The three-parameter Lennard-Jones
Accurate representation of thermodynamic and transport properties is essential to process engineers to design and optimize equipment and chemical processes. Second virial coefficient is an important quantity which is useful in calculating vessel size from volumetric data, heating requirements from calorimetric data, and stage requirements from phase equilibrium data. Transport properties such as viscosity, thermal conductivity, and diffusion coefficient are critically important parameters in many engineering applications: for the determination of pipeline, heatexchanger and separation equipment size, mass transfer efficiency of reservoir of oils, and the power required to pump fluid [
The intermolecular forces are of great importance to scientists in a wide field of disciplines as information of these interactions provides the progress of collisions between molecules and determines the bulk properties of substances. Approximation of thermodynamic and transport properties from statistical mechanics requires a realistic intermolecular potential [
A realistic intermolecular potential allows the calculation of thermodynamic and transport properties. A lot of studies have focused on individual properties like second virial coefficient or viscosity for the determination of intermolecular potential parameters [
Several investigators [
The objective of this study is to represent thermodynamic property (second virial coefficient) and transport properties (viscosity, thermal conductivity, and diffusion coefficient) of noble gases (He, Ne, Ar, Kr, and Xe) and their binary mixtures at low density using a single set of modified Lennard-Jones
In this paper, special focus was placed on the Lennard-Jones
These potential parameters can be fitted by least-squares analysis and lead to provide accurate calculations of dilute gas thermodynamic property (second virial coefficient) and transport properties (viscosity, thermal conductivity, and diffusion coefficient) of noble gases, as summarized below.
From statistical mechanics, the relations between second virial coefficient and intermolecular potential functions were theoretically derived; in particular, explicit expression of the second virial coefficient for the Lennard-Jones
In the present study, our observations on the accurate approximation not only of thermodynamic property (second virial coefficient), but also of transport properties (viscosities, thermal conductivities, and diffusion coefficients) in the dilute gaseous phase of noble gases were made by introducing temperature-correction parameter
Then the second virial coefficient can be calculated from (
For interaction of different molecular species, the combining rules are used for the molecular distance, energy, and reduced temperature-correction parameter for mixture computations:
For spherical molecules, these equations are of high accuracy for the prediction of second cross-virial coefficient
Transport properties (viscosity, thermal conductivity, and diffusion coefficient) at low density can be calculated by using Chapman-Enskog kinetic theory [
Since the Chapman-Enskog gas kinetic theory uses a common basis for the evaluation of viscosity and thermal conductivity, the statistical expression for the thermal conductivity involves the same collision integral as does the viscosity. For a pure monoatomic gas at low density, which has no rotational or vibrational degrees of freedom, thermal conductivity was calculated through a rigorous analysis by Brokaw [
Various prediction methods for estimating mixture thermal conductivity have appeared, one of which is essentially empirical and it is reduced to some form of the Wassiljewa equation [
The Chapman-Enskog expression for binary diffusion coefficient of dilute gas is presented by Hirschfelder et al. [
As a part of systematic program of our researches, modified Lennard-Jones
Using (
A critical review of the literature on second virial coefficient was achieved by Dymond et al. [
Table
Potential parameters of Lennard-Jones (12-6) Potential with a reduced temperature-correction parameter.
Group |
|
|
|
---|---|---|---|
Helium |
|
|
|
Neon |
|
|
|
Argon |
|
|
|
Krypton |
|
|
|
Xenon |
|
|
|
Deviations between experimental and calculated second virial coefficients of pure noble gases.
Compound | Number of data points | Average RMSD in |
Δ |
Reference | ||||
---|---|---|---|---|---|---|---|---|
Present study | Dymond et al. | L-J | Kihara | Tsonopoulos | ||||
Regression results | ||||||||
| ||||||||
Helium | 304 | 5.44 | 5.07a | 10.9 | 10.8 | 39.1 | 2–1473 | [ |
Neon | 55 | 0.28 | 0.34 | 0.45 | 1.38 | 1.56 | 44–873 | [ |
Argon | 105 | 0.40 | 0.53 | 2.43 | 1.73 | 1.88 | 75–773 | [ |
Krypton | 157 | 2.87 | 3.18 | 5.75 | 3.67 | 6.90 | 107–873 | [ |
Xenon | 114 | 2.50 | 2.67 | 4.32 | 2.53 | 3.51 | 160–973 | [ |
| ||||||||
Average | 735 | 3.33 | 3.29 | 6.79 | 5.99 | 18.6 | ||
| ||||||||
Prediction results | ||||||||
| ||||||||
Helium | 8 | 4.13 | 1.08 | 10.8 | 4.29 | 14.9 | 343–374 | [ |
Xenon | 9 | 0.50 | 1.37 | 2.57 | 2.11 | 2.57 | 206–273 | [ |
| ||||||||
Average | 17 | 2.21 | 1.23 | 6.44 | 3.14 | 8.37 |
Comparisons of the proposed method with other existing methods are shown in Table
Comparison of measured and calculated second virial coefficients for He.
Comparison of measured and calculated second virial coefficients for Ne.
Comparison of measured and calculated second virial coefficients for Ar.
Comparison of measured and calculated second virial coefficients for Kr.
Comparison of measured and calculated second virial coefficients for Xe.
In Table
Deviations between experimental and calculated viscosities of pure noble gases.
Compound | Number of data points | Average RMSDr in |
