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Viscosity of argon and of argon- mixtures under Title pressures

Author(s) Hongo, Masaru

The Review of Physical of Japan (1979), 48(2): 63- Citation 71

Issue Date 1979-02-10

URL http://hdl.handle.net/2433/47064


Type Departmental Bulletin Paper

Textversion publisher

Kyoto University The Review of Physical Chemistry of Japan Vol. 48 No. 2 (1978)

THE REVIEN` Or PHYSICAL CHEMISTPY OY JAPA:.', Vni. 48, No. 2, 3978 fi3




The viscosity of argon and of four argon-ammonia gaseous mixtures was measured using an oscillating disk viscometer at temperatures, 25, 50, 75, and 100°C; for argon, at the pressure range up to about 120x10s Ya; and for argon-ammonia mixtures, up to around the saturated of ammonia at each temperature. The accuracy of the measurements was estimated to be within t0.3po. The viscosity values of dilute binary mixtures were calculated by applying a correction factor, which was set up by use of critical compressibility factors. The calculated values were in better agreement with the experimental ones than those calculated by original Chapman-Enskog's method. The initial dependence of the viscosity, qo t (3q/8p) o--s, of argon-ammonia mixtures was obtained from [be experimental values, and [be e6ec[s of [be concentra- tion of nonpolar and of temperature on the initial density dependence were com- pared with [hose id the case of the -ammonia system and of the -am- monia system, where q is viscosity of gas, p densfty, and pa the viscosity extrapolated to zero density. It was concluded from the comparison that molecular association of polar gases was hindered by the presence of nonpotar and by a rise in tem- perature, and that the larger the molecular weight of a nonpolar gas was, the more strongly the nonpolar molecules hindered moecnlar association of polar substances, By taking into account the mole fraction of nonpolar gases, the initial density de- pendence of [he viscosity could be correlated with the temperature reduced by the cri[i- tal temperature of [he mixtures, and a similar tendency was observed regardless of the system.


This study is one of the researches to measure the gas viscosity of nonpolar-polar mixtures con- taining ammonia as a polaz gas under pressures. The viscosities of the nitsogea-ammonia systemll and of the hydrogen-ammonia system'] were akeady determined, and the viscosities of azgoa and of argon-ammonia mixtures are presented in this paper In order to investigate the effect o[ the molec- ular weight of a nonpolar gas on the viscosity of a polar gas, argon was used because its moleculaz weight is lagger than that of nitrogen. The viscosity of the argon-ammonia system under pressures was measured by Iwasaki et al.a1 using as oscillating disk viscometer, but only at 20 and 30°C. The viscosity at atmospheric psessure was measured by Chakraborti et al.+~ (25 to 80°C)using a capillary-

(Received September 30, ]978) + Presented in part at The 18th High Pressure Conference, Kyoto, Nov. 25th. 19i7 1) M. Hongo and H. Iwasaki, This lourna{ 47, 90 (1977) 2) M. Hongo and H. Iwasaki, ibid., 48, 1 (1978) 3) H. Iwasaki, J. Restin, and A. Nagashima, J. Cltem. Phys., 40, 2988 (1964) 4) P.K. Chakraborti and P. Gray, Trans. Aaraday Sa., 61, 2422 (196>) The Review of Physical Chemistry of Japan Vol. 48 No. 2 (1978)

64 ]1. Aongo

flow viscometer and by Rakshit et als> (-35 to 35°C) by [he use of an oscillating disk viscometer. In this study, the measurements of the viscosity of azgon-ammonia mixtures were performed on a precision oscillating disk viscometer, which w•asthe same as that previously usedr•z>,at temperatures of 25, 50, i 5, and 100°C, and Deer the range of pressure up to about 120 x IOs Pa for azgon and up to around the saturated vapor pressure of ammonia at each temperature for argon-ammonia mixtures. The mole fractions of argon in the mixtures were approximately 0.2, 0.4, 0.6, and 0.8.

