Linking viscosity to equations of state using residual entropy scaling theory

doi:10.21203/rs.3.rs-1977918/v1

Download PDF

Research Article

Linking viscosity to equations of state using residual entropy scaling theory

https://doi.org/10.21203/rs.3.rs-1977918/v1

This work is licensed under a CC BY 4.0 License

You are reading this latest preprint version

In our previous work (J. Chem. Eng. Data 2021, 66, 3, 1385–1398), a residual entropy scaling (RES) approach was developed to link viscosity to residual entropy (a thermodynamic property calculated with an equation of state, EoS) using a simple polynomial equation for refrigerants. Here, we present an extension of this approach to a much wider range of fluids: all pure fluids and their mixtures whose reference EoS and experimental viscosity data are available. A total of 84877 experimental points for 124 pure fluids and 351 mixtures are collected from 1846 references. The investigated pure fluids contain a wide variety of fluids from light gases with quantum effects at low temperatures to dense fluids and fluids with strong intermolecular association. More than 68.2% (corresponding to the standard deviation) of the evaluated experimental data agree with the RES model within 3.2% and 8.0% for pure fluids and mixtures, respectively. Compared to the recommended models implemented in the REFPROP 10.0 software (the state-of-the-art for thermophysical property calculation), if the dilute gas viscosity is calculated in the same way, our RES approach yields similar statistical agreement with the experimental data while having a much simpler formulation and fewer parameters. To use our RES model, a software package written in Python is provided in the supporting information.

Viscosity

Entropy Scaling

Multi-parameter Helmholtz equation of state

Mixture

According to the laws of thermodynamics, with an equation of state (EoS, typically a Helmholtz-energy equation or a pressure-explicit function with the independent variables temperature and density), and an equation for the isobaric heat capacity of the ideal gas, all thermodynamic properties (density, entropy, enthalpy, speed of sound, etc.) of a pure fluid can be calculated. After decades of development, the commonly-used reference thermophysical property software packages (such as REFPROP10.0 [1], TREND 5.0 [2] and CoolProp 6.4.1 [3]) include such reference multi-parameter EoS. These reference EoS were fitted to comprehensive and evaluated experimental data, and some of them have accuracies that only few experimental techniques can achieve, e.g., the EoS of Span et al. [4] for nitrogen yields a relative uncertainty of less than 0.02% in density at atmospheric conditions. Nowadays, some of the most accurate reference EoS (e.g., Span et al. [4] for nitrogen, Wagner and Pruß [5] for water) are used to calibrate new experimental setups, and new experimental data are compared with these accurate reference EoS before publication. Nonetheless, transport properties (such as viscosity, thermal conductivity, and self-diffusion coefficient), are significantly less investigated in terms of both modeling and measurements than thermodynamic properties represented by the accurate reference EoS. Calculating a transport property requires independent equations and the typical calculation uncertainty (k = 2) is in the order of 5% or higher.

In our previous work [6], a residual entropy scaling (RES) approach was developed to link the viscosity of pure refrigerant fluids to the residual entropy (a thermodynamic property obtained from an EoS) using a simple polynomial equation with 4 global parameters and a fluid-specific scaling factor for each pure fluid. In that work, this RES approach yields similar statistical agreement with evaluated experimental data as the recommended models in the REFPROP 10.0, the state-of-the-art for thermophysical property calculation. With the aim of linking viscosity to the accurate reference EoS for additional pure fluids, this work will extend the RES approach to all pure fluids whose reference EoS are available in REFPROP 10.0 and whose experimental viscosity data are available to us. In total, 124 pure fluids are investigated in this work, and some of them, e.g., hydrogen, water, and n-decane, have significantly different thermophysical properties than those of refrigerants. Thus, the simple polynomial equation with 4 global parameters developed in the previous work [6] cannot be used to accurately describe all the 124 pure fluids. A major task in this work is to classify these pure fluids into different groups and obtain global parameters for each group. Subsequently, a mixture model is proposed and compared to experimental data. For this purpose, a comprehensive literature search was carried out. Experimental data of 351 binary mixtures were obtained among the 7626 (= 123 × 124 / 2) possible pairs using the ThermoData Engine (TDE) database version 10 [7], and data of 4 multi-component mixtures were collected from peer-reviewed publications[8, 9]. This work aims to present an alternative reference viscosity model for fluids of industrial importance and the model will be implemented in the TREND software package [2, 10].

The RES approach expresses transport properties in terms of thermodynamic properties, which can be obtained directly from an EoS. Various approaches based on RES have been proposed and verified for viscosity of the Lennard-Jones fluid [11] and hundreds of real fluids (e.g., hydrocarbons, [12–14] refrigerants, [6, 15–17], or other commonly used fluids [18, 19]), as well as thermal conductivity of some real fluids [17, 20–24]. Generalized RES approaches for viscosity of more than 100 pure fluids have been developed by Lötgering-Lin et al. [19] and Dehlouz et al. [25]. Here the approach developed in our previous work [6] is extended and the mixing rule is slightly modified.

The fluid viscosity η is calculated as the sum of the dilute gas viscosity η_ρ◊0(T) and the residual part η_res(s^r):

$$\eta ={\eta }_{\rho 0}\left(T\right)+{\eta }_{\text{res}}\left({s}^{\text{r}}\right)$$

The dilute gas viscosity η_ρ◊0(T) at temperature T of a pure fluid is calculated with the Chapman-Enskog [26] solution of the Boltzmann transport equation, assuming the interactions between molecules can be roughly captured by those of Lennard-Jones (L-J) particles with 12 − 6 potential:

$${\eta }_{\rho 0}\left(T\right)=\frac{5}{16}\sqrt{\frac{m{k}_{\text{B}}T}{\pi }}\frac{1}{{\sigma }^{2}{{\Omega }}^{\left(\text{2,2}\right)*}}$$

where m, in units of kg is the mass of one molecule; k_B = 1.380649⋅10^− 23 J⋅K^− 1 is the Boltzmann constant; σ is the collision diameter of the L-J particle; and Ω^(2,2)* is the reduced collision integral obtained by integrating the possible approach trajectories of the particles. Neufeld et al.[27] gives an empirical correlation of Ω^(2,2)* as a function of temperature as:

$${{\Omega }}^{\left(\text{2,2}\right)*}=1.16145\cdot {\left({T}^{*}\right)}^{-0.14874}+0.52487\cdot \text{e}\text{x}\text{p}(-0.77320\cdot {T}^{*})+2.16178\cdot \text{e}\text{x}\text{p}(-2.43787\cdot {T}^{*})$$

where T^* = k_BT/ε is the dimensionless temperature, and ε/k_B is the reduced L-J pair-potential energy. The non-polynomial terms are neglected in this work as REFPROP 10.0 [1] does. The L-J parameters (σ and ε) in this work were obtained from REFPROP 10.0 as listed in Table S1 in the supporting information (SI).

