title the viscosity of nitrogen-ammonia system under pressures … · 2019. 3. 29. · the...

Title The viscosity of nitrogen-ammonia system under pressures

Author(s) Hongo, Masaru; Iwasaki, Hiroji

Citation The Review of Physical Chemistry of Japan (1977), 47(2): 90-101

Issue Date 1977-12-25

URL http://hdl.handle.net/2433/47051

Right

Type Departmental Bulletin Paper

Textversion publisher

Kyoto University

The Review of Physical Chemistry of Japan Vol . 47 No. 2 (1977)

90 THR REVIEW OP PHYSICAL CHEaI raTR\' OP JAPA\, VOL. 47, No. 2, 1977

THE VISCOSITY OF NITROGEN-AMMONIA SYSTEM

UNDER PRESSURES'

BY MASARG HONGO ASD HIROJI IWASAFI

The vistosilies of nitrogen, ammonia and their mixtures have hecn measured by the use of an improved oscillating disk type viuometer at [he temperatures of 25, 50, i5 and I00°C, and in the pressure range, up to about 12Dx10s Pa for nitrogen and up to around the saturated vapor pressure of ammonia for both ammonia and nitrogen-ammonia gaseous mixtures. The accuracy of the measurements is estimated to be within }0.3ga.

The initial pressure (deasity)dependence of the viscosity of ammonia and nitrogen-ammonia mixtures, that is, p,-t (3p12P)a-a (or p,-t i8T/an)a-w) where 9 is the viscosity of gases, C- is the viscosity extrapolated to zero pressure (oc density), P is pressure and

p is density, changes its sign from negative to positive with an increase in not only temperature but also the mole traction of nitrogen.

Introduction

Viscosity of gases that is one of transport coef}icienU, alike diffusion coefficient and thermal

conductivity, has heen required not only as a clue to clarify molecular interactions but also as an

important physical property in chemical engineering.

Though fairly accurate experimental data at high temperature or at high pressure have been

reported, most of them are the data about aonpolar molecules at low pressurel> and at high pres-

surezl and about their mixtures at low pressure7?, and some of them are the data about polar mole-

cules under pressuresa•ss) and about binary gas miztures containing polaz molecules at low- pres-

sure7l. There is only one investigation shout nonpolar-polar gas mixture under pressuresal.

' Presented at The 16th High Pressure Conference at Kagoya, I)ec. 2nd, t9i3

I) R..4. Dawe and E. B. Smith, J. Chem. Phyr.. 52, 693 (1970), J. Rtstin, S. T. Ro and W..4. Wakeham, ibid., 56, 4119 (1972). ,4. A. CIIHord. P. Gray and A. C. Scott, 1. C. S. Faraday I, 71, 875

(1975) 2) ~. \iichels. ~. Botzen and YV. Schuucman, Physf(a, 20, 1141 (1954), E. G. Reynes and G. Thodos,

ibid., 30, 1529 (1964), J. A. Gracki, G. P. Flynn and J. Ross, J. Charm. Phys., 53. 3856 (1969) 3) J. Kestin and S. T. Ro. Ber, Burrsengar. physik. Chem., 78, 20 (1974), D. t\'. Gough, G. P. ~lattfiews

and E. B. Smith, J. C. S. Faraday 1, 72, 645 (1976) 4) H. Iwasaki and /N. Takahashi, Hu!!. Cheer, Soc. Japan, 48, 988 (t975)

5) L. T. Carmichael, H. H. Reamer and B. H. Sage, J. Chem. Eng. Dafa, 8, 400 (1963) 6) H. Iwasaki and J1. Takahashi, This Journal, 38, l8 (1968)

7) L. G. Burcb and C. J. G.Raw, J. Chem. Phyr., 47, 2798 (1967), A. B. Rakshit and C, 5. Roy, Plrysira, 78, 153 (1974)

8) H. bvasaki, J• Kestin and a. Vagashima, J. Chem. Phys., 40, 2988 (1964)

The Review of Physical Chemistry of Japan Vol. 47 No. 2 (1977)

'f he Viscosih~ of Xitroge n-Ammonia System l'nder Pressures 9l

The viscosity of pure gases and gas mixtures at low pressure has theoretically been treated by

Chapman and Enskog9l, and [hat of nonpolar dense gases was theoretically studied by Enskogto)•

But Che viscosity of polar gases and gas mixtures under high pressure has not theoretically been

treated yet. In order to develop the theory for [he viscosity of polar gases and gas mixtures under

pressures, the precise experimental data of the viscosity are more needed. So, the viscosity of

nitrogen-ammonia gas mixture, as an example ot'the nonpolar-polar system, has been measured at

25, 50, 75 and 100-C using an improved oscillating disk type viscometer. Por nitrogen, the measure-

ments have been performed up to about 120x10' Pa, and for ammonia and nitrogen-ammonia

mixtures, up to around the saturated vapor pressure of ammonia at each temperature, i. e., about

lOX 105 Pa at 25-C, 20X 105 Pa at 50-C, 35X 205 Pa at 75`C and 60x 105 Pa at l00°C.

