temperature accuracy of 0.01 K). The physical parameter values in function of
temperatures and concentrations are presented in Tables 1–4.
ð2Þ
2
η ¼ d þ e cM þ f cM
ð3Þ
2
ð4Þ
where η is the viscosity in N·s·m−2, T is the temperature in K, cM is the
molar concentration (mol/L) and a–f are the fitting parameters. The regression coefficients for both models ranged between 0.961 and 0.997.
The values of a ranged between 1.718 · 10−3 and 1.953 · 10−3, b
ranged between − 0.04289 · 10− 3, and c ranged between
0.00026 · 10−3 and 0.00029 · 10−3, respectively. The a and c are positively influenced by the concentration (r = 0.835*** and r = 0.781, respectively) and b is not influenced significantly by the temperature
(r = −0.044 ns).
The parameters d of Eq. (4) ranged between 0.245 · 10− 3 and
0.944 · 10−3, e ranged between 0.180 · 10−3 and 1.038 · 10−3 and f
ranged between 0.290 · 10− 3 and 1.117 · 10− 3, respectively. The d
and e are negatively influenced by the temperature (r = − 0.957***
and r = − 0.877, respectively) and f is positively influenced by the
temperature (r = 0.904***). The mean deviation modulus between
the prediction and experimental values and average ranged between
0.172% and 0.564%.
3.2. Influence of temperature and concentration on the surface tension
The solution surface tension (computed using the Auerbach
relation) ranged between 0.030 and 0.038 N/m. A linear evolution of
the surface tension with temperature (Fig. 2) can be observed. The evolution of the surface tension with temperature was subjected to linear
regression to see its prediction using the following equation:
σ ¼gþhT þiT
2
ð5Þ
where σ — surface tension in N/m, g, h and i are constants, and T —
temperature (K).
In Fig. 2, the evolution of surface tension and solution concentration
for glucose is presented. The g values ranged between 0.040 and 0.041, h
ranged between − 0.00015 and − 0.00016, while i ranged between
1.96 · 10−7 and 2.00 · 10−7. The g and i values are influenced positively
by the concentration (r = 0.977*** and r = 0.926*** respectively), and h
is influenced negatively by the concentration (r = −0.945***).
M. Oroian et al. / Journal of Molecular Liquids 207 (2015) 145–151
Table 1
Ultrasonic velocity (u, m/s) evolution with temperature.
C (mol/L)
Table 2
Density (ρ, kg/m3) evolution with temperature.
u (m/s)
Glucose
C (mol/L)
Fructose
Galactose
Sucrose
Maltose
Lactose
ρ (kg/m3)
Glucose
Fructose
Galactose
Sucrose
Maltose
Lactose
1501.8
1503.4
1505.2
1507.0
1508.8
1510.5
1512.3
1514.0
1515.5
1517.1
298.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
998.20
998.80
999.60
1004.40
1001.00
1001.60
1002.00
1002.70
1003.30
1003.90
1000.40
1001.00
1001.80
1002.60
1003.40
1004.10
1004.70
1005.20
1005.90
1006.70
1001.00
1001.60
1002.30
1002.90
1003.50
1004.20
1004.80
1005.60
1006.20
1006.90
1021.02
1021.63
1022.35
1022.96
1023.57
1024.28
1024.90
1025.71
1026.32
1027.04
1002.29
1002.89
1003.59
1004.19
1004.80
1005.50
1006.10
1006.90
1007.50
1008.20
1003.19
1003.79
1004.49
1005.09
1005.69
1006.39
1007.00
1007.80
1008.40
1009.10
1468.2
1469.8
1471.5
1473.3
1475.0
1476.7
1478.5
1480.1
1481.6
1483.2
1470.9
1472.5
1474.3
1476.0
1477.8
1479.4
1481.2
1482.9
1484.3
1485.9
308.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
990.21
990.81
991.60
996.36