Experimental Method and Calculation of Viscosity

The gas viscosity was evaluated by the same method as that used by Iwasaki et als> The em- pirical value Cs' of the apparatus Constant. Cx, required for the evaluation of the viscosity was deter- mined by the calibration measurements which were made using nitrogen at temperature of 25°C and at pressures below 25 X lOs Fa. The value of Cx' obtained from the calibration measurements was 1.1355 from 25 to 75°C, and 1.1378 at 100`C. The density of azgon was obtained through the PV-values by Michels et al.r> and that of argon- ammonia mixtures was evaluated from the l'ri-chartel in the same way as that used in the previous papersl•~, where Vri is the ideal reduced molar volume. Argon was supplied from the Nippon Co., Ltd. and its purity was above 99.994%. Am- monia was purified through as described beforer>. The experimental accuracy was estimated to be within -*0.3%.


The viscosity values obtained for argon ate shown in Table 1 and plotted as a viscosity vs. density diagram is Fig. 1. The deviations of [he measured viscosity values from the smoothed turves aze all within -*0.2%. The slopes of the viscosity isotherm, (or/8p) r, are always positive and almost the same is the experimental conditions, where r/ is viscosity of gas and p is density. The viscosity of azgon under pressures, so iar, was measured by Michels et afsl from 0 to 75°C below 2000 x IO° Pa; by Iwasaki et at.lo> from 25 to 150`C up to 130x 1G°Pa; by Flynn et al.ll> from-78 [0 100°C below 200 x 10° Pa; by Reyaes et al.~> from 100 to 200`C up to 830 X lOs Pa; and by Gracki et al.ls> from -100 to 25°C below 170x 10° Pa. These measurements were made using a capillazyAow viscometer, except 3) A.B. Rakshit, C.S. Roy, and A.K. Barua, l: Chem.Pbys., 59, 3633 (1973) 6) H. Iwasaki and J, Restin, Phyrica,29, 1345 (1963) 7) A. ]lichels, Hub. NWijkerand Ak. 1Yijker,ibid., I5, 627 (1949) 8) K. Satoh, "Bussei Josu Suisaaho", ]iazuzen, Japaa (1954) 9) A. ]Iichels, A. Botzen and N. Schuurman, Physito. ]A. 1141 (1931) ID) H. Iwasaki and H. Takahashi, Bull. Chem.Res. Inrt. Non.aqueoas Solutionr, Tohoka Lbiv., 6,61 (1916) 11) G.P. Flynn, R.V. Hanks, N.A. Lemaire, and J, Ross, !. Chern.Phys„ 36, 154 (1963) 12) E,G. Reynes and G. Thodos, Plrysica,30, 1529(1964) 13) J.4. GracL•i,G.P.Plynn and J. Ross, !. Chern.Phys., 51, 3856 (1969) i The Review of Physical Chemistry of Japan Vol. 48 No 2 (1978)

Viscosity of Argon and of Argon-Ammonia Mirtures under Pressures 65

Ta61e 1 Viscosity o5 argon

Pressure Density Viscwity Pressure Density Viscosity lOS Pa tOskg•m-s 10-~ Pa•s IOS Pa l0;kg•m 3 10-~Pa•s

