Viscosity measurements of R32 and R410A to 350 MPa

Accepted Manuscript Title: Viscosity Measurements of R32 and R410A to 350 MPa Author: Scott Bair, Arno Laesecke PII: DOI: Reference:

S0140-7007(17)30296-7 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.07.016 JIJR 3717

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

5-6-2017 10-7-2017 27-7-2017

Please cite this article as: Scott Bair, Arno Laesecke, Viscosity Measurements of R32 and R410A to 350 MPa, International Journal of Refrigeration (2017), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.07.016. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Viscosity Measurements of R32 and R410A to 350 MPa

Scott Bair George W. Woodruff School of Mechanical Engineering Center for High-Pressure Rheology Georgia Institute of Technology Atlanta, GA 30332-0405, U.S.A. Phone: 1-404-894-3273 Fax: 1-404-385-8535 E-Mail:

Arno Laesecke

Material Measurement Laboratory Applied Chemicals and Materials Division 325 Broadway Boulder, CO 80305-3337, U.S.A. Formatted for submission to Int. J. Refrigeration

Date of this version: July 10, 2017

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Contents 1.

Introduction ............................................................................................................................ 3

2.

Molecular Aspects and Materials .......................................................................................... 3

3.

Falling Cylinder Viscometer .................................................................................................. 6

4.

Results.................................................................................................................................. 10 4.1

Comparison with Literature Data for R32 ............................................................... 11

4.2

Comparison with Literature Data for R410A .......................................................... 12

5.

Data Correlation ................................................................................................................... 14

6.

Concluding Remarks............................................................................................................ 15

7.

Acknowledgment ................................................................................................................. 15

8.

References ............................................................................................................................ 15 Tables and Figures ................................................................................................................19

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Highlights     

Refrigerants pure R32 and in binary mixture with R125 (R410A) Viscosity measurements with falling cylinder viscometer Three temperatures 313.15 K, 348.15 K, 393.15 K with pressures to 350 MPa Comparisons with literature data and models Substantial expansion of known viscosity for these refrigerants

Abstract Viscosity measurements were performed with a falling cylinder viscometer on difluoromethane (R32) and the refrigerant blend R410A (R32+R125 with 50 % by mass) at the temperatures 313.15 K, 348.15 K, and 393.15 K with pressures to 350 MPa. The measurement results are compared with literature data and with data calculated with an extended corresponding states (ECS) model. The agreement with literature data is closer for R410A than for R32 while the deviations from the ECS model are higher for R410A than for R32. Correlations that represent the new results as functions of temperature and pressure within their uncertainty are also reported.

Keywords Binary mixture; Falling body viscometer; molecular interactions; refrigerants; tribology; viscosity.

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1.

Introduction

Even though their production will be phased down [1], hydrofluorocarbons (HFC) will continue to be used as working fluids in vapor compression cycles. Minimizing tribological problems for higher efficiency of such systems requires knowledge of the properties of HFCs not only along the vapor pressure curve but to elevated temperatures and pressures [2]. High temperature – high pressure properties are also needed for use of fluids as supercritical solvents which has been suggested for difluoromethane (CH2F2, R32) [3]. Besides, HFCs are of generic physicochemical interest with regard to their molecular interactions either as pure fluids or as mixtures and viscosity is a property that resolves these interactions with high sensitivity. Viscosity measurements of difluoromethane, CH2F2 (R32), and of the binary mixture of R32 and pentafluoroethane, C2HF5 (R125), at the mole fraction of xR32 = 0.6976 (mass fraction wR32 = 0.5) were carried out in this work at pressures up to 350 MPa and on three isotherms at 313.15 K, 348.15 K, and 393.15 K (40 °C, 75 °C, 120 °C). The refrigerant designation of the mixture is R410A [4]. This report begins with considerations of molecular aspects of the constituent compounds which is followed by a discussion of the sample fluids and their purity. Instruments and measurements are discussed in the second part, followed by the presentation of the results. Comparisons with literature data show how the present results agree with certain other wide-ranging measurements. The report closes with recommendations for future studies.

2.

Molecular Aspects and Materials

Difluoromethane (CH2F2, R32) should be seen in context with other small molecules with unique properties such as water (H2O), ammonia (NH3), or carbon dioxide (CO2). The unique feature of R32 is its polarity which is incompletely characterized by its gas-phase dipole moment of 1.978±0.007 D [5] with 1 debye = 3.335 640 95×10−30 C·m [6]. For comparison, the gas-phase