992.99
993.59
993.98
994.68
995.27
995.87
992.40
992.99
993.79
994.58
995.37
996.07
996.66
997.16
997.85
998.65
992.99
993.59
994.28
994.88
995.47
996.17
996.76
997.56
998.15
998.84
1012.85
1013.46
1014.17
1014.77
1015.38
1016.09
1016.70
1017.51
1018.11
1018.82
994.27
994.87
995.57
996.16
996.76
997.45
998.05
998.84
999.44
1000.13
995.16
995.76
996.45
997.05
997.65
998.34
998.94
999.73
1000.33
1001.03
1445.0
1446.5
1448.2
1450.0
1451.7
1453.3
1455.1
1456.7
1458.1
1459.7
1438.0
1439.5
1441.3
1443.0
1444.7
1446.3
1448.1
1449.7
1451.1
1452.6
1440.7
1442.2
1443.9
1445.7
1447.4
1449.0
1450.7
1452.4
1453.8
1455.3
318.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
983.28
983.87
984.66
989.39
986.04
986.63
987.03
987.72
988.31
988.90
985.45
986.04
986.83
987.62
988.41
989.09
989.69
990.18
990.87
991.66
986.04
986.63
987.32
987.91
988.50
989.19
989.78
990.57
991.16
991.85
1005.76
1006.36
1007.07
1007.67
1008.27
1008.98
1009.58
1010.38
1010.99
1011.69
987.31
987.91
988.60
989.19
989.78
990.47
991.06
991.85
992.44
993.13
988.20
988.79
989.48
990.07
990.66
991.35
991.95
992.74
993.33
994.02
1412.4
1413.9
1415.6
1417.3
1419.0
1420.6
1422.3
1423.9
1425.3
1426.8
1415.3
1416.8
1418.5
1420.2
1421.8
1423.5
1425.1
1426.7
1428.2
1429.7
1408.4
1409.9
1411.6
1413.3
1415.0
1416.6
1418.3
1419.9
1421.3
1422.8
1411.0
1412.5
1414.2
1415.9
1417.6
1419.2
1420.9
1422.5
1423.9
1425.4
328.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
975.42
976.00
976.78
981.48
978.15
978.74
979.13
979.81
980.40
980.99
977.57
978.15
978.93
979.72
980.50
981.18
981.77
982.26
982.94
983.72
978.15
978.74
979.42
980.01
980.60
981.28
981.87
982.65
983.23
983.92
997.72
998.31
999.01
999.61
1000.21
1000.91
1001.50
1002.30
1002.90
1003.60
979.42
980.00
980.69
981.27
981.86
982.55
983.13
983.92
984.50
985.19
980.29
980.88
981.56
982.15
982.74
983.42
984.01
984.79
985.38
986.07
1383.5
1385.0
1387.0
1389.0
1390.7
1392.5
1394.1
1395.3
1397.0
1399.1
1383.4
1384.9
1386.5
1388.2
1389.8
1391.4
1393.0
1394.6
1396.0
1397.5
1386.2
1387.6
1389.3
1390.9
1392.6
1394.2
1395.8
1397.4
1398.8
1400.3
1379.5
1380.9
1382.6
1384.2
1385.9
1387.4
1389.1
1390.7
1392.0
1393.5
1382.0
1383.5
1385.1
1386.8
1388.5
1390.0
1391.7
1393.2
1394.6
1396.1
338.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
966.64
967.22
967.99
972.64
969.35
969.93
970.32
971.00
971.58
972.16
968.77
969.35
970.12
970.90
971.67
972.35
972.93
973.42
974.09
974.87
969.35
969.93
970.61
971.19
971.77
972.45
973.03
973.80
974.38
975.06
988.74
989.33
990.02
990.61
991.21
991.90
992.49
993.28
993.87
994.56
970.60
971.18
971.86
972.44
973.02
973.70
974.29
975.06
975.64
976.32
971.47
972.05
972.73
973.31
973.89
974.57
975.16
975.93
976.51
977.19
1353.7
1355.2
1357.1
1359.1
1360.8
1362.5
1364.0
1365.2
1366.9
1369.0
1353.6
1355.0
1356.7
1358.3
1359.9
1361.4
1363.1
1364.6
1365.9
1367.4
1356.3
1357.8
1359.4
1361.0
1362.6
1364.2
1365.8
1367.3
1368.7
1370.1
1349.8
1351.2
1352.8
1354.4
1356.1
1357.6
1359.2
1360.7
1362.1
1363.5
1352.3
1353.7
1355.3
1356.9
1358.6
1360.1
1361.7
1363.2
1364.6
1366.0
348.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
959.87
960.45
961.22
965.83
962.56
963.14
963.53
964.20
964.78
965.35
961.99
962.56
963.33
964.10
964.87
965.54
966.12
966.60
967.28
968.05
962.56
963.14
963.81
964.39
964.97
965.64