|
Reference | |||||
---|---|---|---|---|---|---|---|---|---|
Present study | L-J | Kihara | Lucas | Simsci | Refprop | ||||
Regression results | |||||||||
| |||||||||
Helium | 9 | 5.27 | 18.3 | 13.2 | 3.23 | 2.05 | 2.83 | 80–1300 | [ |
Neon | 36 | 1.50 | 1.86 | 3.76 | 2.80 | 4.29 | 2.48 | 30–500 | [ |
Argon | 30 | 1.84 | 2.72 | 5.33 | 1.73 | 1.32 | 0.29 | 10–650 | [ |
Krypton | 19 | 2.87 | 12.2 | 8.56 | 1.23 | 0.91 | 1.85 | 150–600 | [ |
Xenon | 23 | 0.49 | 9.88 | 4.10 | 2.50 | 0.57 | 2.13 | 300–430 | [ |
| |||||||||
Average | 117** | 1.90 | 6.60 | 5.74 | 2.25 | 2.08 | 1.78 | ||
| |||||||||
Prediction results | |||||||||
| |||||||||
22 | 4.11 | 8.33 | 2.99 | 4.95 | 0.98 | 3.94 | 50–973 | [ | |
31 | 4.62 | 9.03 | 2.96 | 3.92 | 0.60 | 10.0 | 20–1000 | [ | |
1 | 4.44 | 8.82 | 0.76 | 2.87 | 0.64 | 1.32 | 300 | [ | |
8 | 2.34 | 6.52 | 4.03 | 6.74 | 0.91 | 0.84 | 298–1010 | [ | |
1 | 4.83 | 9.93 | 0.14 | 2.26 | 0.06 | 0.75 | 303 | [ | |
13 | 3.15 | 7.32 | 4.24 | 6.36 | 1.31 | 1.43 | 198–473 | [ | |
8 | 2.90 | 6.86 | 4.17 | 6.42 | 0.40 | 0.53 | 298–973 | [ | |
8 | 2.71 | 6.65 | 4.27 | 6.54 | 0.23 | 0.42 | 298–973 | [ | |
6 | 2.98 | 6.87 | 4.37 | 6.55 | 0.36 | 0.57 | 298–973 | [ | |
9 | 3.26 | 7.90 | 2.47 | 4.72 | 0.33 | 0.49 | 298–678 | [ | |
9 | 2.51 | 6.68 | 3.83 | 6.17 | 0.26 | 0.36 | 298–778 | [ | |
5 | 4.05 | 8.85 | 1.32 | 3.48 | 0.09 | 0.41 | 298–473 | [ | |
1 | 2.91 | 7.66 | 2.66 | 5.3 | 3.68 | 3.46 | 767 | [ | |
6 | 4.24 | 8.91 | 1.37 | 3.54 | 0.35 | 0.32 | 298–512 | [ | |
1 | 5.28 | 10.2 | 0.08 | 2.03 | 0.09 | 0.62 | 292 | [ | |
1 | 5.72 | 10.5 | 0.77 | 1.34 | 0.76 | 0.03 | 291 | [ | |
Helium | 2 | 6.29 | 11.1 | 1.40 | 0.98 | 1.39 | 0.76 | 291 | [ |
2 | 5.06 | 10.1 | 12.7 | 2.12 | 0.13 | 0.60 | 293–303 | [ | |
4 | 5.48 | 10.4 | 0.95 | 1.82 | 0.51 | 0.81 | 237–308 | [ | |
6 | 5.91 | 10.7 | 1.51 | 0.36 | 1.50 | 2.50 | 72–291 | [ | |
10 | 5.01 | 9.61 | 4.31 | 1.77 | 3.08 | 30.8 | 14–293 | [ | |
5 | 5.30 | 10.2 | 0.46 | 2.23 | 1.84 | 1.83 | 297–523 | [ | |
2 | 5.07 | 10.1 | 0.13 | 2.11 | 0.12 | 0.59 | 293–303 | [ | |
1 | 4.85 | 9.99 | 0.02 | 2.16 | 0.14 | 0.54 | 303 | [ | |
10 | 4.94 | 9.75 | 1.01 | 2.86 | 1.40 | 1.38 | 293–523 | [ | |
39 | 6.84 | 10.4 | 2.73 | 6.18 | 5.94 | 22.0 | 14–973 | [ | |
74 | 3.40 | 7.42 | 3.73 | 5.97 | 0.87 | 0.58 | 100–1000 | [ | |
72 | 5.77 | 10.3 | 6.75 | 4.09 | 15.7 | 62.2 | 200–1000 | [ | |
8 | 2.69 | 6.63 | 4.28 | 6.55 | 0.24 | 0.44 | 298–973 | [ | |
11 | 4.70 | 9.22 | 1.89 | 3.51 | 0.46 | 0.49 | 100–600 | [ | |
19 | 5.32 | 9.72 | 3.05 | 4.30 | 0.35 | 1.68 | 80–1000 | [ | |
7 | 1.32 | 4.25 | 5.50 | 7.98 | 3.10 | 3.45 | 250–1000 | [ | |
13 | 3.83 | 8.54 | 1.89 | 4.34 | 2.64 | 2.53 | 373–973 | [ | |
| |||||||||
Average | 415* | 4.49 | 8.76 | 3.75 | 4.82 | 3.97 | 15.1 | ||
| |||||||||
Neon | 27 | 2.04 | 1.54 | 8.00 | 3.14 | 3.04 | 15.2 | 50–973 | [ |
6 | 1.58 | 1.22 | 7.79 | 2.45 | 1.47 | 2.20 | 100–600 | [ | |
8 | 1.58 | 0.72 | 8.36 | 3.65 | 0.57 | 27.4 | 298–973 | [ | |
13 | 1.83 | 1.04 | 8.60 | 3.54 | 1.04 | 21.2 | 298–973 | [ | |
8 | 2.07 | 1.24 | 8.91 | 4.21 | 0.92 | 27.1 | 298–973 | [ | |
6 | 2.22 | 1.37 | 8.97 | 4.30 | 1.09 | 29.8 | 298–973 | [ | |
8 | 2.27 | 1.39 | 9.05 | 4.36 | 1.08 | 26.9 | 298–973 | [ | |
5 | 1.13 | 0.46 | 7.91 | 1.82 | 1.07 | 2.72 | 298–473 | [ | |
7 | 1.80 | 1.00 | 8.66 | 3.64 | 0.91 | 11.3 | 298–778 | [ | |
9 | 1.67 | 0.90 | 8.47 | 2.90 | 1.15 | 3.52 | 298–673 | [ | |
3 | 1.07 | 2.10 | 5.89 | 0.82 | 0.66 | 0.47 | 298–348 | [ | |
3 | 4.46 | 5.53 | 2.74 | 4.21 | 3.99 | 2.91 | 298–348 | [ | |
3 | 0.49 | 1.50 | 6.45 | 0.29 | 0.13 | 1.07 | 298–348 | [ | |
6 | 1.03 | 2.01 | 6.02 | 0.81 | 0.70 | 0.71 | 298–348 | [ | |
3 | 0.27 | 1.17 | 6.78 | 0.22 | 0.58 | 1.39 | 298–348 | [ | |
3 | 0.19 | 1.17 | 6.76 | 0.22 | 0.33 | 1.39 | 298–348 | [ | |
3 | 0.75 | 0.75 | 7.36 | 0.97 | 1.00 | 2.11 | 298–348 | [ | |
3 | 0.56 | 0.52 | 7.38 | 0.81 | 0.97 | 2.04 | 298–348 | [ | |
3 | 0.49 | 0.56 | 7.32 | 0.74 | 0.92 | 1.98 | 298–348 | [ | |
3 | 1.09 | 0.89 | 7.56 | 1.30 | 1.28 | 2.38 | 298–348 | [ | |
3 | 0.58 | 0.50 | 7.39 | 0.83 | 0.99 | 2.06 | 298–348 | [ | |
4 | 0.65 | 0.305 | 7.45 | 0.64 | 1.61 | 1.71 | 237–308 | [ | |
2 | 0.65 | 0.328 | 7.50 | 0.78 | 1.35 | 1.94 | 293–303 | [ | |
5 | 2.20 | 1.986 | 8.31 | 2.24 | 2.10 | 3.38 | 72–291 | [ | |
5 | 1.08 | 2.994 | 8.15 | 1.92 | 9.59 | 7.60 | 20–293 | [ | |
6 | 2.08 | 2.176 | 7.54 | 2.44 | 2.05 | 2.91 | 273–523 | [ | |
2 | 0.65 | 0.328 | 7.50 | 0.78 | 1.35 | 1.94 | 293–303 | [ | |
2 | 1.12 | 2.129 | 5.76 | 1.14 | 0.47 | 0.17 | 291 | [ | |
2 | 0.52 | 0.947 | 6.98 | 0.51 | 0.92 | 1.39 | 291 | [ | |
52 | 0.98 | 1.568 | 7.83 | 1.68 | 6.64 | 13.4 | 20–1000 | [ | |
32 | 1.24 | 0.991 | 7.71 | 3.11 | 0.68 | 22.1 | 100–950 | [ | |
92 | 4.80 | 4.116 | 5.86 | 4.23 | 12.4 | 7.89 | 27–320 | [ | |
8 | 2.08 | 1.242 | 8.92 | 4.21 | 0.93 | 27.1 | 298–973 | [ | |
11 | 1.77 | 2.693 | 5.38 | 1.53 | 1.83 | 1.92 | 100–600 | [ | |
19 | 1.35 | 1.439 | 7.15 | 2.68 | 1.10 | 20.4 | 80–1000 | [ | |
1 | 1.28 | 2.29 | 5.60 | 1.30 | 0.60 | 0.14 | 291 | [ | |
4 | 1.04 | 2.09 | 5.92 | 0.57 | 1.51 | 0.71 | 293–523 | [ | |
| |||||||||
Average | 380* | 2.25 | 2.07 | 7.24 | 2.87 | 4.83 | 12.0 | ||
| |||||||||
Argon | 22 | 2.37 | 2.77 | 7.56 | 2.17 | 2.23 | 2.14 | 50–973 | [ |
63 | 2.78 | 2.25 | 5.85 | 2.38 | 2.98 | 1.94 | 90–500 | [ | |
28 | 1.63 | 1.99 | 6.96 | 1.73 | 1.48 | 1.06 | 87–1000 | [ | |
19 | 2.45 | 2.04 | 6.46 | 2.02 | 1.55 | 8.98 | 173–1597 | [ | |
1 | 1.71 | 0.48 | 6.00 | 0.18 | 0.17 | 0.02 | 298 | [ | |
8 | 1.14 | 2.59 | 8.39 | 2.39 | 0.58 | 1.47 | 298–973 | [ | |
11 | 0.88 | 2.64 | 8.05 | 1.96 | 0.87 | 0.90 | 298–473 | [ | |
6 | 1.20 | 2.92 | 8.25 | 2.23 | 0.97 | 0.61 | 298–767 | [ | |
9 | 1.48 | 3.43 | 8.85 | 2.86 | 1.20 | 3.30 | 298–1124 | [ | |