As introduced by Bell [12, 18], the residual part of viscosity η_res(s^r) can be calculated with:

$${\eta }_{\text{res}}\left({s}^{\text{r}}\right)=\frac{{\eta }_{\text{r}\text{e}\text{s}}^{+}{\rho }_{\text{N}}^{2/3}\sqrt{m{k}_{\text{B}}T}}{{\left({s}^{+}\right)}^{2/3}}$$

$${s}^{+}= -{s}^{\text{r}}/R$$

Here, ρ_N, in units of m^− 3, is the number density; s^r in units of J·mol^− 1·K^− 1 is the molar residual entropy, defined as the difference between the real fluid entropy and the ideal gas entropy at the same temperature and density; and R = 8.31446261815324 J·mol^− 1·K^− 1 is the molar gas constant [28]. In this work, the number density ρ_N and molar residual entropy s^r were calculated with the reference EoS implemented in REFPROP 10.0 [1] using the python CoolProp package 6.4.1 [3] as an interface. The reference EoS for each pure fluid is listed in Table S2 in the SI. The plus-scaled dimensionless residual viscosity ${\eta }_{\text{r}\text{e}\text{s}}^{+}$ is related to the plus-scaled dimensionless residual entropy s⁺ using the following polynomial equations

$$\text{ln}\left({\eta }_{\text{r}\text{e}\text{s}}^{+}+1\right)={n}_{1}\cdot {(s}^{+})+{n}_{2}\cdot {{(s}^{+})}^{1.5} +{n}_{3}\cdot {{(s}^{+})}^{2} +{n}_{4}\cdot {{(s}^{+})}^{2.5}$$

$$\text{ln}\left({\eta }_{\text{r}\text{e}\text{s}}^{+}+1\right)={n}_{\text{g}1}\cdot {(s}^{+}/\xi )+{n}_{\text{g}2}\cdot {{(s}^{+}/\xi )}^{1.5} +{n}_{\text{g}3}\cdot {{(s}^{+}/\xi )}^{2} +{n}_{\text{g}4}\cdot {{(s}^{+}/\xi )}^{2.5}$$

Eq. (6) is for a pure fluid with fluid-specific fitted parameter n_k (k = 1, 2, 3, 4), and Eq. (7) is for a group of pure fluids with global fitted parameters n_gk (k = 1, 2, 3, 4) and a fluid-specific scaling factor ξ for each pure fluid.

To extend the RES model to mixtures, a predictive mixing rule is adopted. The dilute gas viscosity η_ρ◊0,mix is calculated with the approximation of Wilke [29]:

$${\eta }_{\rho 0,\text{m}\text{i}\text{x}}=\sum _{i=1}^{N}\frac{{x}_{i}\bullet {\eta }_{\rho 0,i}}{{\sum }_{j=1}^{N}{x}_{j}\bullet {\phi }_{ij}}$$

with

$${\phi }_{ij}=\frac{{(1+{({\eta }_{\rho 0,i}/{\eta }_{\rho 0,j})}^{1/2}\bullet {({m}_{j}/{m}_{i})}^{1/4})}^{2}}{{(8\bullet (1+{m}_{i}/{m}_{j}\left)\right)}^{1/2}} ,$$

where x_i is the mole fraction of component i and m_i is the mass of one molecule of component i. The mole fraction weighted average m_mix of the components is used to replace the effective mass of one particle m in Eq. (4):

$${m}_{\text{m}\text{i}\text{x}}= \sum _{i}{x}_{i}\bullet {m}_{i}$$

Attempts to use a mass fraction weighted average result in a negligible statistical difference. Then, in contract to our previous work [6], the mole fraction weighted average coefficient n_k,mix is utilised to substitute the parameters n_k in Eq. (6), i.e.,

$${n}_{k,\text{m}\text{i}\text{x}}= \sum _{i}{x}_{i}\bullet {n}_{k,i}$$

where n_k,i (k = 1,2,3,4) are fitted n_k parameters of component i. It is important to note that, only if a pure fluid does not have fluid-specific fitted parameters, the n_k (k = 1, 2, 3, 4) are replaced by n_g1/ξ, n_g2/ξ^1.5, n_g3/ξ², and n_g4/ξ^2.5, respectively.

3.1. Data collection and selection

In total, 51841 experimental (T, p, η) values of 124 pure fluids and 33036 experimental (x, T, p, η) values of 351 mixtures were collected. These experimental data were obtained from approximately 1846 literature sources, detailed citations of which are provided in the Supporting Information – Detailed Plots and References (SI-DPR). The same method as in our previous work [6, 24] to correct a small portion of data from the TDE database (less than 0.1%, mainly due to mistakes in data transfer from original sources to the database), and the same filters to sort out inappropriate data were carried out. A summary of the numbers of literature sources and the numbers of values screened out by each filter for each pure fluid and each mixture are listed in Tables S3 and S4 in the SI, respectively. In total, 6.2% of pure-fluid and 8.9% of mixture data were filtered out. The temperature, pressure (and composition for mixture) ranges of the evaluated data are summarized in both tables as well. For reproducibility, all experimental data except for those exceeding limits of the reference EoSs (one of the filters) are illustrated in ${\eta }_{\text{r}\text{e}\text{s}}^{+}$ vs. s⁺ plots in 124 figures for pure fluids and 351 figures in mixtures in the SI-DPR. The ${\eta }_{\text{r}\text{e}\text{s}}^{+}$ vs. s⁺ points of most pure fluids collapse into a single curve, along with some noise due to the poor quality of certain experimental data. However, for fluids with quantum effects at low temperatures, such as hydrogen, deuterium (D₂) and helium, the ${\eta }_{\text{r}\text{e}\text{s}}^{+}$ vs. s⁺ points do not collapse well. This implies a limitation of the current RES approach: it does not work well for quantum fluids. In additions, one could expect that the RES model would not work for superfluids (e.g., He-4 at 2.17 K), whose viscosity is zero.

3.2. Correlation for pure fluids

In the first step, the fluid-specific n_k parameters in Eq. (6) were obtained for those pure fluids with a sufficient quantity and good quality of experimental data in both liquid and gas phases. The results are listed in Table 1. The method to fit the n_k parameters as well as the global n_g,k parameters to be discussed below is described in our previous work [6]. Then, the classification of the 124 pure fluids was carried out to achieve an ultimate goal: the RES model with the global n_g,k parameters and the fluid-specific scaling factor ξ yields the best statistical agreement with experimental data for each pure fluid while the number of groups was kept as small as possible.