966.22
966.99
967.56
968.24
981.82
982.40
983.09
983.68
984.27
984.95
985.54
986.33
986.92
987.60
963.81
964.38
965.06
965.64
966.21
966.89
967.47
968.24
968.81
969.49
964.67
965.25
965.92
966.50
967.08
967.75
968.33
969.10
969.68
970.35
298.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
1502.8
1504.6
1506.5
1508.7
1510.3
1512.1
1513.2
1515.0
1516.8
1518.2
1503.4
1505.1
1507.2
1509.4
1511.3
1513.2
1514.9
1516.2
1518.1
1520.4
1503.3
1504.9
1506.7
1508.5
1510.3
1512.0
1513.8
1515.5
1517.0
1518.6
1506.3
1507.9
1509.7
1511.5
1513.3
1515.0
1516.8
1518.5
1520.0
1521.6
1499.0
1500.6
1502.4
1504.2
1506.0
1507.7
1509.5
1511.2
1512.7
1514.3
308.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
1471.9
1473.7
1475.5
1477.7
1479.2
1481.0
1482.1
1483.8
1485.6
1487.0
1472.5
1474.1
1476.2
1478.4
1480.2
1482.1
1483.7
1485.0
1486.9
1489.1
1472.4
1473.9
1475.7
1477.5
1479.2
1480.9
1482.7
1484.3
1485.8
1487.4
1475.3
1476.9
1478.7
1480.4
1482.2
1483.9
1485.6
1487.3
1488.8
1490.3
318.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
1441.6
1443.3
1445.2
1447.3
1448.8
1450.5
1451.6
1453.3
1455.0
1456.4
1442.2
1443.8
1445.8
1447.9
1449.8
1451.6
1453.2
1454.5
1456.3
1458.5
1442.1
1443.6
1445.4
1447.1
1448.8
1450.4
1452.2
1453.8
1455.2
1456.8
328.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
1412.0
1413.7
1415.4
1417.5
1419.0
1420.7
1421.7
1423.4
1425.1
1426.4
1412.5
1414.1
1416.1
1418.2
1420.0
1421.7
1423.3
1424.6
1426.3
1428.5
338.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
1382.9
1384.6
1386.3
1388.4
1389.8
1391.5
1392.5
1394.2
1395.8
1397.1
348.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
1353.2
1354.8
1356.5
1358.5
1359.9
1361.5
1362.5
1364.1
1365.8
1367.0
u = 0.10%.
147
U = 0.09%.
148
M. Oroian et al. / Journal of Molecular Liquids 207 (2015) 145–151
Table 3
Viscosity (η · 103, N·s/m2) evolution with temperature.
C (mol/L)
Table 4
Surface tension (σ, N/m) evolution with temperature.
η · 103 (N·s/m2)
Glucose
C (mol/L)
Glucose
Fructose
Galactose
Sucrose
Maltose
Lactose
0.926
0.935
0.941
0.948
0.957
0.964
0.973
0.982
0.990
0.999
0.037
0.037
0.037
0.037
0.037
0.037
0.037
0.037
0.038
0.038
0.037
0.037
0.037
0.037
0.037
0.037
0.037
0.038
0.038
0.038
0.037
0.037
0.037
0.037
0.037
0.037
0.037
0.038
0.038
0.038
0.038
0.038
0.038
0.038
0.038
0.038
0.038
0.038
0.039
0.039
0.037
0.037
0.037
0.037
0.037
0.037
0.037
0.037
0.038
0.038
0.037
0.037
0.037
0.037
0.037
0.037
0.037
0.038
0.038
0.038
0.694
0.701
0.706
0.711
0.717
0.723
0.729
0.736
0.742
0.749
0.702
0.708
0.713
0.719
0.725
0.730
0.737
0.744
0.750
0.756
308.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.035
0.035
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.035
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.037
0.037
0.037
0.037
0.037
0.037
0.037
0.037
0.035
0.035
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.036
0.490
0.494
0.498
0.502
0.506
0.510
0.515
0.519
0.524
0.528
0.472
0.477
0.480
0.484
0.488
0.492
0.496
0.501
0.505
0.509
0.477
0.482
0.485
0.489
0.493
0.497
0.501
0.506
0.510
0.515
318.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.034
0.034
0.034
0.034
0.034
0.035
0.035
0.035
0.035
0.035
0.034
0.034
0.034
0.034
0.035
0.035
0.035
0.035
0.035
0.035
0.034
0.034
0.034
0.034
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.036