8 | 1.17 | 3.03 | 8.45 | 2.43 | 0.63 | 1.54 | 298–973 | [ | |
7 | 1.21 | 2.97 | 8.24 | 2.36 | 0.73 | 1.41 | 298–973 | [ | |
5 | 0.92 | 1.99 | 7.36 | 1.33 | 0.95 | 0.62 | 298–473 | [ | |
5 | 0.85 | 1.95 | 7.36 | 1.29 | 0.92 | 0.60 | 300–473 | [ | |
2 | 8.16 | 6.93 | 11.4 | 5.32 | 6.43 | 7.39 | 55–90 | [ | |
1 | 2.01 | 0.12 | 5.79 | 0.34 | 0.31 | 0.07 | 273 | [ | |
1 | 3.90 | 1.56 | 4.81 | 1.25 | 6.76 | 26.7 | 1373 | [ | |
1 | 1.98 | 0.21 | 5.77 | 0.41 | 0.40 | 0.19 | 293 | [ | |
1 | 2.99 | 0.62 | 5.40 | 0.89 | 5.27 | 12.3 | 1100 | [ | |
1 | 5.90 | 3.55 | 3.33 | 2.25 | 9.28 | 80.4 | 1873 | [ | |
9 | 0.94 | 2.79 | 8.22 | 2.08 | 0.80 | 0.49 | 298–773 | [ | |
6 | 1.18 | 2.84 | 8.17 | 2.16 | 0.85 | 0.45 | 298–770 | [ | |
8 | 0.93 | 2.68 | 8.07 | 1.95 | 0.93 | 0.46 | 298–673 | [ | |
21 | 2.21 | 0.83 | 5.73 | 0.83 | 0.89 | 0.39 | 202–394 | [ | |
5 | 12.8 | 13.9 | 17.4 | 13.6 | 12.2 | 11.4 | 775–1053 | [ | |
7 | 12.0 | 12.7 | 15.9 | 12.5 | 11.7 | 29.9 | 775–1838 | [ | |
5 | 3.75 | 1.70 | 5.30 | 1.20 | 5.79 | 36.5 | 569–1838 | [ | |
6 | 5.64 | 4.66 | 8.52 | 3.63 | 3.25 | 3.96 | 72–291 | [ | |
2 | 1.79 | 0.44 | 11.2 | 0.27 | 0.26 | 0.11 | 293–303 | [ | |
1 | 2.19 | 0.01 | 5.59 | 0.60 | 0.58 | 0.37 | 291 | [ | |
5 | 5.22 | 4.39 | 8.44 | 3.36 | 3.00 | 3.72 | 72–291 | [ | |
4 | 2.00 | 0.48 | 5.92 | 0.55 | 1.08 | 1.46 | 293–523 | [ | |
2 | 1.72 | 0.50 | 6.00 | 0.23 | 0.22 | 0.09 | 293–303 | [ | |
2 | 1.90 | 0.31 | 5.83 | 0.37 | 0.36 | 0.20 | 293–303 | [ | |
8 | 2.09 | 0.49 | 5.83 | 0.64 | 1.10 | 1.47 | 293–523 | [ | |
46 | 13.3 | 13.4 | 15.0 | 13.3 | 13.3 | 13.3 | 90–1000 | [ | |
124 | 1.55 | 2.99 | 8.44 | 2.59 | 0.90 | 6.64 | 100–1600 | [ | |
68 | 2.21 | 1.35 | 5.62 | 1.55 | 2.17 | 1.04 | 87–700 | [ | |
135 | 1.53 | 2.67 | 7.81 | 2.21 | 1.46 | 1.34 | 80–1000 | [ | |
63 | 1.60 | 1.43 | 6.50 | 1.13 | 1.50 | 0.57 | 90–500 | [ | |
1 | 1.52 | 0.66 | 6.17 | 0.01 | 0.00 | 0.14 | 300 | [ | |
8 | 1.17 | 3.04 | 8.81 | 2.44 | 0.64 | 1.53 | 298–973 | [ | |
11 | 1.65 | 1.53 | 6.50 | 1.24 | 1.43 | 0.56 | 100–600 | [ | |
20 | 4.41 | 3.96 | 8.23 | 3.19 | 3.18 | 3.52 | 60–1000 | [ | |
7 | 0.85 | 1.43 | 7.06 | 0.82 | 1.29 | 2.98 | 250–1000 | [ | |
5 | 2.19 | 2.35 | 7.11 | 1.97 | 1.7 | 1.72 | 323–523 | [ | |
5 | 0.81 | 1.48 | 6.98 | 0.76 | 0.58 | 0.47 | 298–423 | [ | |
4 | 1.59 | 1.10 | 6.34 | 0.59 | 0.50 | 0.38 | 298–373 | [ | |
| |||||||||
Average | 787* | 2.75 | 3.14 | 7.85 | 2.84 | 2.44 | 3.76 | ||
| |||||||||
Krypton |
29 | 3.41 | 6.47 | 8.26 | 3.40 | 4.00 | 59.7 | 50–3273 | [ |
6 | 2.96 | 4.24 | 6.53 | 1.85 | 1.84 | 3.40 | 100–600 | [ | |
1 | 3.90 | 1.95 | 4.82 | 0.83 | 0.50 | 0.91 | 293 | [ | |
2 | 3.40 | 2.59 | 5.36 | 0.58 | 0.51 | 1.53 | 293–300 | [ | |
8 | 1.70 | 6.11 | 7.76 | 2.28 | 1.88 | 3.05 | 298–973 | [ | |
6 | 1.92 | 5.77 | 7.54 | 2.15 | 1.83 | 3.18 | 298–767 | [ | |
8 | 1.89 | 6.25 | 7.86 | 2.51 | 2.07 | 3.20 | 298–973 | [ | |
8 | 1.88 | 6.07 | 7.67 | 2.25 | 1.83 | 2.97 | 298–973 | [ | |
9 | 1.60 | 6.61 | 8.20 | 2.80 | 2.40 | 3.27 | 298–1151 | [ | |
9 | 1.87 | 5.82 | 7.53 | 2.05 | 1.71 | 3.10 | 298–778 | [ | |
6 | 1.98 | 5.68 | 7.45 | 2.06 | 1.75 | 3.09 | 298–770 | [ | |
1 | 5.59 | 0.36 | 3.27 | 2.47 | 2.13 | 0.70 | 293 | [ | |
1 | 5.08 | 0.84 | 3.74 | 1.97 | 1.64 | 0.21 | 293 | [ | |
1 | 5.42 | 0.52 | 3.42 | 2.30 | 1.95 | 0.54 | 293 | [ | |
12 | 2.01 | 5.43 | 7.27 | 1.83 | 1.57 | 2.93 | 298–773 | [ | |
4 | 2.59 | 3.19 | 6.23 | 1.14 | 1.28 | 2.56 | 237–308 | [ | |
2 | 4.93 | 0.82 | 3.82 | 1.96 | 1.63 | 0.43 | 273–293 | [ | |
2 | 3.80 | 2.13 | 4.93 | 0.70 | 0.37 | 1.02 | 273–293 | [ | |
2 | 3.72 | 2.10 | 4.40 | 0.69 | 0.68 | 1.10 | 273–293 | [ | |
1 | 4.34 | 1.49 | 3.82 | 1.27 | 0.90 | 0.48 | 293 | [ | |
15 | 2.54 | 5.66 | 7.18 | 2.0 | 1.87 | 5.45 | 293–1600 | [ | |
78 | 2.12 | 5.77 | 7.43 | 2.06 | 1.69 | 2.60 | 300–1300 | [ | |
71 | 4.64 | 4.98 | 7.24 | 3.83 | 3.77 | 4.28 | 119–950 | [ | |
235 | 2.02 | 6.98 | 8.64 | 3.61 | 3.57 | 12.5 | 80–2000 | [ | |
51 | 8.49 | 7.44 | 8.66 | 7.50 | 7.45 | 7.40 | 125–500 | [ | |
8 | 1.86 | 6.08 | 7.69 | 2.26 | 1.84 | 2.99 | 298–973 | [ | |
10 | 4.62 | 2.00 | 4.19 | 2.0 | 2.09 | 0.26 | 150–600 | [ | |
26 | 1.89 | 6.29 | 7.95 | 3.19 | 3.20 | 13.4 | 140–2000 | [ | |
| |||||||||
Average | 612* | 3.03 | 6.18 | 7.94 | 3.42 | 3.32 | 10.2 | ||
| |||||||||
22 | 5.51 | 7.31 | 5.84 | 2.10 | 9.51 | 12.3 | 50–973 | [ | |
6 | 5.06 | 6.39 | 5.33 | 1.86 | 6.59 | 12.0 | 100–600 | [ | |
17 | 2.09 | 4.22 | 4.46 | 2.18 | 1.34 | 6.71 | 173–797 | [ | |
8 | 3.13 | 7.60 | 5.87 | 1.42 | 2.11 | 7.94 | 298–973 | [ | |
9 | 3.04 | 7.43 | 5.86 | 1.34 | 2.24 | 4.06 | 298–778 | [ | |
7 | 1.24 | 2.65 | 3.75 | 2.51 | 0.46 | 5.94 | 202–298 | [ | |
4 | 3.75 | 5.22 | 6.18 | 2.20 | 3.08 | 2.30 | 237–308 | [ | |
3 | 0.53 | 2.62 | 2.99 | 2.32 | 0.74 | 2.90 | 273–373 | [ | |
Xenon | 2 | 0.26 | 2.42 | 3.24 | 2.83 | 0.66 | 3.45 | 291 | [ |
9 | 2.45 | 6.88 | 5.27 | 1.07 | 1.42 | 8.06 | 293–1000 | [ | |
41 | 2.88 | 7.43 | 5.61 | 1.22 | 1.72 | 16.1 | 300–1300 | [ | |
67 | 2.32 | 5.41 | 4.68 | 1.97 | 1.32 | 12.0 | 165–1250 | [ | |
130 | 3.77 | 6.66 | 9.69 | 1.43 | 3.44 | 8.68 | 105–1000 | [ | |
47 | 3.54 | 5.07 | 5.27 | 3.74 | 3.34 | 6.56 | 170–500 | [ | |
8 | 3.11 | 7.52 | 5.77 | 1.60 | 2.08 | 7.96 | 298–973 | [ | |
9 | 1.99 | 3.64 | 3.42 | 3.04 | 1.80 | 3.59 | 200–600 | [ | |
14 | 2.45 | 5.87 | 4.93 | 1.85 | 1.42 | 8.25 | 180–1000 | [ | |
| |||||||||
Average | 403* | 3.21 | 6.10 | 6.57 | 1.93 | 2.87 | 9.44 | ||
| |||||||||
Overall | 2597** | 3.09 | 5.06 | 6.92 | 3.15 | 3.31 | 9.19 |
The average RMSDr value between a total of observed and regressed 117 viscosity data for five noble gases was found to be 1.90%, indicating that the present work is quite comparable to the Refprop Database correlations [
Comparison of measured and calculated viscosities for He.