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dipole moment of water is 1.84 D. A more practical and intuitive indicator of the intermolecular attractions that emanate from polarity is the critical temperature in absolute units of kelvin. That of R32, Tc = 351.255 K [7] is higher than the critical temperature of the other HFC that was involved in the present measurements R125, Tc = 339.173 K [8]. However, while critical temperatures have been used as scale factors for corresponding states methods since 1880 [9], their limitation becomes obvious when substances with similar critical temperatures but different molecular structures are compared. For instance, carbon dioxide (CO2) and ethane (C2H6) have close critical temperatures of 304.1282 K and 305.32 K, respectively, but their other properties differ significantly [10]. A more accurate indicator for the balance between intermolecular repulsions and attractions is the length of the vapor pressure curve, the temperature difference between the critical point and the triple point, Tc – Tt [10]. The reason is that a liquid phase cannot exist when the intermolecular potential does not have an attractive part. Then, the length of the vapor pressure curve is zero. Therefore, the length of the vapor pressure curve is a direct measure for the attractions between molecules. This temperature difference Tc – Tt is 214.92 K for R32 and 166.65 K for R125 (373.936 K for water) thus underscoring the strong attractions between the R32 molecules. For carbon dioxide and ethane the values are 87.54 K and 214.95 K, respectively, indicating stronger repulsions between the carbon dioxide than between the ethane molecules. Significantly more details about molecular interactions are gained from calculating molecular sizes, shapes and charge distributions from first principles [11]. Such quantumchemical calculations were carried out in this work for R32 and of R125. Their objective is to solve the Schrödinger equation which is possible in closed form only for the hydrogen atom. Approximating assumptions are necessary to calculate more complex molecules. Here, density functional theory at the B3LYP theory level with the 6-311** basis set for the wave function was used. Figure 1 shows the resulting structures of R32 and R125 in various orientations at the approximate molar composition of R410A of 7:3. The molecules are shown as isosurfaces of the

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electron density distribution at the value of 0.002 electrons·au-3 (with 1 atomic unit au = 5.292 nm being the Bohr radius of hydrogen). This surface represents approximately 99 % of a molecule. The markers on the surfaces indicate areas that are inaccessible for other molecules of the same species. These areas are directly related to the size and shape-dependent void volumes between molecules. The electrostatic potential is color-mapped onto the isosurfaces from red (negative charge) to blue (positive charge). This indicates the charge distribution in the molecules and their polarity on a common scale for both R32 and R125. The most negative charge of -96 kJ·mol-1 occurs at the two fluorine atoms of R32 and the highest positive charge of 188 kJ·mol-1 is located at the hydrogen atom of R125. Thus, in the mixture R410A these centers of opposite partial charges will attract each other preferably, develop H…F halogen bonds [1214], and introduce more structure in the liquid. The color of the fluorine atoms in R125 indicates that they are less negatively charged than those in R32 while the hydrogens in R32 are less positively charged than that in R125. Nevertheless, the polarity of the pure species induces also structure in these fluids. The particular geometry of R32 favors an interlocking of these molecules [15]. This ordering effect due to electrostatic attractions is an important part of the explanation of why the viscosity of R32 exceeds that of larger non-polar molecules [16]. The effect is less pronounced in R125 because this molecule is larger and the positively charged hydrogen is shielded sterically by the rest of the molecule. Difluoromethane of electronic grade had been obtained at NIST Boulder from a commercial supplier and analyzed by gas chromatography and mass spectrometry. No impurities were detected. The fluid was condensed from the vapor space of a supply cylinder of 26.9 liters internal volume into a laboratory stainless steel cylinder of 150 cm3 volume that had been cleaned and evacuated to 10-7 mm Hg (1.3×10-5 Pa). During the condensation, the laboratory cylinder was cooled with ice water. The filling was stopped when 100 g of difluoromethane had been collected in the laboratory cylinder. The sample was then degassed by fully immersing the laboratory cylinder into liquid nitrogen for 45 minutes to freeze the difluoromethane and

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subsequent vacuum pumping on it. Pumping was stopped when the pressure leveled off at 4.2×10-5 mm Hg (0.0056 Pa). The cylinder was then returned to room temperature to melt the sample. This freezing and pumping cycle was repeated eight more times. The laboratory sample cylinder was then sent to Atlanta (Georgia) where the viscosity measurements were carried out. The R410A sample was obtained from a commercial source at Atlanta (Georgia). It had been used in a previous series of viscosity measurements of refrigerant+lubricants mixtures [17].

3.

Falling Cylinder Viscometer

Falling body viscometers are prevalent in high-pressure work. The use of gravity to provide the shear stress removes the need to power the experiment through the containment vessel and the force provided by gravity is remarkably repeatable. The falling body may be a rolling ball or a falling cylinder. The cylinder falls within a cylindrical tube which is generally arranged so that the pressure is equal inside and outside so that the bore diameter depends on pressure only through the compressibility of the structure. The falling cylinder (sinker) may be guided along the center of the bore by hydrodynamic action [18] or mechanically [19] by lugs arranged circumferentially at each end. Hydrodynamic centering requires that the cylinder fall some distance before the measurement to achieve the centering. With mechanical centering a measurement may begin immediately and may be quite short, as little as 10% of the cylinder length in this case. It is found that polishing the lugs, so the surface of each lug presented to the bore is curved, improves repeatability, an indication of possible hydrodynamic lift at the interface. For the present instrument, a linear variable differential transformer (LVDT) [20] situated outside of the pressure containment vessel constantly detects the sinker position. Useful fall times may vary 1:50,000 for a given cylinder. Changes to the geometry of the cylinder can change the fall velocity by 1:5000. Viscosities ranging over more than 1:108 may therefore be