Experimental apparatus

The principle of the measurements of gas viscosity was the same as• that of Iwasaki et uf.11> and

Sestin et af.t~ The modifications were undertaken in order to increa;ethe precision of the measure-

ments.

The suspension system of ehe viscometer is shown in Fig. 1. An oscillating disk (~ was made of

nonmagnetic stainless steel (SUS-316), and two fixed plates Q and three spacers Q were made of

quartz. 'T'hey were polished Co make their working surfaces which fated each other optically fiat and parallel. The [op and bottom ends of x fused quartz wire ®of about 0.002cm in din. were

gripped in [he center of the two small conical jaws ®and 0, and assembled to the cylinder ®and the mirror holder ®by the tightening nuts ©and ®. The thicker part of truncated cone of the

conical jaws ©was about O.Oicm in din. In order to fix the wire at the center of [be jaw chucks, a

leading groove was set on Che. renter of the longitudinal section. The mirror ®(0.4X0.3XO.O7cm)

was made of quartz with aluminum backing. Vertical adjustment was obtained with the aid of the

screw thread between the cylinder (qj and the nut ~~y, and angular adjustment by turning Che nut Q~.

After these adjustments, the cylinder was fixed to the plate ®by the bolt ®and the bushing ®.

The parts shown in numbers, ®'~ and ;~, were made of super-invar, i, e., iron-nickel-cobalt alloy,

whose thermal-expansion coefficient was comparable to that of quartzt3>. The rest of the suspension

rys[em was the same as that used by Iwasaki of a1.11> The characteristics of the suspension system are given in Table 1. This oscillating system was assembled so that the separation between b+ and

b: was equal using a thickness gage accurate to 0.0365cm. All these preparations were performed

before this system was fixed in the high pressure vessel which was separated into [be upper part

9) J. 0. Hirschfalder, C. F. Cuniss and R. B. Bird, "Dlolecular Theory of Gases and Liquids`, John 14'iley ie Sons, .~'ew fork (1954)

!O) S. Chapman and T. G. Cowling, "The Stathematical Theory of 'von-IInitorm Gases", Cambridge University Press (1961)

1l) H. Iwasaki and H. Takahashi, Rull. Chem. Rer, Inr(. Nonaqueous .Solutions, Tokoku Univ., 6, bl (t956) lt) J, Kestin and W. Leidenfrost, Brown Uuiv. Report d/+891/12 (1960)

13) H. \Sasumoty. Kiaeoku no Kenkyu, 8, 237 (1931)

The Review of Physical Chemistry of Japan Vol. 47 No 2 (1977)

72 ~1. HnnRO and Fi. Iwasaki

G

na

ae

Aa

a

n

17161 (15

i i10

s

8

~o ,.~otiv~~

11 121 ( 1

n: ~: ~: O O: ~: ~: @~: ~~,;

Pig.I p osauating asl: Spacer Conical jat~~s Cylinder Tightening nut Screx Jiirror Bolt Ylate

Sus ension

®: o: ©: ~: u~: ~: ~: iii:

system Fired plate

Quartz wire Tightening nut Conical jaws Mirror holder Rasher Nut Bushing

Table 1 Characteristics of suspension system (25'CJ

Total separation between fined plates

tipper separation

Lower separation

Radius of disl:

Thidness of disl:

\tomen[ of inertia of suspension system

Natural period of oscillation and damping decrement 2a'C

50'C

7SC

100°C

D=0.1 i 53 }0.0002cm

bt-0.0372}0.0003cm

Lr=0.0372i0.0005cm

K=L3997}O.OOOlcm

d=O.IOl2}O.OOOICm

7=4.8109}O.OOlig • cm"-

To-22.198 s Ao-3.0 x l0's

To~22,3775 do~5,2x10's

Te-22.556 s !0->.4 x l0_s

Ta~22.336s .fo~3.6x10's


The Viscosity of Nitrogen-:lmmania System Cnder Pressures 93

and the lowei one equipped with a quartz window. By turning two setsoi three fine adjustment

screws, the tsrorking surfaces of the oscillating disk and the fixed plates were controlled [o he hori-zontal and parallel. The pressure vessel was mounted at the center of adouble-walled oil thermo-

stat. In the instruments of Avasaki er alts] and kestin et al.!Z> the rotating motion of the oscillating

disk was given by applying a magnet just at the start of the motion. but in this apparatus, in order

to remove a possible magnetic influence upon the viscometer and experimental duids, the rotating

motion was started by hand with a slight and careful Cwist of the whole thermostat nn a ball bearing which was fixed on the base.