Table 1

Fluid information and the specific fitted parameters
REFPROP fluid name	IUPAC chemical name	Group	ξ	z^a	n₁	n₂	n₃	n₄
13BUTADIENE	buta-1,3-diene	2	1.2808	1	-0.017021	0.222555	0.005860	-0.000968
1BUTENE	but-1-ene	5	0.8358	1	-0.568834	1.260511	-0.530198	0.079007
22DIMETHYLBUTANE	2,2-dimethylbutane	3	0.9673	1	-0.418930	1.432587	-0.754272	0.136166
23DIMETHYLBUTANE	2,3-dimethylbutane	3	1.0367	1	-0.236495	0.611806	-0.167783	0.018056
3METHYLPENTANE	3-methylpentane	5	0.8681	1	-0.319195	1.092907	-0.523287	0.085641
ACETONE	acetone	4	0.9361	1	-0.501124	1.194414	-0.521023	0.079149
ACETYLENE	acetylene	3	0.9987	0
AMMONIA	ammonia	7	0.9131	1	-0.376313	0.720574	-0.249516	0.040922
ARGON	argon	2	0.9467	1	0.259438	-0.351232	0.501277	-0.104356
BENZENE	benzene	4	0.8374	1	-0.382425	0.724804	-0.179889	0.015300
BUTANE	n-butane	3	1.0264	1	-0.259640	0.710755	-0.231108	0.029646
C11	undecane	5	1.0603	1	-0.704023	1.144166	-0.400741	0.047600
C12	dodecane	5	1.1030	1	-0.390227	0.768065	-0.259094	0.030017
C16	hexadecane	5	1.2379	1	-0.251917	0.596410	-0.197091	0.021960
C1CC6	methylcyclohexane	3	0.9780	0
C22	docosane	6	1.1612	0
C2BUTENE	(2Z)-but-2-ene	5	0.8198	1	-0.354195	1.186950	-0.579667	0.097360
C5F12	dodecafluoropentane	5	0.8561	0
C6F14	tetradecafluorohexane	5	0.8883	0
CF3I	trifluoro(iodo)methane	3	0.9398	0
CHLORINE	chlorine	3	0.8843	1	-1.263564	3.099758	-1.676284	0.295784
CHLOROBENZENE	chlorobenzene	4	0.9251	1	-0.300023	0.705398	-0.234565	0.030712
CO	carbon monoxide	2	1.0000	0
CO2	carbon dioxide	3	1.0216	1	0.001398	0.040877	0.250600	-0.075953
CYCLOHEX	cyclohexane	3	0.8970	1	-0.526095	1.671415	-0.897889	0.166776
CYCLOPEN	cyclopentane	3	0.9492	0
CYCLOPRO	cyclopropane	3	0.9563	0
D2	deuterium	1	1.3540	1	0.083331	0.286279	-0.604175	0.519011
D2O	heavy water	8	1.0444	1	-0.825882	1.539515	-0.785343	0.144697
D4	octamethylcyclotetrasiloxane	6	0.8414	0
D5	decamethylcyclopentasiloxane	6	0.8495	0
DEA	diethanolamine	7	1.2999	0
DECANE	decane	5	1.0269	1	-0.435268	0.876185	-0.314288	0.039133
DEE	ethoxyethane	3	1.1519	1	-0.372419	0.768991	-0.244370	0.027608
DMC	dimethyl carbonate	3	1.1864	0
DME	methoxymethane	3	1.0852	1	-0.307048	0.687719	-0.196096	0.019352
EBENZENE	ethylbenzene	4	0.9680	1	-0.629068	1.217427	-0.482740	0.067534
EGLYCOL	ethylene glycol	7	1.2171	0
ETHANE	ethane	3	0.9540	1	-0.128502	0.476311	-0.076977	0.000889
ETHANOL	ethanol	7	1.1358	1	-0.852589	1.441829	-0.642822	0.104060
ETHYLENE	ethene	3	0.9363	1	0.295887	-0.034282	0.109584	-0.018529
ETHYLENEOXIDE	ethylene oxide	3	1.0468	1	-0.056194	0.834574	-0.463712	0.089027
FLUORINE	fluorine	2	1.0619	1	0.025629	0.176291	0.127929	-0.038269
H2S	hydrogen sulfide	7	0.7577	0
HCL	hydrogen chloride	7	0.7266	1	0.542616	-1.177825	1.065538	-0.232856
HELIUM	helium	1	1.6627	0
HEPTANE	n-peptane	5	0.9286	1	-0.315700	0.748377	-0.262970	0.033985
HEXANE	n-hexane	5	0.8918	1	-0.316955	0.778418	-0.275857	0.035942
HYDROGEN	hydrogen	1	1.0116	1	-1.206453	6.976684	-11.044067	5.578522
IBUTENE	isobutene	3	1.0177	1	-0.444833	1.048503	-0.428961	0.066669
IHEXANE	isohexane	5	0.8683	1	-0.532893	1.091236	-0.415373	0.056226
IOCTANE	isooctane	5	0.8326	1	-0.270805	0.893555	-0.372847	0.055506
IPENTANE	isopentane	3	1.0277	1	-1.097359	1.833365	-0.720624	0.099021
ISOBUTAN	isobutane	3	0.9490	1	-0.221993	0.805091	-0.321556	0.051331
KRYPTON	krypton	2	0.9265	1	0.231878	-0.421850	0.703290	-0.194222
MDM	octamethyltrisiloxane	6	0.9024	1	0.028762	0.247080	-0.033094	-0.001855
MEA	monoethanolamine	7	1.1803	0
METHANE	methane	2	1.0232	1	0.140367	-0.046685	0.245800	-0.050594
METHANOL	methanol	7	1.0738	1	0.636480	-0.443842	0.121691	0.006254
MLINOLEA	methyl linoleate	6	1.2573	0
MLINOLEN	methyl linolenate	6	1.2762	0
MM	hexamethyldisiloxane	6	0.8314	1	-0.279651	1.220999	-0.584716	0.086516
MOLEATE	methyl oleate	6	1.1928	0
MPALMITA	methyl palmitate	6	1.0726	0
MSTEARAT	methyl stearate	6	1.1142	0
MXYLENE	m-xylene	4	0.9963	1	-0.544321	1.024103	-0.384918	0.052733