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measured. The cylindrical sinker (6.35 mm diameter), the hollow cylinder in which it falls, and a volume compensation piston are all contained in a sealed cartridge which is removed from the containment vessel for filling. Modifications to the viscometer described in [21] were necessary for filling the viscometer cartridge under pressure. The filling procedure is also explained in ref [21]. The uncertainty of pressure for the sample liquid including the seal friction of the volume compensation piston is estimated to be the greater of 1 MPa or 0.5 %. Using the equation of state (EoS) for R32 by Tillner-Roth and Yokozeki [7] and the mixture model for R410A as implemented in NIST Standard Reference Database 23 REFPROP, version 9.1 [22] the corresponding uncertainties in density u were calculated at the measured temperatures 313.15 K, 348.15 K, and 393.15 K and pressures up to 350 MPa. Figure 2 illustrates the extrapolation behavior of the EoS for R32 beyond its maximum pressure of 70 MPa. It is physically correct and free from artefacts. The uncertainties are all negligible except for the data at 10 MPa and 348.15 K (R32 -2.2 % ≤ u ≤ 1.9 %, R410A -2.5 % ≤ u ≤ 2.1 %). The uncertainty of the measured temperature is estimated to be 0.4 K, and the temperature can be controlled to within 0.3 K of the target temperature. The working equation for the viscometer is 

 



s 

  C 1 

 t ,

(1)

where the mass density of the liquid and the sinker are  and s (7750 kg·m-3), respectively, and t

is the time interval for the signal from the linear variable differential transformer to change by

100 mV near the terminal end of a fall which can be as much as 6 mm. This change in signal corresponds to a displacement of the cylinder of approximately 1.0 mm. To improve repeatability for these measurements, an enlarged measurement window of 300 mV was utilized for all measurements. The sinker was of the “cup” type with C  1.28 mPa as explained in ref [23].

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Because at the lowest pressures the anticipated viscosities were expected to be less than previously measured in this device, an interesting modification to the sinker was tested. A new “cup” sinker was fabricated with a cup shaped magnesium alloy core surrounded by a 0.28 mm thick sleeve of 430 stainless steel, which is magnetic. The core and sleeve were fastened with a light interference fit. Average density was 3.61 g/cm3. The calibration runs were not repeatable with this sinker. On examination, the steel sleeve had moved with respect to the magnesium core. The cause can be found by comparing the compressibility of magnesium, 0.028 GPa-1, with that of steel, 0.006 GPa-1. The interference vanishes for pressure above 100 MPa. This sinker design has been abandoned. The calibration of the steel “cup” sinker was tested with n-octane and the data of Harris et al. [24] at (25, 50 and 75) °C and at (0.1, 100 and 200) MPa and the data of Caudwell et al. [25] at (25, 50, 75 and 100) °C and at (0.1, 20, 100 and 200) MPa. The percent deviations from the published viscosities showed a dependence on viscosity as seen in Figure 3. There are two limitations to the minimum viscosity which can be accurately measured. First, the terminal velocity must be attained before the measurement window is reached. This limitation is avoided with the present sinker but is reached with faster (larger C) sinkers in low viscosity liquids. The time for rotating the viscometer and locking in the upright position is 0.2 seconds. The equation of motion of the sinker is the solution of a second order differential equation for which all parameters are known. With   0.1 mPa·s, 99 % of terminal velocity is reached in 7 ms after falling 0.06 mm, assuming that the viscometer is inverted instantaneously. Second, operation in the turbulent regime must be avoided or accounted for. The dimensionless Reynolds number characterizes a transition to turbulent flow .

(2)

Here, V is the terminal fall velocity and L is a characteristic length so that Re is inversely proportional to  2 . Different definitions of L have been employed to study the effect of

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turbulence on viscosity obtained with falling cylinder viscometers. With bore diameter, D = 6.35 mm, and sinker diameter, d = 6.137 mm, we have the definition of Lohrenz et al. [26],  D2  d2  ln  D / d    2 = 0.021 mm , 2  D d 

Ld

(3)

the definition of Isdale and Spence [27], L

d

2

= 190 mm ,

Dd

(4)

the definition by various authors [28, 29], L

d

2

= 3.0 mm ,

Dd

(5)

and the definition by Scott [30], L

d



Dd

2



4

D  d 

2

8d

 ... ≈ 3.0 mm .

(6)

Employing the Isdale and Spence definition of L, equation (4), Harris [31] found that his viscometer calibration factor increased by about 1% at Re = 2200. For internal flow, the characteristic length is typically the dimension of the duct in the cross-flow direction, which in this case would be  D  d  2 . However, V is the velocity of the sinker, not the velocity of the liquid. For a “solid” sinker moving in a closed cylindrical bore, the volume flowrate is V

 D2  d 2   u   , 4 4  

d

2

(7)

so that the average liquid velocity, neglecting the velocity of the sinker, is approximately u

d

2

D d 2

2

V .