0.036
0.036
0.034
0.034
0.034
0.034
0.034
0.034
0.035
0.035
0.035
0.035
0.034
0.034
0.034
0.034
0.035
0.035
0.035
0.035
0.035
0.035
0.362
0.365
0.368
0.370
0.374
0.376
0.380
0.383
0.387
0.390
0.380
0.383
0.386
0.389
0.392
0.395
0.399
0.402
0.406
0.409
0.366
0.370
0.372
0.375
0.378
0.381
0.385
0.388
0.391
0.395
0.370
0.373
0.376
0.379
0.382
0.385
0.389
0.392
0.395
0.399
328.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.034
0.034
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.034
0.034
0.034
0.034
0.034
0.034
0.034
0.034
0.034
0.034
0.034
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.034
0.034
0.297
0.300
0.303
0.307
0.308
0.310
0.313
0.315
0.317
0.320
0.294
0.297
0.299
0.301
0.304
0.306
0.309
0.312
0.314
0.317
0.309
0.312
0.314
0.316
0.319
0.321
0.324
0.327
0.330
0.333
0.298
0.300
0.303
0.305
0.308
0.310
0.313
0.315
0.318
0.321
0.301
0.304
0.306
0.308
0.311
0.313
0.316
0.319
0.321
0.324
338.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.031
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.033
0.033
0.033
0.033
0.033
0.033
0.033
0.031
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.032
0.250
0.252
0.255
0.258
0.259
0.261-0.263
0.264
0.267
0.269
0.247
0.249
0.251
0.253
0.255
0.257
0.260
0.262
0.264
0.266
0.260
0.262
0.264
0.266
0.268
0.270
0.273
0.275
0.277
0.280
0.250
0.252
0.254
0.256
0.258
0.260
0.263
0.265
0.267
0.270
0.253
0.255
0.257
0.259
0.261
0.263
0.265
0.268
0.270
0.273
348.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.030
0.030
0.030
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.030
0.030
0.030
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.030
0.030
0.030
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.032
0.032
0.032
0.030
0.030
0.030
0.030
0.031
0.031
0.031
0.031
0.031
0.031
0.030
0.030
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
Galactose
Sucrose
Maltose
298.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.901
0.910
0.917
0.928
0.936
0.953
0.963
0.973
0.983
0.987
0.916
0.924
0.934
0.944
0.949
0.955
0.963
0.968
0.977
0.984
0.906
0.914
0.920
0.927
0.935
0.942
0.951
0.960
0.968
0.976
0.951
0.959
0.966
0.974
0.982
0.989
0.998
1.007
1.016
1.025
0.917
0.925
0.932
0.939
0.947
0.954
0.963
0.971
0.979
0.988
308.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.683
0.689
0.695
0.703
0.709
0.722
0.730
0.737
0.744
0.748
0.694
0.700
0.708
0.715
0.719
0.723
0.730
0.734
0.740
0.745
0.686
0.692
0.697
0.702
0.709
0.714
0.720
0.727
0.733
0.739
0.720
0.727
0.732
0.738
0.744
0.749
0.756
0.763
0.770
0.776
318.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.464
0.469
0.473
0.478
0.482
0.491
0.496
0.501
0.506
0.509
0.472
0.476
0.481
0.487
0.489
0.492
0.496
0.499
0.504
0.507
0.467
0.471
0.474
0.478
0.482
0.486
0.490
0.494
0.499
0.503
328.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.360
0.363
0.366
0.371
0.374
0.381
0.385
0.389
0.393
0.394
0.366
0.369
0.373
0.377
0.379
0.382
0.385
0.387
0.390
0.393
338.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.293
0.296
0.298
0.301
0.304
0.310
0.313
0.316
0.319
0.321
348.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.246
0.248
0.250
0.253
0.255
0.260
0.263
0.266
0.268
0.270
U = 0.26%.
σ (N/m)
298.15 K
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
Fructose
Lactose
U = 0.10%.