Comparison of measured and calculated viscosities for Ne.
Comparison of measured and calculated viscosities for Ar.
Comparison of measured and calculated viscosities for Kr.
Comparison of measured and calculated viscosities for Xe.
It is mentioned here that for each dilute noble gas at 0.1 MPa pressure, the Refprop Database provides selected viscosity data valid in specific temperature ranges, for example, 4–2219 K for helium, 27–1037 K for neon, 87–2992 K for argon, 119–1124 K for krypton, and 164–1100 K for xenon. In this work, their recommended viscosity data were fitted separately for each substance by least-squares analysis to obtain smoothing functions, usually reciprocal temperature expressions of third order, which were used to represent viscosity data at the same temperature as those of experimental data for the reasonable comparisons. Prediction results from the Refprop correlations are observed to be not in reliable agreement with measured viscosity data, especially near upper and lower limits of temperature ranges specified previously, as shown in Table
The next stage of this work is to calculate other properties such as thermal conductivity and self-diffusion coefficient, not used for parameter determinations, using the same set of potential parameters determined earlier. As shown in Table
Deviations between experimental and calculated thermal conductivities of pure noble gases.
Compound | Number of points | Average RMSDr in |
|
Reference | |||
---|---|---|---|---|---|---|---|
Present study | L-J | Simsci | Refprop | ||||
64 | 7.77 | 10.7 | 2.94 | 3.52 | 70–1000 | [ | |
8 | 2.61 | 5.16 | 0.78 | 1.03 | 298–1010 | [ | |
8 | 2.33 | 4.40 | 1.68 | 1.32 | 298–973 | [ | |
8 | 2.41 | 4.42 | 1.75 | 1.27 | 298–973 | [ | |
27 | 5.04 | 7.95 | 1.09 | 1.81 | 275–725 | [ | |
93 | 6.10 | 9.10 | 7.20 | 20.1 | 20–1000 | [ | |
8 | 2.47 | 4.67 | 1.30 | 0.95 | 298–973 | [ | |
4 | 10.2 | 13.5 | 4.98 | 4.16 | 303–363 | [ | |
2 | 7.72 | 11.2 | 2.35 | 1.25 | 303 | [ | |
25 | 3.66 | 6.21 | 1.41 | 4.52 | 50–973 | [ | |
6 | 4.01 | 6.76 | 1.19 | 1.91 | 100–600 | [ | |
11 | 4.95 | 7.65 | 1.44 | 1.95 | 100–600 | [ | |
Helium | 29 | 6.90 | 9.60 | 2.50 | 2.80 | 80–1000 | [ |
102 | 6.80 | 9.50 | 4.70 | 12.5 | 20–1000 | [ | |
14 | 0.41 | 0.64 | 0.24 | 0.31 | 350–1000 | [ | |
6 | 7.94 | 11.0 | 3.37 | 3.18 | 303–589 | [ | |
52 | 5.90 | 8.60 | 5.50 | 17.4 | 20–1000 | [ | |
5 | 11.0 | 14.0 | 6.88 | 7.20 | 250–600 | [ | |
1 | 5.40 | 8.76 | 0.09 | 1.04 | 596 | [ | |
1 | 7.24 | 10.3 | 1.72 | 0.53 | 291 | [ | |
4 | 10.4 | 13.6 | 5.11 | 4.19 | 308–363 | [ | |
2 | 4.68 | 7.32 | 1.32 | 0.07 | 302–793 | [ | |
1 | 6.33 | 9.56 | 0.92 | 0.09 | 311 | [ | |
1 | 6.57 | 10.0 | 1.20 | 0.08 | 302 | [ | |
13 | 2.16 | 4.39 | 1.06 | 0.29 | 373–973 | [ | |
| |||||||
Average | 495* | 5.90 | 8.59 | 3.94 | 9.47 | ||
| |||||||
8 | 1.52 | 0.62 | 1.07 | 2.91 | 298–973 | [ | |
8 | 2.50 | 1.16 | 0.66 | 3.87 | 298–973 | [ | |
1 | 1.04 | 0.54 | 1.10 | 2.53 | 291 | [ | |
8 | 2.74 | 1.41 | 0.66 | 4.11 | 298–973 | [ | |
29 | 3.50 | 2.53 | 0.94 | 4.11 | 90–1300 | [ | |
44 | 1.36 | 0.86 | 1.65 | 2.40 | 275–1275 | [ | |
111 | 2.83 | 2.65 | 5.95 | 12.7 | 27–1000 | [ | |
8 | 2.55 | 1.17 | 0.76 | 3.92 | 298–973 | [ | |
4 | 1.67 | 3.25 | 2.10 | 0.84 | 303–363 | [ | |
3 | 1.25 | 0.76 | 1.02 | 2.14 | 313–363 | [ | |
Neon | 22 | 2.40 | 1.70 | 2.40 | 4.36 | 50–973 | [ |
6 | 1.81 | 1.34 | 1.09 | 3.25 | 100–600 | [ | |
11 | 1.48 | 3.03 | 2.50 | 2.04 | 100–600 | [ | |
15 | 2.92 | 1.63 | 0.53 | 4.01 | 273–1100 | [ | |
111 | 2.17 | 2.35 | 1.59 | 4.48 | 27–1500 | [ | |
24 | 2.92 | 1.41 | 1.01 | 5.94 | 350–1500 | [ | |
4 | 1.39 | 2.96 | 1.50 | 0.37 | 303–318 | [ | |
1 | 1.36 | 2.90 | 1.53 | 0.14 | 311 | [ | |
1 | 0.20 | 1.39 | 0.32 | 1.73 | 296 | [ | |
1 | 1.04 | 0.53 | 1.11 | 2.54 | 291 | [ | |
2 | 5.86 | 4.27 | 4.28 | 7.50 | 302–793 | [ | |
| |||||||
Average | 422* | 2.41 | 2.08 | 2.63 | 6.20 | ||
| |||||||
21 | 2.09 | 2.72 | 1.07 | 1.00 | 202–394 | [ | |
3 | 2.15 | 3.97 | 0.48 | 5.08 | 90–273 | [ | |
1 | 1.75 | 2.95 | 4.90 | 4.23 | 1373 | [ | |
1 | 0.14 | 4.35 | 1.09 | 2.98 | 291 | [ | |
9 | 1.06 | 5.27 | 0.53 | 1.24 | 298–1124 | [ | |
8 | 1.21 | 5.11 | 0.49 | 1.17 | 298–973 | [ | |
8 | 1.53 | 5.71 | 0.66 | 0.99 | 298–973 | [ | |
8 | 1.48 | 5.66 | 0.77 | 1.09 | 298–973 | [ | |
66 | 1.76 | 4.50 | 1.25 | 1.60 | 90–2000 | [ | |
14 | 2.25 | 6.41 | 2.36 | 2.57 | 331–645 | [ | |
97 | 1.74 | 4.98 | 0.80 | 0.99 | 280–1390 | [ | |
122 | 2.55 | 6.17 | 1.26 | 5.23 | 87–3300 | [ | |
235 | 2.10 | 5.97 | 1.02 | 2.20 | 80–2000 | [ | |
63 | 2.74 | 3.09 | 3.08 | 5.05 | 90–500 | [ | |
63 | 3.82 | 4.80 | 3.40 | 3.53 | 90–500 | [ | |
8 | 1.36 | 5.50 | 0.54 | 1.10 | 298–973 | [ | |
3 | 0.77 | 4.70 | 1.37 | 2.70 | 313–363 | [ | |
Argon | 29 | 2.63 | 5.64 | 2.48 | 7.10 | 50–3273 | [ |
6 | 1.92 | 4.11 | 2.46 | 5.20 | 100–600 | [ | |
11 | 1.65 | 3.37 | 1.39 | 3.07 | 100–600 | [ | |
54 | 2.02 | 5.78 | 1.07 | 2.55 | 80–2000 | [ | |
118 | 1.67 | 4.82 | 1.21 | 2.14 | 88–2500 | [ | |
24 | 1.70 | 6.20 | 0.50 | 0.90 | 350–1500 | [ | |
4 | 2.73 | 3.57 | 1.65 | 0.77 | 273–593 | [ | |