Now, to write Re as in eq. (2)

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2 2  d d V  D  d  Re   V    2 2 2D  d    2  D  d 

resulting in L 

d

(8)

2

2D  d 

= 1.5 mm.

(9)

Employing this definition, the 1% increase in calibration factor reported by Harris [31] would occur at Re = 17. The percent deviations of the n-octane calibration measurements from published viscosities are plotted vs. Reynolds number in Figure 4.

4.

Results

The measured viscosities for R32 and R410A are listed in Tables 1 and 2, respectively, along with Re numbers calculated with the definition of equation (9). Most of these data were recorded at Re > 17. Therefore, they are likely to carry a systematic uncertainty due to secondary or turbulent flow. There have been many studies of this contribution to the measured viscosity with attempts to develop corrections [26, 29]. However, as long as not even a uniform definition of the Reynolds number has been accepted for such viscometers (see preceding section), it is difficult to quantify this uncertainty. Based on our long-term experience and on the comparisons with literature data in the next two sections we estimate the expanded uncertainties of the results for R32 to be 6 % below a density of 1150 kg·m-3 decreasing to 3 % above. Because the blend R410A has a higher viscosity than R32, smaller expanded uncertainties are estimated for the present results of this fluid. Viscosities below 0.120 mPa·s are considered uncertain to 5 % while the uncertainty of all other viscosities of R140A should not exceed 2.5 %. The viscosity-pressure dependences of the present results are shown in Figures 5 and 6 for R32 and for R410A, respectively. The only literature data for R32 that were not measured at saturation are three isotherms of Assael et al. [32] with a vibrating-wire viscometer in the compressed liquid region up to 20 MPa and six isotherms of Takahashi et al. [33] in the gas

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region up to 10 MPa with an oscillating-disk viscometer. The present measurements overlap only with the literature data of Assael et al. [32] at 10 MPa and 313.15 K and extend the pressure range for the viscosity of R32 by a factor of 17.5. The most wide-ranging literature data for R410A are the measurements of Laesecke [34] with a torsional quartz vibrator viscometer. Included in Figure 6 are data on four isotherms from that study that were not influenced by electroviscous effects. The widest overlap with the present data occurs at 360.7 K between 20 MPa and 64.45 MPa. Thus, the extension of the pressure range for the viscosity of R410A by the present results is only by a factor of 5.4. 4.1

Comparison with Literature Data for R32

A more detailed comparison of the present results with literature data is most suitably performed in terms of density as independent variable. Figure 7 shows percent deviations of selected viscosity data for liquid R32 relative to values that were calculated with the extended corresponding states (ECS) model of Huber et al. [35]. The deviations of the present results pattern in a steadily decreasing trend from 8 % at 906 kg·m-3 to -5 % at 1362.71 kg·m-3. While the deviations at 348.15 K and 393.15 K largely coincide within 2 % over the entire range, the deviations at 313.15 K deviate from this pattern at the three lowest pressures/densities. The data at 50 MPa and 25 MPa deviate by 3.4 % and 1.9 %, respectively, from the ECS model while the viscosity value at 10 MPa deviates by 5.4 %. It is clear that the viscosities at the lowest pressures on each isotherm are burdened with the highest uncertainties due to secondary flow or turbulence. The literature data that are closest to the present results at their lower densities are measurements of Ripple and Matar [36] with a sealed gravitational capillary viscometer with a coiled capillary [37] and the data of Assael et al. [32] that were measured with a vibrating wire viscometer and an estimated uncertainty of 0.5 %. Ripple and Matar [36] corrected their measurement results for the radial acceleration that the liquid experiences in the coiled capillary. However, Laesecke et al. [38] showed that this

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correction was insufficient. They also measured R32 in a sealed gravitational capillary viscometer that Ripple had built with a straight vertical capillary so that radial acceleration does not occur. Their results are systematically lower than those of Ripple and Matar [36] with deviations in Figure 7 ranging between -2 % and 0.7 %. Knowing that the data of Ripple and Matar [36] carry an unaccounted systematic uncertainty, one may conclude that the deviations of the data of Assael et al. [32] between 4.1 % and 5.3 % are also due to an unaccounted systematic uncertainty. This conclusion is also supported by the data of Oliveira and Wakeham [39] who measured saturated liquid R32 with a very similar vibrating wire viscometer than Assael et al. [32]. Their results deviate in the density range of the data of Assael et al. [32] only between -0.7 % and 2.1 %. Figure 7 indicates that the deviations of the remaining literature data for saturated liquid R32 are somewhat more consistent with those of Laesecke et al. [38]. The data of Bivens et al. [40] were correlated by Geller et al. [41]. These authors published another viscosity data set for R32 [42] with slightly different deviations. The increase of their deviations below 900 kg·m-3 to almost 13 % occurs also in the data of Oliveira and Wakeham [39] and those of Sun et al. [43]. Deviations scattering between -3.3 % and 4.5 % are seen for the data that Heide and Schenk [44] determined with a Höppler falling sphere viscometer. Considering the deviations of the viscosity data in Figure 7 and their actual uncertainties it appears that the pressure dependence of the ECS model is too strong at the pressures of the new results reported here. Since the viscosities were measured at the lower range limit of the viscometer, more detailed conclusions cannot be drawn from these results. 4.2