M. Oroian et al. / Journal of Molecular Liquids 207 (2015) 145–151
a
b
1.000
280.00 300.00 320.00 340.00 360.00
149
1.200
η·103 (N·s m-2)
η·103 (N·s·m-2)
1.000
0.800
0.600
0.400
0.200
0.100
0.000
Temperature (K)
0
0.05
Concentration (mol/L)
Fig. 1. Influence of temperature (a) and concentration: 0.01 mol/L, 0.02 mol/L, 0.03 mol/L, 0.04 mol/L, 0.05 mol/L,
0.10 mol/L (b) on glucose viscosity: 298.15 K, 308.15 K, 318.15 K, 328.15 K, 338.15 K and 348.15 K.
b
0.039
0.038
0.037
0.036
0.035
0.034
0.033
0.032
0.031
0.030
0.07 mol/L, 0.08 mol/L,
0.09 mol/L and
0.040
0.038
σ (N/m)
σ (N/m)
a
0.06 mol/L,
0.1
0.036
0.034
0.032
280
300
320
340
Temperature (K)
360
0.030
0.00
0.02 0.04 0.06 0.08
Concentration (mol/L)
Fig. 2. Influence of temperature (a) and concentration 0.01 mol/L, 0.02 mol/L, 0.03 mol/L, 0.04 mol/L, 0.05 mol/L,
0.10 mol/L (b) on glucose surface tension: 298.15 K, 308.15 K, 318.15 K, 328.15 K, 338.15 K and 348.15 K.
Similarly, a correlation was developed to allow the prediction of the
surface tension for the solutions as a function of molar concentration by
means of 1st grade polynomial fitting. The following correlation is the
regression equation:
σ ¼ j þ k cM
ð6Þ
where σ — surface tension in N/m, cM — is the concentration expressed
in mol/L, and j and k — fitting parameters. The regression coefficients
were higher than 0.985. The values of j ranged between 0.030 and
0.036 and k ranged between 0.007 and 0.009. Both coefficients are
negatively influenced by the temperature (r = −0.915***). The relative
deviation modulus was lower than 0.5.
0.06 mol/L,
0.10
0.07 mol/L, 0.08 mol/L,
0.09 mol/L and
The 3rd model applied is presented in Eq. (9):
ln σ ¼ H þ F=ðη þ GÞ
ð9Þ
where E, F and G are the substance-dependent coefficients.
The 4th model applied is presented in Eq. (10):
1=m
ln σ ¼ H þ I= η
þJ
ð10Þ
where H, J and m are the substance-dependent coefficients.
The main goal of this article was to check the suitability of different
models to correlate the surface tension and viscosity evolution of 3
mono- and 3 di-saccharides at ten different concentrations (0.01, 0.02,
0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09 and 0.10 mol/L).
3.3. Correlation between surface tension and viscosity
In 1966, Pelofsky [10] proposed the first model for correlating the
surface tension and viscosity:
0.03900
0.03800
0.03700
lnσ ¼ lnA þ B=η
ð7Þ
0.03600
0.03500
where A and B are the adjusting parameters. The empirical relationship
can be applied to both organic and inorganic pure fluids and mixtures.
The second model applied for the saccharide surface tension–viscosity correlations was proposed by Ghatee et al. for ionic liquids [13]. The
model (a modified Pelofsky model) expression is presented in Eq. (8):
lnσ ¼ lnC þ D η
−0:3
where C and D are substance-dependent coefficients.
ð8Þ
0.03400
0.03300
0.03200
0.03100
0.03000
0.000
0.200
0.400
0.600
0.800
1.000
Fig. 3. Surface tension–viscosity evolution for the glucose solutions
308.15 K, 318.15 K, 328.15 K, 338.15 K and 348.15 K.
1.200
298.15 K,
150
M. Oroian et al. / Journal of Molecular Liquids 207 (2015) 145–151
The data were fitted using the Multitab 17 trial version. The prediction accuracies of the four models have been checked computing the deviation modulus. The correlations between the surface tension and the
Table 5
The relative deviation modulus for the surface tension correlation models.