N2O	nitrous oxide	2	1.1498	1	0.238669	-0.888434	1.380744	-0.512840
NEON	neon	2	0.8513	1	-0.053490	0.212844	0.249905	-0.065619
NEOPENTN	neopentane	3	0.8947	1	0.578043	-0.634370	0.533785	-0.110045
NF3	nitrogen trifluoride	3	0.8347	0
NITROGEN	nitrogen	2	1.0026	1	0.189619	-0.254456	0.425706	-0.091456
NONANE	nonane	5	0.9945	1	-0.281994	0.798972	-0.313366	0.042291
OCTANE	octane	5	0.9600	1	-0.805538	1.334348	-0.496366	0.064006
OXYGEN	oxygen	2	0.5852	0
OXYLENE	o-xylene	4	0.9474	1	-0.645048	1.264604	-0.515565	0.074785
PENTANE	n-pentane	3	1.0814	1	-0.284070	0.816025	-0.313464	0.044544
PROPANE	propane	3	0.9720	1	-0.447455	1.043338	-0.410156	0.061797
PROPYLEN	propene	4	0.8216	1	-0.467544	1.248152	-0.571907	0.093538
PROPYLENEOXIDE	2-methyloxirane	3	1.0753	0
PROPYNE	propyne	3	1.0116	0
PXYLENE	p-xylene	4	0.9814	1	-0.502268	0.962573	-0.351675	0.047166
R11	trichloro(fluoro)methane	3	0.9687	1	-0.383059	0.948054	-0.356293	0.052278
R113	1,1,2-trichloro-1,2,2-trifluoroethane	3	0.9528	1	-0.484778	1.163438	-0.477142	0.073278
R114	1,2-dichlorotetrafluoro-ethane	3	0.9748	0
R115	1-chloro-1,1,2,2,2-pentafluoroethane	3	0.9502	1	-0.126314	0.573158	-0.183284	0.027940
R116	hexafluoroethane	3	0.8675	0
R12	dichloro(difluoro)methane	3	0.9783	1	0.046502	0.092489	0.176708	-0.054179
R1224YDZ	cis-1-chloro-2,3,3,3-tetrafluoropropene	3	1.1337	1	-0.247442	0.377731	0.035523	-0.029350
R123	2,2-dichloro-1,1,1-trifluoroethane	3	1.0431	1	-0.254732	0.701225	-0.230030	0.029718
R1233ZDE	trans-1-chloro-3,3,3-trifluoropropene	3	1.1249	0
R1234YF	2,3,3,3-tetrafluoropropene	3	1.0709	0
R1234ZEE	(1E)-1,3,3,3-tetrafluoro1-propene	3	1.0929	1	-0.271954	0.627868	-0.173580	0.017966
R124	1-chloro-1,2,2,2-tetrafluoroethane	3	1.0287	1	-0.792595	1.486421	-0.602246	0.087380
R125	1,1,1,2,2-pentafluoroethane	3	1.0323	1	-0.342489	0.784896	-0.251320	0.030741
R13	chloro(trifluoro)methane	3	0.9871	1	-0.374525	0.896176	-0.322568	0.045587
R1336MZZZ	(Z)-1,1,1,4,4,4-hexafluorobut-2-ene	3	1.1567	1	-0.048441	-0.041878	0.288999	-0.077647
R134A	1,1,1,2-tetrafluoroethane	3	1.0604	1	-0.242200	0.597796	-0.159025	0.016428
R14	tetrafluoromethane	3	0.9927	1	0.065405	0.013901	0.255525	-0.081542
R141B	1,1-dichloro-1-fluoroethane	3	0.9976	0
R142B	1-chloro-1,1-difluoroethane	3	1.0140	1	-0.070931	0.151631	0.175283	-0.056545
R143A	1,1,1-trifluoroethane	3	1.0349	1	-0.100784	0.177178	0.177172	-0.061736
R150	1,2-dichloroethane	3	1.0266	0
R152A	1,1-difluoroethane	3	1.0592	1	-0.252717	0.579230	-0.142847	0.014116
R161	fluoroethane	3	1.0000	0
R21	dichloro(fluoro)methane	3	1.0319	1	-0.368823	0.779720	-0.220997	0.020458
R218	octafluoropropane	3	0.9961	1	-0.413098	0.896325	-0.309494	0.042448
R22	chloro(difluoro)methane	3	1.0347	1	-0.392734	0.942682	-0.364107	0.053545
R227EA	1,1,1,2,3,3,3-heptafluoropropane	3	1.0596	0
R23	trifluoromethane (fluoroform)	3	1.0845	1	-0.328322	0.666185	-0.184776	0.020813
R236EA	1,1,1,2,3,3-hexafluoropropane	3	1.0479	0
R236FA	1,1,1,3,3,3-hexafluoropropane	3	1.0913	0
R245CA	1,1,2,2,3-pentafluoropropane	3	1.0441	0
R245FA	1,1,1,3,3-pentafluoropropane	3	1.0810	1	-0.335358	0.819786	-0.306797	0.045028
R32	difluoromethane	3	1.1175	0
R40	chloromethane	3	0.9944	1	-0.007418	-0.192097	0.514124	-0.145914
R41	fluoromethane	3	1.0000	0
RC318	octafluorocyclobutane	3	0.9804	0
RE245FA2	2,2,2-trifluoroethyl difluoromethyl ether	3	1.1252	0
RE347MCC	1,1,1,2,2,3,3-heptafluoro-3-methoxypropane	3	1.0812	0
SF6	sulfur hexafluoride	2	1.0885	1	0.108901	-0.319451	0.606005	-0.167470
SO2	sulfur dioxide	2	1.3323	1	0.289680	-0.710013	0.661319	-0.137567
TOLUENE	toluene	4	0.9193	1	-0.731827	1.367906	-0.555558	0.080860
WATER	water	8	1.0036	1	-0.669333	1.418565	-0.797172	0.160096
XENON	xenon	2	0.9636	1	-0.489295	1.106419	-0.431597	0.088648
^a The quantity and quality of the experimental data are good (z = 1) or not good (z = 0) enough to fit fluid specific n₁, n₂, n₃ and n₄ parameters.