Comparison with Literature Data for R410A

The new viscosities reported here for R410A are between 6 % and 41 % higher than those that were measured for R32. Therefore, they carry less uncertainty due to secondary flow and turbulence than the results for R32. Figure 8 shows percent deviations of selected viscosity data

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for liquid R410A relative to values that were calculated with the extended corresponding states (ECS) model of Huber et al. [35]. The deviations of the present results show a similar patttern as those for R32, however it is more consistent. Above 1200 kg·m-3 the deviations of the three isotherms are within 2 % of each other. Overall, the deviations range from 8.5 % at the lowest pressures to -12.7 % at the highest pressure of 350 MPa at 313.15 K. There are fewer literature data for the viscosity of R410A but they are wider ranging than those for R32. Heide and Schenk [44] measured with the Höppler falling sphere viscometer the saturated liquid of three concentrations of the binary mixture R32 + R125. Their data at the R32 mass fractions of 0.753 and 0.51 agree with the present results within their estimated uncertainty of 2 %. Laesecke [34] measured R410A in two different viscometers to detect electroviscous effects that may occur in the torsional quartz vibrator viscometer (TQV) where the sample is exposed to an electric field alternating at about 39 kHz. The reference instrument was the sealed gravitational capillary viscometer that had also been used for the measurements of R32 [38]. Figure 8 shows that the deviations of the data from the capillary viscometer are consistent with the deviations of the present data at 313.15 K and with the deviations of the data of Heide and Schenk [44] at the mass fractions 0.753 and 0.51. At densities below 1200 kg·m-3 the deviations of the four isotherms that Laesecke measured with the TQV at 340 K, 360 K, 390 K, and 420 K continue the pattern that is formed by the other results above that density. The present results agree particularly well with the TQV-data at 340 K and 360 K with exception of the data points at the two lowest pressures at 393.15 K and the lowest pressure at 348.15 K. These measurements at the lower application limit of the viscometer deviate systematically because of unaccounted effects of secondary flow and turbulence. Systematic deviations are also exhibited by the data of Zhang and He [45] although their expanded uncertainty is reported as ±0.42 %. Above 1100 kg·m-3 the deviations exceed 4 %. In summary, the new results and the literature data for the viscosity of R410A show considerable consistency. Their deviations from values calculated with the ECS model of Huber

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et al. [35] indicate a systematic curvature that is most likely due to the density terms in the viscosity correlation for the reference fluid R134a.

5.

Data Correlation

Similarly as in our previous work [21], the comparisons in the preceding section show that the ECS model of Huber et al. [35] does not extrapolate reliably to the pressures of the present results. It overpredicts viscosities because of the singular character of the free-volume term in the residual viscosity contribution

.

In order to facilitate the accurate use of the present results in engineering calculations, they were correlated by a functional form that is widely considered the most accurate relationship for the slower-than-exponential pressure response occurring for low viscosity liquids. See for example eq. (10) in [25]. This correlating function was proposed by McEwen in 1952 [46] and reads in its isothermal form (10)

Table 3 lists the adjusted parameters of eqs. (10-13) and their associated units so that the viscosity  is obtained in mPa·s with the pressure p in GPa. Here, 0 = ∂ln()/∂p is the slope of the viscosity at p = 0. Of course, this definition involves a fictitious state because the material would be a gas in the limit of zero pressure. The McEwen equation (10) may be modified for temperature by introducing temperature functions in 0, 0, and q. The Andrade equation [47] has been implemented in 0(T) according to ,

(11)

where Ea is the activation energy for flow, R = 8314.4598(48) J(kmol·K)-1 is the universal gas constant [48], and T is the absolute temperature in kelvin. In addition, hyperbolic temperature dependencies were introduced in the parameters 0 and q

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, .

(12) (13)

The regressed parameters are listed in Table 3 with the averages of the absolute relative deviations (AARD) from the experimental data. The measured viscosities of R32 are represented with an AARD of 1.1 % and those of R410A with an AARD of 1.4 %. Both values are well within the estimated uncertainty of the experimental data.

6.

Concluding Remarks

New data for the viscosity of R32 and R410A have been measured at higher pressures than in previous investigations of these fluids. Comparisons with literature data show agreement within the experimental uncertainty and consistency with measurements in capillary viscometers (R32) and with measurements in a torsional quartz vibrator viscometer (R410A). Present correlations do not extrapolate to the pressures of this investigation and can be improved on the basis of the new data. Especially R32 deserves further study because, similar to water (H2O), it is a unique small and polar molecule whose properties correspond due to its size, shape, and charge distribution to those of larger non-polar molecules. The results of this study can be employed to accurately predict film thickness in concentrated contacts [2].