zs°c ]s°c

1.23 o.oolsJ 2zs.1 1.2E C. 9a1]3 z ss.s 1.4J 0.00" 3E 226.6 1.26 o. ao193 25fi.6 z.sz o,aooos z 2s.J 2.03 C. ev ns 26fi .4 s.e6 O.CDe12 226.8 5,17 o. 9D]1D 25].0 5.12 0.00922 226.9 10.11 0. 91388 25].5 lu._s 0.01632 2z e.l 2 D. 37 0. 92815 259.] 10.19 0,0163] ?3 ).9 41.36 C. 05350 26u,1 20.33 0.03323 229.9 61.11 0. C8E 25 2E 0.5 23.'4 0.03919 231.0 BL 43 C. 1152 2]4.5 41.17 O.Ofi 797 235.4 102.91 n_, 14398 180:] 61.73 O. 1C3C 242.0 113.39 e. 16669 ?8E.4 93.18 0,1396 249.] 10V.69 O. 1J63E zse.E vv°c 125. 3D 0.21291 26].9 125.35 0.2129E 2E B.2 1,23 0. 09159 272.8 1.36 0. 991]0 2]3.8 50°C ?,03 0. 09262 2]3.5 5.06 C. 9 a65Y 2]3.6 1.24 0',00183 242.0 10.11 o. 01398 1 ]u.$ l.sz 0.00225 242.1 ?D.zJ o. 92E 1Y 2]6.4 ..54 o.oo2ze z 42.o 40.4E 0. 0522] 280.0 6.12 o,DO7n 242.8 61.05 0. 0]893 205.1 5.12 O.OOJSJ 242.7 82,12 o. 'a s2 290.1 1o.lz D.D1496 243.5 loz.sa 0. 132uV 235.9 lD.ls 0.01508 2 Y3.5 122.01 0. 15]16 381.] 20.42 0,03054 245.4 125.98 0. 1fi 219 302.0 41.1E 0.06212 258.0 61.29 0.09299 25s.6 91.39 D.1?YO 261.1 102.24 0115638 2 J0.1 121.54 D.166'S 2 J6.9 1?1.54 D.1es=s 277.5

~_ . P 300 z,•. ,j ~~

1gK. 150 Ar(0.600~Nj{,(0,2001 SOL e 4 F ~, Ar(0.603 O - ~G 1 100 0 T.~ 250 T :y Ar(0,406) O

o: present work 7 li0 Ar(0200)~NH O: Graoki •t al ~~/ v: Flynn et al ~~~ aawasakl et a110I NH, e: Micftels et al.ol .: ReYnes et al;v 0 0.1 0.2 0 0.05 Deosity (l0ykg•m 9) Density (103kg•m-') Fig, 1 Viscosity of argon Fig. 2 Viscosity of argon-ammonia system at 100'C

that of Iwasaki et at.lol who used an oscillating disk viscometer. As shown in Fig. 1, the viscosity values obtained in this work are in agreement with those obtained in the investigations mentioned above within the experimental error. The Review of Physical Chemistry of Japan Vol. 48 No 2 (1978)

T' M. Hongo

The viscosity measurements for four argon•ammonia mixtures were carried out at the same tem- peratures as for argon and at pressures up to around the saturated vapor pressure of ammonia at each temperature, i.e., ahout lOx fps Pa a[ 25°C, 20x 106 Pa at SO°C,35 x 106 Pa at 75°C, and 60X lOs Pa at 100°C. The viscosity values obtained (or the mixtures are given in Table 2. The results obtained for the gaseous mixtures at 100`C are shown is Fig. 2. The viscosity values of pure ammonia shown in Fig. 2 are those reported in Ref. 1. As shown inFig. 2, the initial slope of the viscosity-density curves for the gaseous mixtures, (8pJ8p)p-.o, increases as the mole fraction of argon increases, and becomes aeady constant above 0.406 mole fraction of aggon.

Table 2 Viscosity of argon-ammonia mixtures

Pressure Density Viscosity Pressure Density Viscosity Pressure Density Viscosity lOs Pa 103kg•m 3 10'%Pa•s lOS Pa 103 kg•m 3 10-%Pa•s lOS Pa ]03 kg•m-3 10'%Pa•s