Ultimately, the 124 pure fluids were classified into eight groups, as given in Table 1 and illustrated in Fig. 1. From groups 1 to 8, the fluids are mainly but not exactly: (1-LG) light gases with quantum effects at low temperatures, mainly hydrogen and its spin isomers and helium; (2-G) gaseous fluids, e.g., the noble gases; (3-LHC) a majority of light hydrocarbons and halogenated hydrocarbons (refrigerants); (4-B) fluids with benzene rings and similar fluids; (5-MHC) medium hydrocarbons and similar fluids; (6-HHC) heavy hydrocarbons and dense fluids; (7-LA) fluids with light intermolecular association among molecules like methanol; (8-SA) fluids with strong intermolecular association among molecules, such as water. Group 3-LHC is intentionally preferred as it contains the largest number of fluids and we prefer to have a global parameter set for as many pure fluids as possible. The global n_g,k parameters for each group are listed in Table 2; the fluid-specific scaling factors in each group are given in Table 1 and illustrated in Fig. 1. Experimental data of each group collapse into the individual global ${\eta }_{\text{r}\text{e}\text{s}}^{+}$ vs. s⁺ curves as shown in Fig. 2; more details can be found in Figures S3 in the SI.

Table 2

Global fitted parameters of each group
Group	n_g1	n_g2	n_g3	n_g4
1	-0.449854	3.219854	-5.298638	2.975827
2	0.101609	-0.156239	0.440241	-0.113646
3	-0.448046	1.012681	-0.381869	0.054674
4	-0.657607	1.1549	-0.437437	0.059896
5	-0.368714	0.764423	-0.261237	0.031913
6	0.645294	-0.186122	0.041308	-0.002865
7	-0.726184	1.369572	-0.652048	0.116681
8	-0.663915	1.401829	-0.780113	0.155976

According to Fig. 1, there is a relation between ξ and s⁺ _crit, the plus-scaled dimensionless residual entropy at the critical point. For example, ξ / s⁺ _crit is roughly a value of 0.7 in group 3, and for a group with heavier components, the value of ξ / s⁺ _crit decreases. This factor is in good agreement with the scaling shown by Bell [13, 30]. Adopting the classification and the rough value of ξ / s⁺ _crit, the RES model could serve as a fully predictive model for other chemically similar pure fluids.

A summary of the relative deviations of the experimental viscosity η_exp from values η_RES calculated with the RES model is shown in Fig. 3, and more details are given in Figures S4 in the SI. For clarity, more detailed plots are provided in 124 figures in the SI-DPR. It is important to note again, fluid-specific n_k parameters are preferred in all calculations in this work and only if they are not available in Table 1, global parameters n_gk are used. As a result, more than 68.2% of the experimental data agree with the RES model within 3.2% (corresponding to the standard deviation). For better reproducibility of this work, a Python package for viscosity calculation using the RES approach is provided in the SI, and sample viscosity calculations for each pure fluid are listed in Table S5 in the SI.

Here we defined average relative deviation (ARD) and average of the absolute value of relative deviation (AARD) of the experimental values η_exp from the model calculations η_RES as:

$$\text{A}\text{R}\text{D}= \frac{{\sum }_{i}^{N}\left[\right({\eta }_{\text{e}\text{x}\text{p},i} - {\eta }_{\text{R}\text{E}\text{S},i})/{\eta }_{\text{R}\text{E}\text{S},i}]}{N}$$

$$\text{A}\text{A}\text{R}\text{D}= \frac{{\sum }_{i}^{N}\left|({\eta }_{\text{e}\text{x}\text{p},i} - {\eta }_{\text{R}\text{E}\text{S},i})/{\eta }_{\text{R}\text{E}\text{S},i}\right|}{N}$$

where N is the total number of the experimental data points for a given fluid. The values of ARD and AARD denote the systematic offset and scatter, respectively, of the experimental data from the model. The ARD for each pure fluid are shown in Fig. 3 and the AARD are listed in Table S3 in the SI. Ideally, ARD should be approximately zero for pure fluids as the RES model for pure fluids is anchored to the experimental data. However, considering the existence of low-quality data and the possible uncertainties due to the modeling of the dilute gas, the absolute value of ARD for only 91 and 113 of the 124 pure fluids are less than 1.0% and 2.0%, respectively. For those with larger ARD, there are either only gas phase data available (e.g., R116, R161, and krypton), conflicting datasets (see the gourd-shaped pattern for isopentane, ammonia, and acetylene in Fig. 3), obviously inaccurate dilute gas viscosity calculation (xenon and butane, deviation plots not converge around zero at zero s⁺ limit, see the figures in the SI-DPR), or very few experimental data available (5 data only for cyclopropane). For pure fluids for which more than 1000 experimental data points are available, the absolute ARD values are generally less than 1.0% and all are less than 2.0%.

We compared the performance of the RES model with the recommended model of each pure fluid implemented in the REFPROP 10.0, short for REFPROP-models. The REFPROP-models are 41 reference correlations [31–66] for 43 pure fluids, the extended corresponding states (ECS) model [67–69] for 77 pure fluids, and the friction theory model [47, 70] for 3 pure fluids; details are documented in Table S2 in the SI. There is no viscosity model for NF₃ in REFPROP 10.0. The REFPROP-models fail in the calculation of very few experimental data (less than 0.38%, exceeding the model limit, see more details in Table S3 in the SI) at the given temperature and pressure. Detailed plots of the relative deviations of the experimental viscosity η_exp from values η_REFPROP calculated with the REFPROP-models for each experimental point are provided in 124 figures in the SI-DPR. The AARD from the experimental data to the RES model and the REFPROP-models are listed in Table S3 in the SI. The RES model yields smaller or equal AARD (i.e., smaller scatter) for 55 pure fluids out of 124 fluids compared to the REFPROP-models; this value becomes 61 out of 124 if the dilute gas viscosity in the RES model is calculated in the same way as the REFPROP-models do (achieved by setting pressure zero using the recommended models in REFPROP).

Additional comparisons were made to the RES approach developed by Lötgering-Lin et al. [19], where the residual entropy is calculated with the PCP-SAFT EoS [71]. The calculations with the PCP-SAFT EoS were carried out with the TREND 5.0 package [2] and the model parameters were obtained from the supporting information of Lötgering-Lin et al. [19]. The generalized RES approach developed by Dehlouz et al. [25] was not compared here as their approach is not yet developed for mixtures and the needed I-PC-SAFT EoS [72] or tc-PR cubic EoS [73] are not available to us. There are 35 pure fluids for which all three models (the REFPROP-models are considered as one model here) can be applied. For a fair comparison, approximately 6% of the evaluated experimental data were further filtered out; these are mainly near the phase boundaries as the PCP-SAFT EoS predicts different phase boundaries than the multi-parameter reference EoS. Relative deviations of the experimental data from the three models are statistically shown in Fig. 4 and detailed plots are given in Figure S4-4 in the SI. The ARD for the 35 fluids are shown in Fig. 4 and the AARD are listed in Table S6 in the SI. Our RES model yields the smallest AARD (i.e., smallest scatter) for 11 pure fluids while that for model of Lötgering-Lin et al. [19] is best for 3 fluids.