7.

Acknowledgment

Bair was supported in this work by the Georgia Tech Foundation.

8.

References

[1]

D. Coulomb, International milestone agreement on the phase-down of HFC production and consumption in Kigali, Int. J. Refrig., 73 (2017) v-vi.

[2]

S. Bair, W. Habchi, M. Baker, D.M. Pallister, Quantitative Elastohydrodynamic FilmForming for an Oil/Refrigerant System, J. Tribol. (2017) DOI: 10.1115/1.4036171.

Page 16 of 31

16

[3]

X. Han, J. Ke, N. Suleiman, W. Levason, D. Pugh, W. Zhang, G. Reid, P. Licence, M.W. George, Phase behaviour and conductivity of supporting electrolytes in supercritical difluoromethane and 1,1-difluoroethane, Phys. Chem. Chem. Phys., 18 (2016) 1435914369.

[4]

J.M. Calm, G.C. Houhrahan, Refrigerant Data Summary, Engineered Systems, 11 (2001) 74-88.

[5]

C.W. Meyer, G. Morrison, Dipole Moments of Seven Refrigerants, J. Chem. Eng. Data, 36 (1991) 409-413.

[6]

E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, A.J. Thor, IUPAC Green Book on Quantities, Units and Symbols in Physical Chemistry, 3rd Edition, 2nd Printing, Reprint 2008. IUPAC and RSC Publishing, Cambridge, UK, 2008.

[7]

R. Tillner-Roth, A. Yokozeki, An International Standard Equation of State for Difluoromethane (R-32) for Temperatures from the Triple Point at 136.34 K to 435 K and Pressures up to 70 MPa, J. Phys. Chem. Ref. Data, 26 (1997) 1273-1328.

[8]

E.W. Lemmon, R.T. Jacobsen, A New Functional Form and New Fitting Techniques for Equations of State with Application to Pentafluoroethane (HFC-125), J. Phys. Chem. Ref. Data, 34 (2005) 69-108.

[9]

J.M.H. Levelt Sengers, How Fluids Unmix. Discoveries by the School of Van der Waals and Kamerlingh Onnes, Edita, Royal Netherlands Academy of Sciences (KNAW), Amsterdam, 2002.

[10] A. Laesecke, C.D. Muzny, Reference Correlation for the Viscosity of Carbon Dioxide, J. Phys. Chem. Ref. Data, 46 (2017) 013107. [11] W.J. Hehre, A Guide to Molecular Mechanics and Quantum Chemical Calculations, Wavefunction, Inc., Irvine, CA, 2003. [12] B.J.C. Cabral, R.C. Guedes, R.S. Pai-Panandike, C.A. Nieto de Castro, Hydrogen bonding and the dipole moment of hydrofluorocarbons by density functional theory, Phys. Chem. Chem. Phys., 3 (2001) 4200-4207. [13] G.R. Desiraju, P.S. Ho, L. Kloo, A.C. Legon, R. Marquardt, P. Metrangolo, P. Politzer, G. Resnati, K. Rissanen, Definition of the halogen bond (IUPAC Recommendations 2013), Pure Appl. Chem., 85 (2013) 1711-1713. [14] A. Shahi, E. Arunan, Hydrogen bonding, halogen bonding and lithium bonding: an atoms in molecules and natural bond orbital perspective towards conservation of total bond order, inter- and intra-molecular bonding, Phys. Chem. Chem. Phys., 16 (2014) 22935-22952. [15] M. Lísal, V. Vacek, Effective potentials for liquid simulation of the alternative refrigerants HFC-32: CH2F2 and HFC-23: CHF3, Fluid Phase Equilib., 118 (1996) 61-76. [16] A. Laesecke, R.F. Hafer, D.J. Morris, Saturated Liquid Viscosity of Ten Binary and Ternary Alternative Refrigerant Mixtures. Part I: Measurements, J. Chem. Eng. Data, 46 (2001) 433-445.