25°C 50°C ]s°c

Art6 Ar(D.600)-3i ~(O.V00) ar(o. ]941-f1Y..(0. 20fi3 1.13 0.00108 129.5 1. 14 0.00342 196 ,Y 1.24 o. cc uo 23u .~ 1.33 0.0011] i9.5 1. 3G D.00149 196 ,] 2.03 0.00247 23u .v 2.53 0.00223 125.5 ]. D2 O.OGI31 196 .5 E.09 0.00619 .z 4•5L 0.00399 129.2 3. 04 0.00349 196 .8 10,11 0.01231 23E .1 6.E5 0.00691 129.0 5. 12 0.00599 19] .2 15.13 0.019f4 ?3] .o e.E] D.DD 7e7 1z=.n 10. 33 0.011]3 19] .B 25.30 C.01136 236 .9 10.18 D.oostl2s lze.e 15. 26 0.01803 19B .5 36.16 0.04640 3u0 .8 25 0.02uu0 199 3?.41 ?41.5 Ar

iwauki •t ato

i ~ ~ (,

~ experimental value3

___ valuesD calculaleA y original theory : Lnakgeorli tl i ..-_...._ values WculaleE by using Eq.(11

i The Review of Physical Chemistry of Japan Vol. 48 No. 2 (1978)

Viscosity of Argon and of Argon•Ammonia bfix[ures under Pressures 67

o°` d~ 2i0 9 2i0 T 2 •h G ;2: r .

0 o ro ~15G i i i ~ 5 n 200 i G a zoa i i i i 0 0 i i i i i i T T.o 0 150 i ~o o: preaml worM ts~ V 7 Pakeltll M al.o

f00 t00

0 0.5 1.0 0 0.5 1.0 Diole fraction of argon Sfole (racoon of argon Fig. 3 Viscosity of argon-ammonia Fig. 4 Comparison of experimental system at atmospberic pres- value with original theore- sure tical one end calculated one using Eq. (l) in argon-am- monia system

The viscosity values at atmospheric pressure (1.013x IOs Pa) were determined in this work through the extrapolation of the vistosity vs. pressure curves to I atm, and aze shown in Fig. 3 in comparisonwith the other investigations: by Iwasakf et at.al (20 and 30°C),by Chakraborti et al.U (25, 35, and SO°C),and by Rakshit el alsl (5 and 35°C).The values obtained by Iwasaki et al.al show the similar tendency with those obtained in this work,but those obtained by Chakrabortiet al.<1are found to be roughly lineaz and those obtained by Raksbit et als> are seen to be more convex than those ob- tained in this work.


Prediction of gas siscosity for nonpolar-polar mixtures by applying a correction factor Accordingto Chapman-Enskog'stheoryl~, [he gas viscosity of a dilute binary mixture is given to the first approximationby Eq. (8.2-22) in Ref. 14. If the force constants of pure componentsaze known, the viscosity of binary mixtures can be obtained theoretically. The Leonard-Jones potential function was applied for the nonpolar moleculesand the Stockmayer potential function was done for the polar molecules. The force constants of argon were determined by use of the theoretical equation to the third approsirrlation,Eq. (8.2-19) in Ref. 14, and [be present experimental viscosity values at

14) J.O.Hirschfelder, C.F. Curtissand R.B.Bird, "Molecular Theory of Gasesnod ",John 1Viley &Sons, Inc., New York (1954) The Review of Physical Chemistry of Japan Vol. 48 No. 2 (1978)

6B M. Honga atmospheric pressure. The force constants obtained were as follows: Ar: uo=3.44_[.], en(k=116[R] where ao and eo are the Lennard-Jones potential parameters. The Weore[icatviscosity of azgon (r,], required for the calculation of the viscosity of the binazy mixtures [pmt:]i in Eq. (g.2-22) in Ref. 14 was calculated from Eq. (g.2-19) (k=3) using its force constants presented above and that of ammonia [r_]i had been already calculated in Ret. 2. The Force constantsbetween nonpolar and polar moleculeswere obtained from the combining law, Eqs. (8.6-3) and (g.6-4) in Ref. 14. The theoretical viscosity values of the binary mixtures based on Chapman-Enskog'stheory are shownby the dashed line, and the experimental values obtained in this work are denoted by the solid line in Fig. 4. As shown in this figure, the deviation of the theoretical values from the experimental ones is 2 °6 at maximum. In order to make the deviation smaller, a coaection factor was introduced into the combining law as follows: (Enp~k)~=zvo~k~(Zca)~-i-(ZeV)y')-f (1) where e~pis a force constant between nonpolar and polaz molecular interactions obtained from Eq. (8.6-4) in Ref. 14; k is the Boltzman constant; and Z~„ and Zip aze critical compressibilityfactors of nonpolar and polar substances,respectively. The viscosity values of the gaseous mixtures obtained by applying Eq. (1) are shown by the dotted line in Fig. 4. Apparently the values calculatedby using Eq. (1) agree better with [he experimental ones than the original theoretical ones do in the argon- ammonia system, as well as in the hydrogen-ammoniasystem and in the nitrogen-ammoniasystemzl.