Pressure above 13 x 105 Pa was measured by the pressure balance of free piston [}'pet+?, and up

to 15 x 105 Pa by the precision Bourdon gage. 'Che Bourdon gage was calibrated by the use of a

diiterent pressure balance designed for moderate pressure. The accuracies of the pressure balance

and the Bourdon gage were both within -1-0.01 X.105 Pt[.. In the pressure measuring system. a C-tube

type detector containing mercury for balancing of pressure tvas set up between the gas line and the.

oil line. One side of the U-tube was made of Pyrex glass capillary and the movement of [he metro

ry level was detected by a phototransistor attached to the capillary. The other side sen•ed as a.

mercury reservoir, and connected with the capillary by a stainless sleet pipe. The sensitivity of the

detector was 0.1 cmHg.

The temperature of the pressure vessel and oil in the thermostat was measured by copper-

constantan thermocoupleswhich were calibrated against a platinum resistance thermometer provid-ed with a calibration certificate by the \ational Bureau of Standards. The. accuracy of the tempera-

ture measurement was t0.01'C.

\i[rogen was supplied from the Sippon Oxygen Co.. Ltd., and its purity was 99.99%. Cbm-

mercial ammonia w•as dried with metallic sodium and purified by redistillation four times. The

composition of the mixtures was determined by absorbing ammonia into a normal sulfuric acid

solution.

Calculation of viscosity

The evaluation of the absolute viscosity of ga;e; for the oscillating disk q•pe viscometer w-as

detailed in \ewell's theoryts%. but the calculating method used in the present study is the same as

the modified method used by fivasaki and 6estints>.

I[(thetalibra[ion measurements to determineun empirical value of the constant Cn• in 13q. (I1) in Ref. 16, the empirical value C~ was obtained using nitrogen, whose viscosity wa; accurately

measured, at 25`C and at pressure up to 40x lOSPa, The viscosity value of nitrogen at 15`C wa; calculated from [he following equation as s[andard.17?

14) a. Rumagai and $. I)a[e, Buff, Clean. Res, lost. d'ou-ayucoxr SohUiour, Tolmku Univ., t9, t49 (1969) 15) G. P. \ervell, 2A:6fP; 10, !60 (1939)

i6) H. hvasaki and J, Kestin. Pbysim, 29, 13-45 (1963) t7) J. [zestin and j. FL «'bi[elaw, ibid. 29, 335 (19b3)


94 \l. Hongo and H. Iwasaki

~zrssro=[l7 i.S6t 107.19p+749.6p"-434.OpaJX 10-° I'a. s (1 )

where p is density in g • cm-'. The mean value of C,y' was Cr'=1.1315.

The average of detzations from the mean value was X0.0395, and maximum deviation teas 0.09%. Theoretical value obtained from Eq. (13) in Ref. 16 teas C,v=1.1304.

The densities required for the ralculation were obtained from F. Dinte> for nitrogen and from

F. Datefal for ammonia. The densities of gas mixtures were calculated from Vri chart (Vri: ideal

reduced molar volume) prepared by K. Tezukaml. For nitrogen-ammonia mixtures, the measured

values at 50`C obtained by K. Date''-Il were in agreement with the calculated ones within SOS%.

It was the sufficient accuracy to calculate the viscosity of gases1l. Cx' was checked before and aitec

the series of measurements using nitrogen at 25"C, as it was slightly varied with the change of

temperature etc. The experimental accuracy was estimated to be within -~0.3%.

Results

The experimental results obtained for nitrogen, ammonia and their mixtures are given in

Tables 2 to 4.Figures 2 and 3 show the results for nitrogen and for ammonia, respectively, along

with comparison with the data obtained by other investigators. The viscosity of nitrogen at the

conditions of this work was measured by ~ficheles r! al.zJ (25 to 75'C), Flym et al.~) (25 and

I00°C), Restin et al.%I> (25`C) and Iwasaki~l (25 and 100°C). The data obtained in this work agree

well with those obtained in the above-mentioned investigations within the experimental error at 25,

50 and 75'C, but are about 0.5% higher than those of Iwasaki at 100`C. Among the available vis-

cosity data forammonia under pressures in the litera[uress,s>, [he data obtained by Iwasaki et af.bl

can be compared with those ohtained in this work at each temperature. As can be seen from Fig. 3,

the data of Iwasaki et al. agree a-ell at 25 and 50-C, but are about 0.3% higher at 75`C and about

0.7% higher at. 100°C than those of this work. The viscosity of ammonia shows a steady decrease

with increasing pressure at 25, 50 and 75`C, but takes a minimum in the neighborhood of 30x 105

Pa at 100'C.