4 | 0.49 | 4.15 | 0.68 | 2.20 | 308–363 | [ | |
3 | 1.08 | 3.52 | 0.21 | 1.81 | 300–340 | [ | |
8 | 0.79 | 4.42 | 1.20 | 2.51 | 295–420 | [ | |
60 | 2.03 | 4.95 | 1.16 | 2.04 | 90–2000 | [ | |
7 | 1.41 | 3.86 | 1.09 | 1.43 | 250–1000 | [ | |
1 | 1.40 | 3.19 | 0.25 | 1.52 | 311 | [ | |
1 | 1.14 | 3.41 | 0.06 | 1.93 | 296 | [ | |
4 | 0.50 | 4.15 | 0.67 | 2.20 | 308–363 | [ | |
2 | 3.10 | 7.10 | 2.40 | 2.70 | 302–793 | [ | |
1 | 1.40 | 3.20 | 0.25 | 1.52 | 311 | [ | |
22 | 1.46 | 4.21 | 0.84 | 3.31 | 87–1000 | [ | |
| |||||||
Average | 1089* | 2.11 | 5.22 | 1.31 | 2.82 | ||
| |||||||
Krypton | 9 | 1.90 | 14.8 | 0.82 | 2.93 | 298–1149 | [ |
8 | 1.80 | 14.8 | 0.88 | 3.10 | 298–973 | [ | |
8 | 1.65 | 15.1 | 1.24 | 3.44 | 298–973 | [ | |
18 | 3.20 | 19.5 | 4.18 | 6.57 | 125–1300 | [ | |
5 | 4.88 | 10.6 | 1.94 | 0.94 | 291–318 | [ | |
101 | 2.33 | 14.0 | 1.71 | 3.19 | 119–1900 | [ | |
6 | 3.12 | 13.4 | 2.25 | 3.45 | 100–600 | [ | |
235 | 2.60 | 15.5 | 2.50 | 4.50 | 80–2000 | [ | |
51 | 2.50 | 12.5 | 0.96 | 2.50 | 125–500 | [ | |
8 | 1.75 | 14.9 | 1.10 | 3.28 | 298–973 | [ | |
3 | 0.81 | 15.5 | 3.68 | 5.50 | 313–363 | [ | |
27 | 3.50 | 14.6 | 2.70 | 7.74 | 50–2273 | [ | |
10 | 4.62 | 10.8 | 2.46 | 0.64 | 150–600 | [ | |
109 | 5.80 | 14.4 | 5.33 | 6.25 | 120–2000 | [ | |
24 | 3.00 | 15.9 | 2.50 | 3.50 | 350–1500 | [ | |
5 | 5.76 | 9.80 | 2.67 | 0.78 | 303–318 | [ | |
4 | 4.24 | 11.3 | 1.35 | 1.06 | 308–363 | [ | |
1 | 4.38 | 11.0 | 1.30 | 0.65 | 311 | [ | |
1 | 4.16 | 10.9 | 1.17 | 0.81 | 291 | [ | |
4 | 4.21 | 11.3 | 1.34 | 1.11 | 308–363 | [ | |
2 | 4.06 | 17.4 | 5.03 | 6.98 | 302–793 | [ | |
| |||||||
Average | 639* | 3.22 | 14.7 | 2.70 | 4.35 | ||
| |||||||
7 | 1.29 | 14.2 | 9.68 | 2.32 | 202–298 | [ | |
8 | 3.28 | 14.2 | 2.65 | 1.43 | 298–973 | [ | |
24 | 7.30 | 17.7 | 1.02 | 4.55 | 175–1300 | [ | |
1 | 3.53 | 12.7 | 0.60 | 1.95 | 291 | [ | |
1 | 3.36 | 12.6 | 0.77 | 1.78 | 291 | [ | |
134 | 5.36 | 15.7 | 5.80 | 10.1 | 165–5000 | [ | |
230 | 4.87 | 15.3 | 4.83 | 1.96 | 105–2000 | [ | |
47 | 3.33 | 12.0 | 2.10 | 0.71 | 170–500 | [ | |
8 | 3.29 | 14.2 | 2.64 | 1.43 | 298–973 | [ | |
4 | 3.39 | 13.1 | 0.57 | 2.48 | 303–363 | [ | |
Xenon | 3 | 8.35 | 17.6 | 4.75 | 7.55 | 313–363 | [ |
29 | 5.84 | 14.9 | 8.18 | 2.90 | 50–3273 | [ | |
6 | 5.50 | 12.8 | 5.96 | 2.82 | 100–600 | [ | |
9 | 1.46 | 11.2 | 3.60 | 0.92 | 200–600 | [ | |
95 | 6.40 | 16.7 | 1.74 | 3.93 | 165–1500 | [ | |
24 | 8.00 | 19.0 | 1.20 | 5.10 | 350–1500 | [ | |
6 | 4.20 | 7.60 | 7.87 | 5.20 | 303–318 | [ | |
67 | 5.64 | 16.1 | 5.97 | 10.2 | 165–5000 | [ | |
2 | 9.00 | 19.0 | 3.90 | 7.01 | 302–793 | [ | |
1 | 0.80 | 9.10 | 4.95 | 2.06 | 311 | [ | |
1 | 7.30 | 16.3 | 3.43 | 6.00 | 302 | [ | |
| |||||||
Average | 707* | 5.26 | 15.4 | 4.39 | 4.76 | ||
| |||||||
Overall | 3352** | 3.59 | 9.28 | 2.78 | 4.93 |
Like the case of viscosities, the Refprop Database [
Comparison of measured and calculated thermal conductivities for He.
Comparison of measured and calculated thermal conductivities for Ne.
Comparison of measured and calculated thermal conductivities for Ar.
Comparison of measured and calculated thermal conductivities for Kr.
Comparison of measured and calculated thermal conductivities for Xe.
A total of 237 self-diffusion coefficient data were next tested. As shown in Table
Deviations between experimental and calculated self-diffusion coefficients of pure noble gases.
Compound | Number of points | Average RMSDr in |
|
Reference | ||
---|---|---|---|---|---|---|
Present study | L-J | Fuller | ||||
Prediction results | ||||||
| ||||||
Helium | 17 | 4.72 | 2.04 | 10.6 | 50–623 | [ |
7 | 11.0 | 8.44 | 13.1 | 14–296 | [ | |
Average |
|
|
|
|
||
Neon | 29 | 3.36 | 2.25 | 8.07 | 50–3273 | [ |
17 | 6.85 | 4.93 | 13.2 | 77–6000 | [ | |
20 | 4.72 | 2.78 | 6.50 | 295–1219 | [ | |
1 | 4.55 | 7.77 | 5.96 | 293 | [ | |
Average |
|
|
|
|
||
Argon | 29 | 2.87 | 4.70 | 10.9 | 50–323 | [ |
12 | 4.10 | 3.51 | 14.2 | 90–326 | [ | |
Average |
|
|
|
|
||
Krypton | 29 | 4.00 | 13.92 | 9.70 | 50–3273 | [ |
18 | 6.83 | 16.93 | 3.69 | 199–6000 | [ | |
1 | 4.90 | 8.94 | 3.30 | 293 | [ | |
Average |
|
|
|
|
||
Xenon | 29 | 6.27 | 13.9 | 16.2 | 50–3273 | [ |
27 | 6.02 | 16.9 | 13.1 | 194–15000 | [ | |
1 | 1.06 | 7.40 | 17.2 | 293 | [ | |
Average |
|
|
|
|
||
Overall | 237** | 5.03 | 8.73 | 10.7 |
Comparison of measured and calculated self-diffusion coefficients for He.
Comparison of measured and calculated self-diffusion coefficients for Ne.
Comparison of measured and calculated self-diffusion coefficients for Ar.
Comparison of measured and calculated self-diffusion coefficients for Kr.
Comparison of measured and calculated self-diffusion coefficients for Xe.
The same set of potential parameters estimated from pure gas information was applied to predict mixture properties such as second cross-virial coefficient, mixture viscosity, mixture thermal conductivity, and binary diffusion coefficient with no additional parameters.
Table
Deviations between experimental and predicted second cross-virial coefficients of noble gas mixtures.