Ta61e 3 Value of constants in Eq. (3y'~

Tcmp. ('C) xs. no d e T•10-~

o.DD0D1 lol.D -3.68 -169 1430 0.200 129.9 -0.3'19 - 64.2 488 26 0:397 15].3 i.]1 -210 1060 0.602 184.7 0.=61 31.3 130 0.800 208.1 D.414 16.1 39.2 l.DDD zz6.1 0.461 3.39 0.393

O. DODD1 1'_0.4 -2,ED - 8.63 268 0.211 140.3 -0.0321 - 14.1 90.9 90 O:V03 168.1 l.el - BY.9 106 a.s6D 196.3 D.]30 - 8.77 24.3 0.001 ?2D.s o.eu - ls.e 29.3 1.000 2 Y1.3 0.394 2.Y6 O.18B

D.ooDe1 119.3 -3.30 53.6 - 2s.D '6 D.zez 3Y B.0 O.OS69 .33 11.3 ]6 0.394 1]].4 0.651 - Y.62 ].B1 0.097 208.1 0.364 - 9.03 14,2 0.394 23u.4 0.53] 3.66 4.60 1.OOD 256.1 0.49u 0.]66 O.I16

O.OOD°7 128.9 -1.03 37.3 1.71 0.200 166.3 -0.0076 18.9 - 0.63 100 O.Y06 188.1 0.066 1.6Y 0.370 D.b03 321.9 0,393 - 10.0 13.0 D.e9o 260.0 D.72s s.lz 6,72 l.D6o 272.9 0.430 1.]2 0.173

S) 8~'>to~l-I-a'PtgP2 ~'Y'P3) p: 10-7 Pa•s P: 103kg•m"3~g.cm"3 b) listed in Table 5 is Ref. 1 The Review of Physical Chemistry of Japan Vol. 48 No. 2 (1978)

Viscosity of Argon and of Argon-AmmoniaMixtures under Pressures 69

Inftfal density dependence of the viscosity for argon-emmonfa mixtures The viscosity of gases under pressures depends on pressure or density, and can 6e expressed in a power series expansion in density: where ~o is the viscosity extrapolated to zero density and a'=r~~-' (8q/t3p) p-.e denotes the initial density dependence of the viscosi[yt>. The viscosity of polar gases decreases with increasing pressure or density in lower temperature region, and after having a minimum increases with increasing pres- sure or density above a certain temperature. For polar gases, the decrease in viscosity is obsen'ed in the low pressure or density region below a certain temperature, that is, it is found that a' is negative. In order [o investigate the effect of argon concentration upon a' of argon-ammonia mixtures, the gas viscosity was represented by a Cubit equation of density as follows:

The constants in Eq. (3) were calculated from the experimental viscosity values by means of the least-squares method, and are listed in Table 3. The relation between wand the mole fraction of argon, xA~,at each temperature is shown fn Fig. 5. a' is almost constant above xAr=0.6. Approxi- mating three isothermal points in lower concentration region of azgoa with a straight line, each

z z s e 0 0 _z r _z .: 25'C -J _q ._ zs•c e: 50'C e: 5n'[ o: ]5'C -6 o: )5'C 0: 100'C oapp'~ 0 0,$ l,0 0 0.5 1.0 Mole fraction of argon Bfole fraction of nitrogen Fig. 5 Initial density dcpendence of Fig. 6 Initial density dependence of argon-ammonia system nitrogen-ammonia system

v r e a 0 '3 so 1; e _Z ti •: 25°C zo _q ~° d n: 50°C -6 a: 75°C s to oaoo°[ 0 OS L0 0 os t.o bfole fraction of hydrogen s~~ FIR. 7 Initial density dependence of hydrogen- Fig, 8 Relation between molecular ammonia syslcm weight of nonpolar gas and xn` The Review of Physical Chemistry of Japan Vol. 48 No. 2 (1978)