Figures 4 and 5 show the results obtained for the gas mixtures- at 50 and 100`C. IL is evident

[hat the initial slope of the viscosity. f. e.. (8./8P)P..e where >, is viscosity of gases and P is pres-

sure, changes its sign Irom negative to positive as the mole fraction of nitrogen inueases. Figure 6

;haws the isobaric behavior oI the viscosity of gas mixtures at l00`C. At other temperatures (25 to 75`C), the change of viscosity with pressure was smaller than that at 100°C. There are no other

IB) F. Din, "Thermodynamic Functions of Gases" Col. 3, Butterworths, Laadon (1960) 19) K. Date, This Jou.naf, 43, 1 (1973)

20) R. Satoh. "Bussei Josu Suisanho", xfaruzen, Japan (1954) 21) K. Date, This Journal, 43, 63 (1973)

22) A. Michels and R. O. Gibsoa, Pra. Ray. Sot.. A134, 288 (1931) 23) G. P. Flynn, R. ~`. Hanks, V, A. Lemaire and J. Ross, J. Cdenr. Plrys., 3R, I54 (1963)

24) J. Restio, E. Paykoq and J. V. Sengers, Physfca, V, (19i 1) 25) H. Iwasaki, RuII. Chem. Res. Inst. Non-agneous SofrUions, Tohokn Univ.. 3, 1 U (1953)

1'rassure

IO~Pa

t.zz

1.32

1.x7

2.G0

3.I I

i.99

7.11

lU. 1'1

15.16

20.36

3 L2x

10.93

51, Ix

GI,I6

7 L.96

xz.oz

91.9x

L112 , 7G

Il?.17

I20. C>3

120. r>x

I.?7

1 ,9i

3.U?

5.06

6, 7]

G,71

70,13

l i.4U

?0,31

36,29

i 1, x6

61,76

76, xR

91.94

102.x11

II2,13

122,32

1.3?


The Viscosity of \itrogen-Ammonia System Lnder Pressures 9i

Ta61e 2 Viscosi}' of nitrogen

Ilensi[r

e.cm "'

Viscnsitc

10-' Pa-s

Pmssu n•

10°Pn

Ile nsih

g ''m-'

l isoos it~~

10"'Pass

13s

149

212

294

355

5(ri

xOR

153 X19

31i

549

Gi3

x03

93t

14i

265

i?

S in

5Gi

176

Fxi

25

o.ou

O.UO

0.00

0.00

O.OU

n.00

0.00

0.01

O.OL

U.02

0.03

O.Oi

0.05

0.06

O.Ux

0.09

0.10

O,I1

U.12

0.13

O.I3

so t:

o.aol3z

U,0020,i

0.00315

0.00527

0.00699

0.00699

40105(

U.01G05

0.02116

0.03777

0,053x4

0.0639(,

0.07931

409=i 13

u.lo-n6

0.1142[

0.12413

t

[27

75

DD0.

ux.u

178.2

17x,1

17x,?

178.2

17x.4

178,9

U9.3

180.0

I RO.R

132.6

IR i.5

1 x6,x

I x9.1

l9 L'

194.5

1')?.L

Zoo.-i

203,1

205.9

n)G.u

189.3

189,4

789.5

IR9,7

189,9

189.7

190,i

l')I,0

191.7

l9 i.3

197.1

298.9

202,-i

205.9

208.4

2t1.I

213.7

199.N

2, i8

2.aR

a.15

5.79

9.R•f

15.22

20.2.{

iG,38

51.4 i

61.29

77,07

92.17

]0?. 3.1

1112,37

712,19

12L68

12d .4G

1,23

7.46

2.07

2.ao 2.92

3.26

3,}i

i, 79

5.70

9,19

15.16

19.90

31.00 '10.84

51.81.

61.50

72,60

51,95

91 ,~39

1 [12.50

111.32

121.27

121.32

75L:'(eon tiu uedl

11,00240

0_00240 0,0040? O,OUS60 Q.U095I 0.01469 0.01953 0,03497 0.o492R 0,05857 11,07328 0,08716 0,096363 U. (19640 1 0.7051? 11.11357 0,11600

1uu c

u.o0u1 0.001,2 o.001R7 o.oo2n f1.002Gi 0,00295 0,00337 0,00432 ll, 0051 S

l1, 0082`) 0.01364 11,01789 0,02779 0.036#9 u.o46tS 11,(15460 /I, 06418

0.07216 0,0802? 0.089208 0,0967-i3 0,104]9 0.10499

199.9

199.8

200,1

2170.?