Concentration (mol/L)
Pelofsky
Modified Pelofsky
Glucose
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
3rd model
4th model
0.673
0.562
0.689
0.648
0.539
0.567
0.544
0.514
0.626
0.694
0.469
0.470
0.469
0.468
0.468
0.468
0.468
0.468
0.468
0.467
0.491
0.491
0.491
0.490
0.490
0.490
0.490
0.490
0.490
0.489
0.404
0.404
0.405
0.404
0.406
0.406
0.406
0.405
0.405
0.405
Fructose
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.598
0.598
0.598
0.598
0.597
0.597
0.597
0.597
0.596
0.596
0.469
0.469
0.469
0.468
0.468
0.468
0.468
0.468
0.467
0.467
0.491
0.491
0.491
0.490
0.490
0.490
0.490
0.490
0.489
0489
0.405
0.405
0.406
0.406
0.406
0.405
0.405
0.405
0.405
0.405
Galactose
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.598
0.598
0.598
0.597
0.597
0.597
0.597
0.597
0.596
0.597
0.469
0.469
0.469
0.468
0.468
0.468
0.468
0.467
0.467
0.467
0.491
0.491
0.491
0.490
0.490
0.490
0.490
0.489
0.489
0.489
0.404
0.404
0.404
0.404
0.405
0.406
0.406
0.405
0.405
0.405
Sucrose
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.596
0.596
0.596
0.595
0.595
0.595
0.595
0.595
0.595
0.594
0.467
0.467
0.467
0.466
0.466
0.466
0.466
0.466
0.465
0.465
0.489
0.489
0.489
0.488
0.488
0.488
0.488
0.488
0.487
0.487
0.405
0.405
0.405
0.405
0.404
0.404
0.404
0.404
0.404
0.414
Maltose
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.599
0.598
0.598
0.597
0.598
0.598
0.597
0.597
0.597
0.596
0.469
0.469
0.469
0.468
0.468
0.468
0.468
0.468
0.467
0.467
0.491
0.491
0.490
0.490
0.490
0.490
0.490
0.489
0.489
0.489
0.405
0.405
0.407
0.406
0.406
0.406
0.406
0.405
0.405
0.405
Lactose
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.598
0.598
0.598
0.598
0.597
0.597
0.597
0.597
0.596
0.596
0.469
0.469
0.469
0.468
0.468
0.468
0.468
0.467
0.467
0.467
0.491
0.491
0.491
0.490
0.490
0490
0.489
0.489
0.489
0.489
0.404
0.406
0.406
0.406
0.406
0.406
0.405
0.405
0.405
0.405
viscosity of the substances have been checked at different temperatures
(298.15, 308.15, 318.15, 328.15, 338.15 and 348.15 K).
In Fig. 3, the evolution of the surface tension with viscosity at different temperatures for the glucose solutions is presented. A logarithmic
correlation between these two parameters is observed.
In Table 5, the deviation modulus for the four models is presented. It
seems that the small values of the deviation modulus are observed in
the case of the 4th model, while the highest values are observed in the
case of the Pelofsky model. The deviation modulus decreased in the
next order: Pelofsky model N 3rd model N modified Pelofsky
model N 4th model. The Pelofsky model is giving deviation modulus
ranging between 0.596–0.694 and 0.465–0.470 in the case of modified
Pelofsky model, 0.487–0.491 for the 3rd model and 0.404–0.415 for
the 4th model, respectively. However all the four models can be considered suitable models because the deviation modules are lower than 1%.
However the suitable model can be considered the 4th model, and the
deviation modulus values are closed to 0.4%.
3.4. Correlations between density, ultrasonic velocity and surface tension
The relation between the ultrasonic velocity, density and surface
tension can be expressed using a linear equation as: [14]
logu ¼ ψ logðσ=ρÞ þ ξ
ð11Þ
where u — ultrasonic velocity (m/s), σ — surface tension (N/m), ρ —
density (kg/m3), and ψ and ξ — constants.
All the three parameters of saccharide samples have been subjected
to linear regression to assess the applicability of the equation and to
compute the two constants. The ultrasonic velocity (log u)–density
and surface tension (log (σ/ρ)) for all the saccharide samples analyzed
are plotted in Fig. 4; it can be observed that the evolution of parameters
is a linear one (the regression coefficients is R2 = 0.997), ψ = 0.667 and
ξ = 6.132. We can conclude that the equation is a suitable one to correlate the ultrasonic velocity, density and surface tension for the monoand di-saccharides.
4. Conclusions
All the physical parameters studied for the saccharide solutions
(density, ultrasound velocity, surface tension and viscosity) are influenced negatively by the temperature increasing and positively by the
concentration increasing, respectively. The 4th model used for the correlation of surface tension and viscosity (which employs four coefficients) is the suitable one for the prediction evolution. The correlation
between density, ultrasonic velocity and surface tension of honey samples leads us to obtain a master curve for predicting these parameters
with high accuracy (R2 = 0.997).
Fig. 4. Correlation between ultrasound velocity, density and surface tension for mono- and
di-saccharides.
M. Oroian et al. / Journal of Molecular Liquids 207 (2015) 145–151
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[3] J.H. Irving, J.G. Kirkwood, The statistical mechanical theory of transport processes. IV.
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[4] F. Biscay, A. Ghoufi, P. Malfreyt, Surface tension of water–alcohol mixtures from
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