70 M, Flongo

straight line and ~'=0 cross at the point zqr=0.25, that is, xqr`=0.25 where xq~ is the mole fraction of argon at the point of intersection of straight lines across a'=0. The relation similar to Fig. S is shown in Figs. 6 and 7 for the nitrogen-ammonia system~l and (or the hydrogen-ammonia systemzl, respectively. Figure 6 shows that a' is nearly constant above zx==0.g, and that xxr` is about 0.4 in the nitrogen-ammonia system. Figure 7 shows that x~j~ is about 0.7 in the hydrogen-ammonia system. Thus, it is concluded that a' increases with an increase in temperature and in mole fraction of non- polar gases, and that the smaller the molecular weight of nonpolar gases is, the larger the sa is, where the subscript n denotes a nonpolar gas. Figure 8 shows that an approximately linear relation- ship exists between the molecular weight of nonpolar geses and the xo Polar gases show the initial decrease in viscosity below a certain temperature. Singh et al.ts~ dis- cussed that the anomalous behavior of the viscosity of polar gases was ascribed to moleculaz as- sociation. Therefore, as descrihed in the previous paperst~z>, Figs. 5^-7 suggest that a rise in tem- perature and the presence of nonpolar molecules hinder molecular association of polar gases. Figure 8 shows that the lazger [he molecular weight of a nonpolar gas is, the smaller the z„` is. Namelg this 5gure suggests that the larger the molecular weight of a nonpolar gas is, the more strongly the nonpolar molecules hinder molecular association of polar substances. The critical temperatures of the gaseous mixtures were determined by taking into aaount [he mole fraction is place of the molecular weight of nonpolar gases, and correlated to ¢'. The critical temperature of [he mixtures was calculated by use of Chueh-Prausnitz's methodt6l.

+t 8 a

a 0 m, Fig. 9 Correlation between a~ and reduced temperature T, _z 8 o. pr-NHS system e o' Nr-NHr system e _4 .~Hn-NH. system

J 4 b 8 T.

Tsm=r'OJTrJ+~BiBJrq7 (4) ii BJ=SJVeJya~rSIVL'12/3 (j) i where Tem is true mixture critical temperature. TeJ critical temperature of component j, riJ ao interaction parameter, zJ mole fraction of j, and VrJ critical volume of j. Figure 9 shows the

13) Y. Singb, S.K. Deb and A. Ii. Barua, J. Ckem, Phyr., 46, 4036 (1967) 16) R. C. Reid, J. M. Prausnita and T. K. Sberwood. "Tbe Properties of Gases and Liquids", Tbird Edition, McGraw-Rill Book Co., New S'ork (1917) The Review of Physical Chemistry of Japan Vol. 48 No. 2 (1978)

Viscosity. of Argon and of Argon-Ammonia b7ixtures under Pressures 7( correlation between a' and the reduced temperature, Tr. where Tr=T/T~m. Ia this figure. a similar tendency is observed for the three systems, and this pattern resembles the relations between the reduced second and third virial coefficients and [he temperature reduced 6y [he potential parameters+~.


The author is sincerely grateful to Professor H. Iwasaki for his continuing interest. encourage- ment and helpful discussions duriag this work. The author also wishes to thank Dr. S. Takahashi for many useful suggestions in this paper and Professor T. Makita (Robe Univ.} for valuable advice with the correlation.

Chemical Research Institute of Pon-Aqueous Solutions Tohoku University Sendai Japan