3.3. Prediction for mixtures

For mixtures, a predictive mixing rule was used, see section 2. More than 68.2% of the evaluated experimental data agree with the RES model within 8%. A summary is provided in Fig. 5 showing the ARD (systematic offset) and AARD (scatter) from the experimental data to the RES model for binaries among two groups. For binaries from the same group, the absolute value of ARD is generally less than 2%; in particular, the ARD is only − 0.4% for binaries within group 3 (4856 experimental data). For binaries from different groups, some are very good, e.g., 1982 data from groups 1 and 2 having an ARD of -1.2%, while some are relatively poor, e.g., 3368 data from groups 7 and 8 with an ARD of 17%. There seems to be problems in the EoS for the residual entropy calculations of binaries from groups 7 and 8 (e.g., Ethanol + Water), as will be discussed in the next paragraph, the REFPROP-models which also rely on the EoS fails in most of the calculations for binaries from groups 7 and 8. Regarding asymmetric mixtures of industrial interest, such as refrigerants with lubricants (respectively in group 3 and possibly group 6), and hydrogen with heavy hydrocarbon (groups 1 and 5 or 6) [74], very few experimental data are available. Therefore, Fig. 5 reveals an AARD clearly beyond 10% for groups 3 and 6, and for groups 1 and 5 or 6, the AARD cannot be calculated (no data available).

We first compared the performance of the RES model and REFPROP-models in mixture prediction. Sample viscosity calculations using both RES model and REFPROP-models for each group pairs are listed in Table S7 in the SI. Please note, there are up to four additional binary interaction parameters for each binary in the ECS model (the most commonly adopted model in REFPROP-models), and these parameters are fitted to the available experimental data or otherwise are set to zero. Table S4 in the SI indicates which binary mixtures have binary interaction parameters fitted in the ECS model. The REFPROP-models fail to calculate 21% of the evaluated experimental data at the given temperature and pressure, mainly belonging to binaries including group 7 and group 8, see details in Table S4. After removing these data, statistical results compared to the experimental data are shown in the bottom line of Fig. 5 and listed in Table S4 in the SI. More detailed plots are illustrated in 351 figures in the SI-DPR for each mixture. According to Table S4, the RES model yields lower AARD (scatter) for 161 mixtures out of all 351 mixtures; this value is 185 out of 351 if the dilute gas viscosity in the RES model is calculated in the same way as the REFPROP-models do. According to Fig. 5, the RES model yields lower AARD (scatter) for 12 group pairs out of 18 group pairs where experimental data are available.

We then added the model of Lötgering-Lin et al. [19] into comparison. Considering that there are only 35 pure fluids for which all three models (the REFPROP-models are considered as one model here) can be applied for, the binary mixtures were narrowed down to only 158. For a fairer comparison, approximately 2.8% of the evaluated experimental data at or near phase boundaries was further filtered out as the PCP-SAFT and the multi-parameter reference EoS predict different phase boundaries. The statistical summary of the comparison from experimental data to the three models are listed in Table S8 of the SI and illustrated for some mixtures in Fig. 6; more similar figures and detailed plots are given in Figures S5 in the SI. According to Table S8, our RES model, the REFPROP-models, and the model of Lötgering-Lin et al. [19] have the best agreement with experimental data for 56, 69 and 33 mixtures, respectively. It is interesting to note that, for some binary mixtures, such as n-pentane + toluene, nonane + n-pentane, n-hexane + p-xylene, and decane + p-xylene (see figures in the SI-DPR) experimental data in the liquid phase have similar deviations with all three models, i.e., the models agree with each other while the experimental data deviate.

In this work, we present a simple but accurate residual entropy scaling (RES) approach for all 124 pure fluids whose reference EoS (implemented in REFPROP) and experimental viscosity data are available in the literature. This RES approach links viscosity to the residual entropy using a simple polynomial equation. More than 68.2% (corresponding to the standard deviation) of the evaluated experimental data agree with the RES model within 3.2% for pure fluids. The pure fluids are classified into 8 groups, and fluids with similar physical properties are roughly in the same group. Experimental data of each group collapse into a global residual viscosity vs. scaled residual entropy curve. There is a relation between the fluid-specific scaling factor and the plus-scaled dimensionless residual entropy at the critical point. According to this and adopting the classification, the RES model could serve as a fully predictive model for other pure fluids. To use our RES model, a software package written in Python is provided; besides please note: fluid-specific fitted parameters should be used, and only if they are not available in Table 1, global fitted parameters are used.

Compared to the recommended models implemented in the REFPROP 10.0, the state-of-the-art for thermophysical property calculation, the RES model yields smaller or equal average of the absolute value of the relative deviation (AARD) from the experimental data for 55 pure fluids out of 124 fluids. If the dilute gas viscosity in the RES model is calculated in the same way as the REFPROP-models do, this value becomes 61 out of 124. A sensitivity analysis shows that, for example, a 1.0% change in the residual entropy yields 0.02% and 1.0% changes in the calculated viscosity in the gas and liquid phases, respectively. Therefore, future developments in the reference EoS, which improve the accuracy in the residual entropy calculation, should significantly improve the accuracy of the RES model, mainly in the liquid phase.

With a predictive mixing rule, more than 68.2% of the evaluated experimental mixture data agree with the RES model within 8%. More sophisticated mixing rules for each group pair might achieve better predictions, which would be our future work. Nonetheless, if dilute gas viscosity is calculated in the same way, the RES approach yields similar statistical agreement with the experimental data as the REFPROP-models, while the RES approach has much simpler formulation and fewer parameters.

Regarding future work, considering that the RES approach links viscosity to an EoS with a simple polynomial global equation and requires no extra parameters for mixtures, one could expect that it has great advantages (less complexity and faster calculation) in industrial applications, such as thermo-economic analysis for refrigerant and organic Rankine cycles. Under certain circumstances, if only liquid viscosity is considered (e.g., as is typical for lubricant oils which are more likely in Group 6) only one extra parameter (the fluid-specific scaling factor) is needed to obtain a reliable viscosity value if an equation of state is available. Therefore, interesting future work will be the exploration of the application of the developed RES model to industrial applications. Besides, in order to achieve a much faster calculation and much easier access to industry, suitable cubic EoS could be evaluated for each pure fluid.