Mixtures | Number of points | Average RMSD in |
|
Reference | |||
---|---|---|---|---|---|---|---|
Present study | L-J | Dymond et al. | Tsonopoulos | ||||
Mixtures of noble gases | |||||||
| |||||||
Helium-neon | 18 | 2.05 | 5.82 | 0.94 | 9.40 | 15–323 | [ |
23 | 0.66 | 0.54 | 1.72 | 10.6 | 273–3273 | [ | |
Helium-argon | 21 | 2.03 | 0.92 | 0.44 | 6.85 | 90–773 | [ |
23 | 4.90 | 5.71 | 6.37 | 14.8 | 273–3273 | [ | |
Helium-krypton | 15 | 5.66 | 3.49 | 0.99 | 1.84 | 90–323 | [ |
23 | 8.54 | 12.0 | 12.0 | 15.9 | 273–3273 | [ | |
Helium-xenon | 9 | 10.9 | 6.07 | 0.71 | 7.14 | 120–323 | [ |
23 | 15.8 | 19.7 | 23.3 | 21.5 | 273–3273 | [ | |
| |||||||
Average |
|
|
|
|
|
||
| |||||||
Neon-argon | 30 | 1.68 | 34.9 | 1.00 | 7.72 | 84–475 | [ |
23 | 3.15 | 1.15 | 6.69 | 4.71 | 273–3273 | [ | |
Neon-krypton | 48 | 5.15 | 48.6 | 2.76 | 14.3 | 100–475 | [ |
23 | 3.86 | 3.29 | 8.07 | 6.69 | 273–3273 | [ | |
Neon-xenon | 28 | 16.5 | 39.4 | 2.61 | 17.6 | 162–475 | [ |
23 | 10.8 | 7.36 | 18.9 | 12.5 | 273–3273 | [ | |
| |||||||
Average |
|
|
|
|
|
||
| |||||||
Argon-krypton | 50 | 3.26 | 150.3 |
1.82 | 2.51 | 108–695 | [ |
23 | 1.58 | 16.7 | 2.93 | 4.53 | 273–3273 | [ | |
Argon-xenon | 5 | 12.3 | 125.5 | 0.29 | 12.1 | 173–323 | [ |
23 | 4.60 | 23.9 | 30.0 | 5.76 | 273–3273 | [ | |
| |||||||
Average |
|
|
|
|
|
||
| |||||||
Krypton-xenon | 35 | 7.34 | 173.7 | 1.97 | 5.76 | 160–700 | [ |
23 | 2.34 | 42.6 | 3.40 | 4.44 | 273–3273 | [ | |
| |||||||
Average |
|
|
|
|
|
||
| |||||||
Overall | 489** | 5.73 | 45.0 | 6.25 | 9.28 |
Comparison of measured and calculated second cross-virial coefficients for Ar + Kr mixture.
Prediction results of noble gas mixture viscosities are presented in Table
Deviations between experimental and predicted mixture viscosities of noble gas mixtures.
Mixtures | Number of points | Average RMSDr in |
|
Reference | ||
---|---|---|---|---|---|---|
Present study | L-J | Lucas method | ||||
Helium-neon | 87 | 6.24 | 13.6 | 8.85 | 50–3273 | [ |
7 | 2.40 | 4.87 | 3.56 | 291 | [ | |
10 | 1.93 | 4.93 | 4.39 | 293 | [ | |
32 | 1.75 | 4.77 | 8.18 | 298–973 | [ | |
3 | 2.31 | 4.88 | 3.97 | 293 | [ | |
10 | 2.58 | 5.15 | 3.80 | 293–523 | [ | |
11 | 3.36 | 4.82 | 6.98 | 293–523 | [ | |
31 | 2.22 | 4.96 | 3.67 | 20–523 | [ | |
162 | 2.10 | 8.40 | 7.49 | 100–950 | [ | |
Helium-argon | 87 | 4.49 | 7.31 | 4.95 | 50–3273 | [ |
12 | 3.38 | 4.25 | 3.51 | 293–303 | [ | |
11 | 3.75 | 3.66 | 4.78 | 291 | [ | |
58 | 3.84 | 4.07 | 4.76 | 72–192 | [ | |
40 | 2.98 | 6.06 | 3.63 | 298–993 | [ | |
3 | 3.52 | 0.92 | 6.46 | 293 | [ | |
3 | 4.09 | 3.01 | 5.19 | 293 | [ | |
6 | 3.69 | 3.12 | 5.25 | 293–523 | [ | |
16 | 6.72 | 7.04 | 5.47 | 293–523 | [ | |
123 | 1.29 | 5.18 | 3.20 | 100–1500 | [ | |
28 | 3.14 | 3.23 | 4.45 | 298 | [ | |
12 | 1.26 | 2.44 | 4.57 | 300–1100 | [ | |
6 | 3.62 | 0.51 | 7.15 | 298 | [ | |
Helium-krypton | 87 | 4.60 | 9.41 | 13.4 | 50–3273 | [ |
9 | 4.44 | 7.72 | 9.63 | 291 | [ | |
16 | 4.98 | 5.28 | 10.5 | 303 | [ | |
40 | 7.72 | 8.91 | 5.78 | 298–993 | [ | |
135 | 4.07 | 11.8 | 4.94 | 300–1000 | [ | |
Helium-xenon | 87 | 3.85 | 9.63 | 13.9 | 50–3273 | [ |
10 | 3.41 | 6.11 | 19.2 | 291 | [ | |
18 | 2.50 | 8.85 | 13.6 | 298–778 | [ | |
90 | 2.34 | 9.46 | 12.7 | 300–750 | [ | |
| ||||||
Average | 1250* | 3.52 | 8.34 | 8.33 | ||
| ||||||
Neon-argon | 87 | 1.91 | 3.95 | 4.23 | 50–3273 | [ |
6 | 1.24 | 2.80 | 1.60 | 293 | [ | |
36 | 0.66 | 2.15 | 2.85 | 298–973 | [ | |
26 | 3.87 | 4.34 | 4.24 | 72–291 | [ | |
3 | 1.68 | 1.48 | 0.70 | 293 | [ | |
3 | 1.61 | 0.95 | 0.66 | 293 | [ | |
9 | 1.43 | 1.85 | 0.70 | 291 | [ | |
12 | 3.22 | 3.95 | 3.56 | 293–523 | [ | |
16 | 2.56 | 1.59 | 1.14 | 293–523 | [ | |
162 | 0.95 | 4.28 | 2.72 | 100–950 | [ | |
Neon-krypton | 87 | 2.63 | 10.3 | 3.25 | 50–3273 | [ |
9 | 1.28 | 8.04 | 2.44 | 291 | [ | |
40 | 0.85 | 9.63 | 1.60 | 298–973 | [ | |
126 | 0.78 | 10.5 | 1.55 | 300–950 | [ | |
Neon-xenon | 87 | 4.70 | 11.1 | 3.94 | 50–3273 | [ |
8 | 0.85 | 7.30 | 6.42 | 291 | [ | |
12 | 2.46 | 8.69 | 3.74 | 298–773 | [ | |
90 | 4.70 | 10.2 | 3.11 | 300–750 | [ | |
| ||||||
Average | 819* | 2.46 | 8.11 | 2.95 | ||
| ||||||
Argon-krypton | 87 | 2.69 | 10.7 | 3.13 | 50–3273 | [ |
36 | 0.71 | 10.5 | 1.81 | 298–973 | [ | |
8 | 2.20 | 8.40 | 1.76 | 291 | [ | |
189 | 0.97 | 10.8 | 2.30 | 300–1300 | [ | |
Argon-xenon | 87 | 4.07 | 11.3 | 2.84 | 50–3273 | [ |
9 | 0.64 | 8.04 | 4.01 | 291 | [ | |
12 | 1.87 | 9.15 | 1.61 | 298–773 | [ | |
34 | 2.46 | 10.5 | 2.62 | 173–299 | [ | |
189 | 2.71 | 13.2 | 1.42 | 173–1597 | [ | |
| ||||||
Average | 651* | 2.20 | 11.4 | 2.23 | ||
| ||||||
Krypton-xenon | 87 | 3.97 | 14.5 | 2.71 | 50–3273 | [ |
9 | 1.22 | 11.2 | 2.19 | 291 | [ | |
12 | 2.18 | 14.1 | 1.18 | 298–773 | [ | |
90 | 3.52 | 14.7 | 2.98 | 300–750 | [ | |
| ||||||
Average | 198* | 3.53 | 14.4 | 2.72 | ||
| ||||||
Overall | 2918** | 2.93 | 10.6 | 4.05 |
Comparison of measured and calculated viscosities for He + Ne mixture.
Given in Table
Deviations between experimental and predicted thermal conductivities of noble gas mixtures.