Page 17 of 31

17

[17] S. Bair, M. Baker, D.M. Pallister, The high-pressure viscosity of refrigerant/oil systems, Lub. Sci., (2017) DOI 10.1002/ls.1374. [18] J.B. Irving, A.J. Barlow, An automatic high-pressure viscometer, J. Phys. E: Sci. Instr., 4 (1971) 232-236. [19] P.W. Bridgman, The Effect of Pressure on the Viscosity of Forty-Three Pure Liquids, Proc. Am. Acad. Arts Sci., 61 (1926) 57-99. [20] E.E. Herceg, Handbook of Measurement and Control: An authoritative treatise on the theory and application of the LVDT, Schaevitz Engineering, 1976. [21] A. Laesecke, S. Bair, High Pressure Viscosity Measurements of 1,1,1,2-Tetrafluoroethane, Int. J. Thermophys., 32 (2011) 925-941. [22] E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Maryland, 2013. [23] S. Bair, F. Qureshi, Accurate measurements of pressure-viscosity behavior in lubricants, Tribol. Trans., 45 (2002) 390-396. [24] K.R. Harris, R. Malhotra, L.A. Woolf, Temperature and Density Dependence of the Viscosity of Octane and Toluene, J. Chem. Eng. Data, 42 (1997) 1254-1260. [25] D.R. Caudwell, J.P.M. Trusler, V. Vesovic, W.A. Wakeham, Viscosity and Density of Five Hydrocarbon Liquids at Pressures up to 200 MPa and Temperatures up to 473 K, J. Chem. Eng. Data, 54 (2009) 359-366. [26] J. Lohrenz, G.W. Swift, F. Kurata, An experimentally verified theoretical study of the falling cylinder viscometer, AIChE J., 6 (1960) 547-550. [27] J.D. Isdale, C.M. Spence, A Self-centering Falling Body Viscometer for High Pressures, NEL Report 592, National Engineering Laboratory, East Kilbride, Glasgow, Scotland, 1975. [28] M. Izuchi, K. Nishibata, A high pressure rolling-ball viscometer up to 1 GPa, Jap. J. Appl. Phys., 25 (1986) 1091-1096. [29] C.J. Schaschke, High Pressure Viscosity Measurement with Falling Body Type Viscometers, Int. Rev. Chem. Eng., 2 (2010) 564-576. [30] R. Scott, The Viscosity of Argon, Ph. D. thesis, Imperial College, University of London, 1959. [31] K.R. Harris, Temperature and Density Dependence of the Viscosity of Toluene, J. Chem. Eng. Data, 45 (2000) 893-897. [32] M.J. Assael, J.H. Dymond, S.K. Polimatidou, Measurements of the Viscosity of R134a and R32 in the Temperature Range 270-340 K at Pressures up to 20 MPa, Int. J. Thermophys., 15 (1994) 591-601. [33] M. Takahashi, N. Shibasaki-Kitakawa, C. Yokoyama, S. Takahashi, Gas Viscosity of Difluoromethane from 298.15 to 423.15 K and up to 10 MPa, J. Chem. Eng. Data, 40 (1995) 900-902.

Page 18 of 31

18

[34] A. Laesecke, Viscosity Measurements and Model Comparisons for the Refrigerant Blends R-410A and R-507A, ASHRAE Trans. Symp., 110, part 2 (2004) 503-521. [35] M.L. Huber, A. Laesecke, R.A. Perkins, Model for the Viscosity and Thermal Conductivity of Refrigerants, Including a New Correlation for the Viscosity of R134a, Ind. Eng. Chem. Res., 42 (2003) 3163-3178. [36] D. Ripple, O. Matar, Viscosity of the Saturated Liquid Phase of Six Halogenated Compounds and Three Mixtures, J. Chem. Eng. Data, 38 (1993) 560-564. [37] D. Ripple, A Compact, High-Pressure Capillary Viscometer, Rev. Sci. Instrum., 63 (1992) 3153-3155. [38] A. Laesecke, T.O.D. Lüddecke, R.F. Hafer, D.J. Morris, Viscosity Measurements of Ammonia, R32, and R134a. Vapor Buoyancy and Radial Acceleration in Capillary Viscometers, Int. J. Thermophys., 20 (1999) 401-434. [39] C.M.B.P. Oliveira, W.A. Wakeham, The Viscosity of R32 and R125, Int. J. Thermophys., 14 (1993) 1131-1143. [40] D.B. Bivens, A. Yokozeki, V.Z. Geller, M.E. Paulaitis, Transport Properties and Heat Transfer of Alternatives for R502 and R22, ASHRAE/NIST Refrigerants Conference, ASHRAE, Gaithersburg, MD, 1993, pp. 73-84. [41] V.Z. Geller, M.E. Paulaitis, D.B. Bivens, A. Yokozeki, Viscosities for R22 Alternatives and Their Mixtures with a Lubricant Oil, in: D.R. Tree, J.E. Braun (Eds.) 1994 International Refrigeration Conference at Purdue, Purdue University, West Lafayette, IN, 1994, pp. 49-54. [42] V.Z. Geller, M.E. Paulaitis, D.B. Bivens, A. Yokozeki, Viscosity of HFC-32 and HFC32/Lubricant Mixtures, Int. J. Thermophys., 17 (1996) 75-83. [43] L.-Q. Sun, M.-S. Zhu, L.-Z. Han, Z.-Z. Lin, The Viscosity of Difluoromethane and Pentafluoroethane along the Saturation Line, J. Chem. Eng. Data, 41 (1996) 292-296. [44] R. Heide, J. Schenk, Bestimmung der Transportgrößen von HFKW, Heft 1 Viskosität und Oberflächenspannung, Forschungsrat Kältetechnik e. V., Frankfurt am Main, Germany, 1996. [45] Y. Zhang, M. He, Kinematic Viscosity of R410A and R407C Refrigerant-Oil Mixtures in the Saturated Liquid Phase with Lubricant Mass Fraction in the Range of (0 to 0.0001), J. Chem. Eng. Data, 55 (2010) 2886-2889. [46] E. McEwen, The Effect of Variation of Viscosity with Pressure on the Load-Carrying capacity of the Oil Film between Gear-Teeth, J. Inst. Petroleum, 38 (1952) 646-672. [47] E.N. da C. Andrade, The Viscosity of Liquids, Nature, 125 (1930) 309-310. [48] P.J. Mohr, D.B. Newell, B.N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2014, J. Phys. Chem. Ref. Data, 45 (2016) 043102.