Our next target is to explore the application of our RES approach to a specific group of asymmetric mixtures: light component refrigerants in group 3 mixed with heavy component lubricants which might belong to group 6. Accurate models of these mixtures are extremely important in developing next generation refrigerant systems, however, modeling viscosity of asymmetric mixtures remains a major challenge nowadays [74]. Modeling thermophysical properties of lubricants is demanding itself as commercially available lubricants are all mixtures with components and compositions barely possible to be determined accurately. Traditional thermophysical modelling approaches cannot be used for such lubricants, because these models are generally developed for pure fluids or mixtures with known components and compositions. To tackle this challenge, a novel approach should be developed: assuming each lubricant as a pseudo-pure fluid, characterizing each lubricant with fluid constants (e.g., critical temperature, critical pressure, fluid-specific scaling factor for viscosity, etc.), determining these fluid constants with minimal amount of experiments, and combining this approach to our current RES method.

Acknowledgments

The realization of the project and the scientific work was supported by the German Federal Ministry of Education and Research on the basis of a decision by the German Bundestag (funding code 03SF0623A). The authors gratefully acknowledge this support and carry the full responsibility for the content of this paper.

Authorship contribution statement

X. Yang: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing – original draft, Visualization, Data curation. X. Xiao: Resources, Data curation, Writing – review & editing. M. Thol: Validation, Writing – review & editing. M. Richter: Resources, Writing – review & editing, Funding acquisition. I. H. Bell: Conceptualization, Methodology, Resources, Validation, Writing – review & editing, Supervision.

Supporting Information available

[Python package for residual entropy scaling model calculation]

[Table of names, group and constants of pure fluids]

[Table of reference equation of state and the recommended viscosity model in REFPROP 10.0]

[Table for statistics of the experimental values of pure fluids]

[Table for statistical experimental data summary of fluid mixtures]

[Table for sample viscosity calculations of pure substances with the REFPORP 10.0 and the RES model]

[Table for comparisons of the deviations from experimental data to the three ‘models’]

[Table for sample viscosity calculations of binaries with the recommended models in REFPROP 10.0 and the RES model]

[Table for statistics of the comparison from experimental data to three models for mixtures]

[Figures for viscosity as a function of residual entropy for each group]

[Figures for relative deviation from experimental data of pure fluids to model predictions]

[Figures for relative deviation from experimental data of fluid mixtures to model predictions]

[Detail plots and the reference list of the whole experimental data source]