Mixtures | Number of points | Average RMSDr in |
|
Reference | ||
---|---|---|---|---|---|---|
Present study | L-J | Wassiljewaa | ||||
Helium-neon | 32 | 9.69 | 12.2 | 5.98 | 298–973 | [ |
7 | 2.30 | 4.68 | 1.59 | 291 | [ | |
138 | 5.62 | 8.08 | 3.14 | 275–1175 | [ | |
12 | 11.2 | 13.9 | 7.17 | 303–363 | [ | |
15 | 8.59 | 11.3 | 3.73 | 350–1050 | [ | |
66 | 7.65 | 10.1 | 4.28 | 50–973 | [ | |
7 | 12.6 | 12.2 | 6.08 | 298 | [ | |
8 | 7.14 | 7.62 | 6.27 | 302–793 | [ | |
Helium-argon | 32 | 15.2 | 14.4 | 10.8 | 298–993 | [ |
20 | 8.61 | 9.59 | 12.1 | 291 | [ | |
4 | 12.9 | 12.2 | 8.31 | 273 | [ | |
138 | 9.00 | 7.94 | 5.22 | 275–1025 | [ | |
15 | 10.8 | 9.46 | 5.98 | 350–1050 | [ | |
66 | 8.16 | 7.22 | 3.91 | 50–973 | [ | |
9 | 9.20 | 8.23 | 4.99 | 298 | [ | |
12 | 12.3 | 11.8 | 7.54 | 308–363 | [ | |
8 | 10.6 | 10.5 | 11.6 | 302–793 | [ | |
5 | 10.3 | 9.99 | 5.79 | 311 | [ | |
4 | 9.21 | 8.76 | 6.80 | 273 | [ | |
Helium-krypton | 6 | 8.47 | 6.24 | 3.27 | 302 | [ |
32 | 9.82 | 6.11 | 4.16 | 298–993 | [ | |
9 | 5.00 | 3.12 | 1.88 | 291 | [ | |
15 | 9.92 | 5.27 | 4.18 | 350–1050 | [ | |
66 | 8.76 | 5.81 | 3.68 | 50–973 | [ | |
9 | 5.39 | 3.09 | 2.29 | 291 | [ | |
16 | 10.1 | 9.50 | 4.52 | 308–363 | [ | |
12 | 6.23 | 5.49 | 4.16 | 302–793 | [ | |
Helium-xenon | 4 | 3.95 | 8.95 | 1.97 | 302 | [ |
16 | 4.57 | 7.00 | 3.52 | 303–363 | [ | |
15 | 1.54 | 4.05 | 2.62 | 350–1050 | [ | |
66 | 7.19 | 8.93 | 4.22 | 50–973 | [ | |
10 | 6.19 | 10.02 | 3.61 | 291 | [ | |
8 | 4.17 | 8.2 | 3.43 | 302–793 | [ | |
6 | 4.35 | 9.3 | 2.24 | 311 | [ | |
| ||||||
Average | 888* | 8.11 | 8.42 | 4.73 | ||
| ||||||
Neon-argon | 32 | 3.82 | 4.91 | 4.91 | 298–973 | [ |
9 | 3.59 | 5.91 | 5.08 | 291 | [ | |
12 | 2.87 | 5.15 | 4.36 | 313–363 | [ | |
24 | 3.51 | 5.70 | 6.54 | 350–1500 | [ | |
87 | 2.65 | 4.62 | 5.34 | 50–3273 | [ | |
11 | 0.84 | 2.23 | 1.17 | 311 | [ | |
8 | 0.77 | 2.64 | 2.12 | 298 | [ | |
8 | 5.22 | 7.33 | 7.34 | 302–793 | [ | |
Neon-krypton | 32 | 1.37 | 4.94 | 2.10 | 298–973 | [ |
198 | 25.7 | 32.2 | 28.1 | 275–1275 | [ | |
12 | 0.97 | 8.51 | 2.26 | 313–363 | [ | |
24 | 15.8 | 23.6 | 19.2 | 350–1500 | [ | |
87 | 3.35 | 7.55 | 2.58 | 50–3273 | [ | |
9 | 4.04 | 5.58 | 1.54 | 311 | [ | |
9 | 3.85 | 5.28 | 2.34 | 291 | [ | |
6 | 6.10 | 10.4 | 6.27 | 302–793 | [ | |
Neon-xenon | 9 | 2.11 | 4.50 | 2.18 | 291 | [ |
12 | 5.24 | 8.08 | 4.49 | 303–363 | [ | |
24 | 4.52 | 7.59 | 5.03 | 350–1500 | [ | |
87 | 4.41 | 5.24 | 2.43 | 50–3273 | [ | |
9 | 1.90 | 4.42 | 2.04 | 291 | [ | |
6 | 6.00 | 8.72 | 6.06 | 302–793 | [ | |
| ||||||
Average | 715* | 9.94 | 13.7 | 11.0 | ||
| ||||||
Argon-krypton | 32 | 1.14 | 10.3 | 2.42 | 298–973 | [ |
9 | 5.65 | 5.02 | 3.31 | 291 | [ | |
24 | 2.11 | 9.69 | 2.51 | 350–1500 | [ | |
87 | 2.73 | 10.1 | 3.32 | 50–3273 | [ | |
6 | 4.70 | 5.58 | 2.46 | 311 | [ | |
8 | 5.77 | 5.28 | 3.58 | 291 | [ | |
12 | 3.52 | 7.30 | 1.50 | 308–363 | [ | |
6 | 3.32 | 13.2 | 5.55 | 302–793 | [ | |
Argon-xenon | 9 | 2.63 | 5.59 | 2.94 | 291 | [ |
8 | 10.5 | 17.1 | 10.0 | 311–366 | [ | |
24 | 1.14 | 8.46 | 1.38 | 350–1500 | [ | |
87 | 3.10 | 8.11 | 2.34 | 50–3273 | [ | |
9 | 2.87 | 5.43 | 3.19 | 291 | [ | |
6 | 3.43 | 10.8 | 3.14 | 302–793 | [ | |
6 | 4.05 | 4.03 | 4.94 | 311 | [ | |
| ||||||
Average | 333* | 2.97 | 8.90 | 2.92 | ||
| ||||||
Krypton-xenon | 5 | 4.42 | 14.9 | 3.91 | 302 | [ |
9 | 1.87 | 12.5 | 1.03 | 291 | [ | |
12 | 7.14 | 18.3 | 7.24 | 313–363 | [ | |
24 | 2.35 | 13.7 | 2.37 | 350–1500 | [ | |
87 | 5.13 | 16.0 | 3.97 | 50–3273 | [ | |
9 | 1.76 | 12.4 | 0.92 | 291 | [ | |
10 | 6.06 | 17.5 | 5.90 | 302–793 | [ | |
| ||||||
Average | 156* | 4.51 | 15.5 | 3.75 | ||
| ||||||
Overall | 2092** | 7.65 | 10.8 | 6.50 |
aWassiljewa equation [
Comparison of measured and calculated thermal conductivities for Ne + Kr mixture.
Included in Table
Deviations between experimental and predicted binary diffusion coefficients of noble gas mixtures.