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Figure 1:

Molecular sizes, shapes, and charge distributions of R32 and of R125 at the approximate composition of R410A with the mole fraction x = 0.7 of R32. See text for explanations. ....................................................................................... 21

Figure 2:

Extrapolation behavior of equation of state of R32 by Tillner-Roth and Yokozeki [7] at the pressures and temperatures of the present measurements. ................................................................................................................. 22

Figure 3:

Deviations of the present n-octane measurements from the viscosity correlations published by Harris et al. [24] and Caudwell et al. [25] versus viscosity. .............................................................................................................. 23

Figure 4:

Deviations of the present n-octane measurements from the viscosity correlations published by Harris et al. [24] and Caudwell et al. [25] versus Reynolds number. ................................................................................................ 24

Figure 5:

Viscosity data for R32 measured in this work together with data at 273.15 K, 293.15 K, and 313.15 K of Assael et al. [32] and from 298.15 K to 423.15 K of Takahashi et al. [33]. Lines are drawn to guide the reader. .............................................................................................................................. 25

Figure 6

Viscosity data for R410A measured in this work together with data of Laesecke [34] at 340 K, 360 K, 390 K, and 420 K. Lines are drawn to guide the reader. .............................................................................................................. 26

Figure 7:

Percent deviations of the present results and of literature data from the extended corresponding states model (ECS) for the viscosity of R32 of Huber et al. (2003) [35] as implemented in REFPROP. Data series without temperature labels refer to saturated liquid. Lines are drawn to help the reader discern the deviations of some data series. ............................................ 27

Figure 8:

Percent deviations of the present results and of selected literature data from the extended corresponding states model (ECS) for the viscosity of R410A of Huber et al. (2003) [35] as implemented in REFPROP. Lines are drawn to help the reader discern the deviations of some data series. ....................... 28

Figure 9:

Representation of the measured viscosities of R32 with the McEwen model eqs. (10-13) and the parameters in Table 3. ......................................................... 29

Figure 10: Representation of the measured viscosities of R410A with the McEwen model eqs. (10-13) and the parameters in Table 3. ......................................................... 30

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Table 1. Measured Viscosities and Reynolds numbers of R32. R32 Viscosities in mPa·s t / °C p / MPa  10 25 50 100 150 250 350

40

75

0.115 0.132 0.162 0.212 0.249 0.327 0.407

0.105 0.131 0.176 0.209 0.278 0.345

Re 120

40

75

120

0.102 0.141 0.172 0.227 0.285

102 77 52 30 22 13 8

123 78 43 31 18 11

129 68 46 26 17

Table 2. Measured Viscosities and Reynolds numbers of R410A. R410A Viscosities in mPa·s t / °C p / MPa  10 25 50 100 150 250 350

40

75

0.122 0.152 0.190 0.255 0.315 0.443 0.573

0.115 0.150 0.206 0.259 0.355 0.465

Re 120

40

75

120

0.096 0.119 0.171 0.213 0.296 0.381

91 59 37 21 14 7 4

102 60 32 20 11 6

147 96 46 30 15 9

Table 3. Fitted parameter values for the McEwen model eqs. (10-13) to represent the measured viscosities of R32 and R410A. Material R32 R410A

0 / mPa∙s

0.01006 6.009106

0.011756 5.751106

13.76

15.70

a1 / (K∙GPa )

37.10

-21.11

d0

1.156

1.087

d 1 /K

-160.7

-88.85

-1

E a / (J·kmol ) -1

a 0 / GPa

-1

AARD (see text)

1.1%

1.4%

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Figure 1:

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22

Figure 2:

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Deviation from Published Viscosity

6% 4%

n-octane

2% 0% -2% -4% -6% Harris et al., 1997

-8%

Caudwell et al., 2009

-10%

0

0.5

1

1.5

2

2.5

Viscosity / mPa·s Figure 3:

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Deviation from Published Viscosity

24

6%

n-octane

4% 2% 0% -2% -4% -6%

Harris et al., 1997

-8%

Caudwell et al., 2009 -10%

0.1

1

10

100

Reynolds Number Figure 4:

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Figure 5:

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Figure 6

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Figure 7:

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Figure 8:

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Figure 9:

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Figure 10:

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