E. W. Lemmon, I. H. Bell, M. L. Huber, and M. O. McLinden, (2018).
R. Span, R. Beckmüller, S. Hielscher, A. Jäger, E. Mickoleit, T. Neumann, and S. Pohl, (2020).
I. H. Bell, J. Wronski, S. Quoilin, and V. Lemort, Ind. Eng. Chem. Res. 53, 2498 (2014).
R. Span, E. W. Lemmon, R. T. Jacobsen, W. Wagner, and A. Yokozeki, J. Phys. Chem. Ref. Data 29, 1361 (2000).
W. Wagner and A. Pruß, J. Phys. Chem. Ref. Data 31, 387 (2002).
X. Yang, X. Xiao, E. F. May, and I. H. Bell, J. Chem. Eng. Data 66, 1385 (2021).
M. Frenkel, R. D. Chirico, V. Diky, X. Yan, Q. Dong, and C. Muzny, J. Chem. Inf. Model. 45, 816 (2005).
S. Z. Al Ghafri, M. Akhfash, T. J. Hughes, X. Xiao, X. Yang, and E. F. May, Fuel Processing Technology 223, 106984 (2021).
X. Yang, A. Arami-Niya, X. Xiao, D. Kim, S. Z. Al Ghafri, T. Tsuji, Y. Tanaka, Y. Seiki, and E. F. May, J. Chem. Eng. Data 65, 4252 (2020).
R. Span, R. Beckmüller, A. Jäger, E. Mickoleit, T. Neumann, S. Pohl, B. Semrau, and M. Thol, (2022).
I. H. Bell, R. Messerly, M. Thol, L. Costigliola, and J. C. Dyre, J. Phys. Chem. B 123, 6345 (2019).
I. H. Bell, J. Chem. Eng. Data 65, 3203 (2020).
Ian H Bell, J. Chem. Eng. Data 65, 5606 (2020).
M. B. M. Taib and J. P. M. Trusler, J. Chem. Phys. 152, 164104 (2020).
H. Liu, F. Yang, Z. Yang, and Y. Duan, J. Mol. Liq. 113027 (2020).
I. H. Bell and A. Laesecke, in (2016).
X. Wang, E. Wright, N. Gao, and Y. Li, J. Therm. Sci. 1 (2020).
I. H. Bell, Proc. Natl. Acad. Sci. U.S.A. 116, 4070 (2019).
O. Lötgering-Lin, M. Fischer, M. Hopp, and J. Gross, Ind. Eng. Chem. Res. 57, 4095 (2018).
H. Liu, F. Yang, X. Yang, Z. Yang, and Y. Duan, J. Mol. Liq. 330, 115612 (2021).
W. A. Fouad, J. Chem. Eng. Data 65, 5688 (2020).
M. Hopp and J. Gross, Ind. Eng. Chem. Res. 56, 4527 (2017).
M. Hopp, J. Mele, R. Hellmann, and J. Gross, Ind. Eng. Chem. Res. 58, 18432 (2019).
X. Yang, D. Kim, E. F. May, and I. H. Bell, Ind. Eng. Chem. Res. 60, 13052 (2021).
A. Dehlouz, R. Privat, G. Galliero, M. Bonnissel, and J.-N. Jaubert, Ind. Eng. Chem. Res. 60, 12719 (2021).
J. O. Hirschfelder, C. F. Curtiss, R. B. Bird, and M. G. Mayer, Molecular Theory of Gases and Liquids (Wiley New York, 1964).
P. D. Neufeld, A. R. Janzen, and R. A. Aziz, J. Chem. Phys. 57, 1100 (1972).
E. Tiesinga, P. J. Mohr, D. B. Newell, and B. N. Taylor, Journal of Physical and Chemical Reference Data 50, 033105 (2021).
C. R. Wilke, J. Chem. Phys. 18, 517 (1950).
I. H. Bell, S. Delage-Santacreu, H. Hoang, and G. Galliero, J. Phys. Chem. Lett. 12, 6411 (2021).
S. A. Monogenidou, M. J. Assael, and M. L. Huber, J. Phys. Chem. Ref. Data 47, 023102 (2018).
E. W. Lemmon and R. T. Jacobsen, Int. J. Thermophys. 25, 21 (2004).
S. Avgeri, M. J. Assael, M. L. Huber, and R. A. Perkins, J. Phys. Chem. Ref. Data 43, 033103 (2014).
S. Herrmann and E. Vogel, J. Phys. Chem. Ref. Data 47, 013104 (2018).
M. J. Assael, T. Papalas, and M. L. Huber, J. Phys. Chem. Ref. Data 46, 033103 (2017).
M. L. Huber, A. Laesecke, and R. Perkins, Energy Fuels 18, 968 (2004).
X. Y. Meng, Y. K. Sun, F. L. Cao, J. T. Wu, and V. Vesovic, J. Phys. Chem. Ref. Data 47, 033102 (2018).
A. Laesecke and C. D. Muzny, J. Phys. Chem. Ref. Data 46, 013107 (2017).
U. Tariq, A. Jusoh, N. Riesco, and V. Vesovic, J. Phys. Chem. Ref. Data 43, 033101 (2014).
C. D. Muzny, M. L. Huber, and A. F. Kazakov, J. Chem. Eng. Data 58, 969 (2013).
M. L. Huber, A. Laesecke, and H. W. Xiang, Fluid Phase Equilib. 228–229, 401 (2005).
X. Meng, J. Zhang, J. T. Wu, and Z.-G. Liu, J. Chem. Eng. Data 57, 988 (2012).
X. Meng, F. Cao, J. Wu, and V. Vesovic, J. Phys. Chem. Ref. Data 46, 013101 (2017).
E. Vogel, R. Span, and S. Herrmann, J. Phys. Chem. Ref. Data 44, 043101 (2015).
S. B. Kiselev, J. F. Ely, I. Abdulagatov, and M. L. Huber, Ind. Eng. Chem. Res. 44, 6916 (2005).
P. Holland, B. Eaton, and H. J. Hanley, J. Phys. Chem. Ref. Data 12, 917 (1983).
K. A. G. Schmidt, S. E. Quiñones-Cisneros, J. J. Carroll, and B. Kvamme, Energy Fuels 22, 3424 (2008).
V. Arp, R. McCarty, and D. Friend, Thermophysical Properties of Helium-4 from 0.8 to 1500 K with Pressures to 2000 MPa. Tech (Note 1334, NIST, Boulder, 1998).
E. Michailidou, M. J. Assael, M. L. Huber, I. M. Abdulagatov, and R. A. Perkins, J. Phys. Chem. Ref. Data 43, 023103 (2014).
E. K. Michailidou, M. J. Assael, M. L. Huber, and R. A. Perkins, J. Phys. Chem. Ref. Data 42, 033104 (2013).
E. Vogel, C. Küchenmeister, and E. Bich, Int. J. Thermophys. 21, 343 (2000).
H. W. Xiang, A. Laesecke, and M. L. Huber, J. Phys. Chem. Ref. Data 35, 1597 (2006).
F. Cao, X. Meng, J. Wu, and V. Vesovic, J. Phys. Chem. Ref. Data 45, 013103 (2016).
F. Cao, X. Meng, J. Wu, and V. Vesovic, J. Phys. Chem. Ref. Data 45, 023102 (2016).
E. Vogel, C. Kuechenmeister, E. Bich, and A. Laesecke, J. Phys. Chem. Ref. Data 27, 947 (1998).
B. Balogun, N. Riesco, and V. Vesovic, J. Phys. Chem. Ref. Data 44, 013103 (2015).
Y. Tanaka and T. Sotani, Int. J. Thermophys. 17, 293 (1996).
M. L. Huber and M. J. Assael, Int. J. Refrig. 71, 39 (2016).
M. L. Huber and A. Laesecke, Ind. Eng. Chem. Res. 45, 4447 (2006).
M. L. Huber, A. Laesecke, and R. A. Perkins, Ind. Eng. Chem. Res. 42, 3163 (2003).
C. M. Tsolakidou, M. J. Assael, M. L. Huber, and R. A. Perkins, J. Phys. Chem. Ref. Data 46, 023103 (2017).
Z. Shan, S. G. Penoncello, and R. T. Jacobsen, A Generalized Model for Viscosity and Thermal Conductivity of Trifluoromethane (R-23) (American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., Atlanta, GA (US), 2000).
R. A. Perkins, M. L. Huber, and M. J. Assael, J. Chem. Eng. Data 61, 3286 (2016).
S. E. Quiñones-Cisneros, M. L. Huber, and U. K. Deiters, J. Phys. Chem. Ref. Data 41, 023102 (2012).
S. Avgeri, M. J. Assael, M. L. Huber, and R. A. Perkins, J. Phys. Chem. Ref. Data 44, 033101 (2015).
M. L. Huber, R. A. Perkins, A. Laesecke, D. G. Friend, J. V. Sengers, M. J. Assael, I. N. Metaxa, E. Vogel, R. Mareš, and K. Miyagawa, J. Phys. Chem. Ref. Data 38, 101 (2009).
J. C. Chichester and M. L. Huber, Documentation and Assessment of the Transport Property Model for Mixtures Implemented in NIST REFPROP (Version 8.0) (National Institute of Standards and Technology, 2008).
M. L. Huber, Models for Viscosity, Thermal Conductivity, and Surface Tension of Selected Pure Fluids as Implemented in REFPROP V10. 0 (2018).
M. L. Huber and J. F. Ely, Fluid Phase Equilib. 80, 239 (1992).
S. E. Quiñones-Cisneros and U. K. Deiters, J. Phys. Chem. B 110, 12820 (2006).
J. Gross and G. Sadowski, Ind. Eng. Chem. Res. 40, 1244 (2001).
E. Moine, A. Piña-Martinez, J.-N. Jaubert, B. Sirjean, and R. Privat, Ind. Eng. Chem. Res. 58, 20815 (2019).
Y. Le Guennec, R. Privat, and J.-N. Jaubert, Fluid Phase Equilib. 429, 301 (2016).
M. Thol and M. Richter, Int J Thermophys 42, 161 (2021).

No competing interests reported.

Download PDF

Editorial decision: Major revision
21 Aug, 2022
Reviews received at journal
20 Aug, 2022
Reviewers agreed at journal
20 Aug, 2022
Reviewers invited by journal
20 Aug, 2022
Editor assigned by journal
20 Aug, 2022
Submission checks completed at journal
20 Aug, 2022
First submitted to journal
19 Aug, 2022

You are reading this latest preprint version

Linking viscosity to equations of state using residual entropy scaling theory

Status:

Version 1

Abstract

Figures

1. Introduction

2. Theoretical Background

3. Results

3.1. Data collection and selection

3.2. Correlation for pure fluids

3.3. Prediction for mixtures

4. Conclusion, Discussion And Future Work

Declarations

Acknowledgments

Authorship contribution statement

Supporting Information available

References

Additional Declarations

Supplementary Files

Status:

Version 1