Compound | Number of points | Average RMSDr in |
|
Reference | ||
---|---|---|---|---|---|---|
Present study | L-J | Fuller | ||||
Helium-neon | 26 | 2.45 | 3.77 | 10.6 | 50–1773 | [ |
7 | 1.04 | 3.09 | 8.31 | 200–673 | [ | |
1 | 5.20 | 1.32 | 12.7 | 1000 | [ | |
5 | 2.01 | 6.19 | 3.52 | 65–295 | [ | |
6 | 3.52 | 1.03 | 9.42 | 298–973 | [ | |
26 | 9.89 | 7.35 | 5.09 | 200–1250 | [ | |
20 | 5.27 | 4.93 | 12.7 | 297–1268 | [ | |
1 | 14.0 | 10.6 | 8.99 | 293 | [ | |
14 | 2.81 | 5.29 | 7.79 | 273–683 | [ | |
Helium-argon | 29 | 2.35 | 2.72 | 7.04 | 50–3273 | [ |
7 | 0.56 | 0.12 | 4.91 | 200–673 | [ | |
1 | 8.91 | 8.18 | 0.77 | 1000 | [ | |
3 | 3.15 | 4.11 | 2.93 | 276–346 | [ | |
8 | 2.78 | 3.57 | 4.06 | 298–498 | [ | |
1 | 1.66 | 2.67 | 0.67 | 298 | [ | |
1 | 0.91 | 0.08 | 1.87 | 298 | [ | |
3 | 3.84 | 3.71 | 2.87 | 287–418 | [ | |
6 | 8.30 | 7.80 | 1.68 | 298–1100 | [ | |
1 | 1.21 | 2.22 | 0.17 | 296 | [ | |
1 | 0.58 | 1.63 | 1.11 | 273 | [ | |
1 | 1.69 | 2.75 | 0.01 | 273 | [ | |
2 | 5.42 | 4.92 | 4.23 | 276–418 | [ | |
4 | 1.37 | 2.84 | 2.76 | 90–400 | [ | |
14 | 2.63 | 2.50 | 2.65 | 251–418 | [ | |
17 | 5.01 | 5.08 | 3.39 | 276–1100 | [ | |
8 | 5.69 | 5.05 | 0.65 | 298–993 | [ | |
26 | 6.02 | 5.59 | 2.13 | 200–1250 | [ | |
21 | 9.66 | 8.79 | 6.62 | 298–1272 | [ | |
84 | 8.65 | 8.68 | 5.25 | 118–4500 | [ | |
Helium-krypton | 29 | 2.60 | 7.00 | 5.51 | 50–3273 | [ |
7 | 2.44 | 5.18 | 6.12 | 200–673 | [ | |
1 | 0.88 | 8.40 | 0.34 | 1000 | [ | |
4 | 14.2 | 17.0 | 18.6 | 111–400 | [ | |
8 | 2.04 | 7.40 | 4.22 | 298–993 | [ | |
26 | 5.12 | 2.86 | 3.41 | 200–940 | [ | |
21 | 5.32 | 12.4 | 8.11 | 307–1274 | [ | |
4 | 3.48 | 4.02 | 6.69 | 273–318 | [ | |
Helium-xenon | 29 | 7.21 | 13.1 | 5.35 | 50–3273 | [ |
7 | 5.13 | 11.8 | 4.80 | 200–673 | [ | |
1 | 11.0 | 17.5 | 2.85 | 1000 | [ | |
4 | 6.21 | 12.6 | 6.93 | 169–400 | [ | |
6 | 1.69 | 8.48 | 3.59 | 298–778 | [ | |
26 | 9.4 | 15.6 | 4.93 | 200–940 | [ | |
21 | 9.96 | 16.3 | 6.65 | 297–1270 | [ | |
8 | 7.6 | 13.5 | 8.01 | 273–394 | [ | |
10 | 2.2 | 8.97 | 2.82 | 220–400 | [ | |
2 | 2.3 | 9.1 | 2.97 | 273–315 | [ | |
| ||||||
Average | 557* | 5.80 | 7.61 | 5.72 | ||
| ||||||
Neon-argon | 29 | 2.03 | 3.08 | 5.38 | 50–3273 | [ |
7 | 1.64 | 2.83 | 2.25 | 200–673 | [ | |
1 | 3.38 | 6.84 | 1.17 | 1000 | [ | |
4 | 2.60 | 3.14 | 3.36 | 90–400 | [ | |
8 | 0.76 | 3.61 | 2.50 | 298–973 | [ | |
5 | 5.42 | 1.66 | 4.03 | 90–473 | [ | |
4 | 2.77 | 1.72 | 2.10 | 273–318 | [ | |
26 | 1.86 | 3.76 | 1.51 | 200–940 | [ | |
20 | 5.89 | 7.29 | 4.91 | 297–1274 | [ | |
1 | 3.21 | 7.39 | 7.77 | 293 | [ | |
19 | 3.15 | 3.25 | 3.52 | 194–680 | [ | |
5 | 5.47 | 0.79 | 1.06 | 277–365 | [ | |
Neon-krypton | 29 | 2.06 | 10.4 | 6.99 | 50–3273 | [ |
7 | 2.31 | 10.4 | 8.25 | 200–673 | [ | |
1 | 0.58 | 12.3 | 4.19 | 1000 | [ | |
4 | 4.37 | 9.32 | 6.83 | 111–400 | [ | |
4 | 6.11 | 7.25 | 6.32 | 273–318 | [ | |
8 | 2.75 | 9.80 | 5.78 | 298–973 | [ | |
26 | 3.73 | 13.0 | 8.44 | 200–940 | [ | |
20 | 5.72 | 9.45 | 5.31 | 269–1270 | [ | |
4 | 6.11 | 7.25 | 6.32 | 273–318 | [ | |
Neon-xenon | 29 | 5.49 | 11.8 | 6.50 | 50–3273 | [ |
7 | 4.82 | 11.9 | 7.49 | 200–673 | [ | |
1 | 6.22 | 13.3 | 3.79 | 1000 | [ | |
4 | 4.09 | 11.1 | 6.82 | 169–400 | [ | |
6 | 2.03 | 9.38 | 4.24 | 298–773 | [ | |
26 | 6.97 | 7.81 | 7.58 | 200–940 | [ | |
21 | 8.96 | 15.5 | 9.15 | 297–1270 | [ | |
4 | 1.14 | 8.37 | 4.82 | 273–318 | [ | |
5 | 5.59 | 12.6 | 9.16 | 275–362 | [ | |
| ||||||
Average | 335* | 4.15 | 8.18 | 5.73 | ||
| ||||||
Argon-krypton | 29 | 3.49 | 7.91 | 10.0 | 50–3273 | [ |
7 | 2.37 | 6.02 | 4.28 | 200–673 | [ | |
1 | 0.08 | 8.05 | 0.37 | 1000 | [ | |
1 | 0.33 | 7.03 | 0.26 | 273 | [ | |
4 | 2.26 | 4.42 | 5.99 | 169–400 | [ | |
8 | 8.60 | 5.25 | 19.2 | 77–600 | [ | |
9 | 4.01 | 7.89 | 3.39 | 199–473 | [ | |
5 | 5.85 | 8.91 | 5.25 | 273–473 | [ | |
4 | 3.85 | 3.69 | 2.98 | 273–318 | [ | |
8 | 1.87 | 8.82 | 3.42 | 298–973 | [ | |
11 | 2.23 | 4.79 | 2.89 | 200–400 | [ | |
26 | 9.30 | 15.3 | 10.6 | 200–940 | [ | |
21 | 2.88 | 9.59 | 4.20 | 300–1274 | [ | |
13 | 3.51 | 7.89 | 3.37 | 199–407 | [ | |
Argon-xenon | 29 | 5.48 | 8.62 | 11.5 | 50–3273 | [ |
7 | 2.46 | 6.39 | 6.68 | 200–673 | [ | |
1 | 7.99 | 13.0 | 3.23 | 1000 | [ | |
2 | 5.72 | 6.25 | 6.34 | 195–378 | [ | |
4 | 2.43 | 5.43 | 10.6 | 169–400 | [ | |
4 | 3.16 | 6.25 | 6.88 | 194–378 | [ | |
6 | 1.86 | 6.41 | 3.16 | 298–773 | [ | |
26 | 5.57 | 9.95 | 4.59 | 200–940 | [ | |
21 | 4.18 | 7.51 | 5.35 | 298–1272 | [ | |
19 | 3.79 | 7.11 | 9.07 | 173–1597 | [ | |
13 | 3.93 | 6.96 | 5.83 | 194–394 | [ | |
| ||||||
Average | 279* | 4.48 | 8.42 | 7.16 | ||
| ||||||
Krypton-xenon | 29 | 4.46 | 7.05 | 12.1 | 50–3273 | [ |
7 | 1.38 | 4.42 | 7.54 | 200–673 | [ | |
1 | 4.70 | 10.5 | 4.63 | 1000 | [ | |
4 | 1.38 | 3.27 | 12.2 | 169–400 | [ | |
6 | 1.10 | 4.72 | 2.88 | 298–773 | [ | |
22 | 7.00 | 11.1 | 7.52 | 297–1270 | [ | |
| ||||||
Average | 69* | 4.49 | 7.70 | 9.27 | ||
| ||||||
Overall | 1240** | 4.98 | 7.95 | 6.24 |
Comparison of measured and calculated binary diffusion coefficients for He + Ne mixture.
The three-parameter Lennard-Jones
For the second virial coefficient calculations of pure noble gases, the three-parameter Lennard-Jones
For mixture property predictions, the same set of potential parameters is applied with no additional parameters. Second cross-virial coefficient data calculated by the present study is less feasible to those of Dymond’s correlations and is in better agreement with the observed data than the original Lennard-Jones
In this work, the empirical approach of adding a temperature-correction parameter to the reduced temperature in the Lennard-Jones
Combinational factor in (
Defined by (
Second virial coefficient (cm3 mol−1)
Diffusion coefficient (cm2 sec−1)
Boltzmann constant, 1.3806488·10−23 (JK−1)
Molecular weight (gram mol−1)
Avogadro constant, 6.022·1023 (mol−1)
Pressure (bar)
Distance between molecular centers of molecules 1 and 2 (Ǻ)
Root-mean-square deviation (cm3 mol−1)
Percent relative root-mean-square deviation, relative (%)
Absolute temperature (K)
Reduced temperature,
Intermolecular potential function
Mole fraction in the gas phase
Defined by (
Defined by (
Defined by (
Depth of the potential well [J]
Viscosity (
Thermal conductivity (mW m−1 K−1)
Collision diameter (Ǻ)
Reduced temperature-correction parameter
Collision integral for diffusion coefficient
Collision integral for viscosity.
This paper was supported by the Konyang University Research Fund, in 2012-2013.