200.7

2m ,3

201.9

204.,

206.6

208,.!

21 L1

21 i.5

21(,.5

216.7

218,8

221 .ll

221.6

?11.1

211. i

217,5

?11.7

211,5

21 LG

2lLG

2ll,S

211,E

X12,2

212.9

2t3,4

2b1.7

?16.3

218.0

219.G

221.E

223.3

?25.U

2220

229.2

23 t.5

?30.9


96 Df. Hongo and li. Iwasaki

'f'able3 Viscosiy of ammonia

Pressure

10°Pn

Uensih

K' c m-a

V isc nsily

10-' F'a • s

Pressure

10° Pa

Ilensite

K• cm'a

\' i scos i 1}~

10-' Px• s

1.17

1.19

1.2R

1.3t

1.37

1.71

2.11

2.31

2.G2

i.22 -f. 10

5.16

G.23

7.37

R.20

8.97

9.6G

9.GG

1.22

1.37

?. 15

3.25

5.29

7.tG

t 0,21

6.17

1G.d1

tG.43

l8.da

19.68

19.97

35 L'

u.uansl9 O.OOOR3? u,0oo8I3 0,000918 0, (10096 t 0.001?0 O,OOIAR 0,00163 0.0(11 RC 0.00230 o,o0i95 0,00376 O.U(b{61 0,00555 0,00(?5 0.00693 O,U(1760 0. W760

So ~

o.on07R3 o.oooasa 0.0(1139 O,U0211 0.00349 0,004R0 o,nn7o53 o.nn9393 0.01?li 0,01?15 o.ot393 0,01527 0.01569

100,6

IOO.R

I oo.G

100.7

100,6

tuo.G

Ino.s

100,4

100.?

100,2

99.R

J`l.4

99,1

9R,7

9R.4

9A,1

97.9

97.9

1111,'_

IIU,t

110,0

109,9

109.$

]OR.9

l UR,3

107:7

107,1

107,2

l UG,7

106.3

IoG.G

I, 27

I .-f0

2,63

5,12

Io,la

15,31

20.31

25,26

28,52

30.51

32. i1

33,GR

34,61

35. f5

1,27

1.65

4.15

G.9R

12.69

2u.33

25.26

3n,4R

35,47

4U, f1

15,GA

so,Rl

53.89

55.7•i

57.R4

39.85

GO.G2

75 t

U,OOQ755

0. (10083?

U,UOli7

0.110315

U,U063G5

0,009859

0,01371

(1, OI779

0, (1?075

o.u22GI

0.024G5

(I, 02602

(1,02709

0.02803

tU0 ~

(1,000708

0,000921

(/,OU232

0,00395

0.oo73sa

o,olz29

O,OI57R

0,01970

o,oz37G

o.o2sto

0.03328

0,03893

o,n•s?n

o,n4527

0,04840

11,OSLS7

11.05283

L 19,7

119,5

119,5

L 19,1

I l8, •f

117,7

It7,3

l l7,l

117,11

1IGJ

I1G,8

i IG,G

I IG.G

117.1

128.9

128,8

i 28,7

738.5

128,U

127,8

127,8

127.5

137-H

Izx,3

lz8,c

129.3

129,8

130.?

130.7

131 .H

132.3

viscosity data fo[ nitrogen-ammonia mixtures above atmospheric pressure. 'Che isothermal viscosity values at atmospheric pressure (1.013X 10' Pa) are shown in viscosity-

composition plot in Fig. 7. These values were obtained by extrapolating the relations between the

viscosity of gas mixtures and pressure. The values obtained by Trautz el al.~l agree with those

obtained in this work, but the difference between the values obtained by Pal r! al.~> aad those of

this work is comparatively large.

16) 27)

.lf. Trautz and R. Herberling, ilrur. Plrysik, ]0,

a. R. Pal and A, R. Barua, Indian 1. Pkys, 47

l33 (193Ij 713 (1967)


The V iscositp

'1'ahle 4

of \itrOgen-Ammonia System U9dec Pressures

V iscosiy of ni[rtlgen-ammonia mistures

97

Pressure

toy ra

Ikosi h- \'iscOSi n•

N•rm-' 10~'Yo•x

Prc-sur•

10' Pa A•cm""' 10"Ya•s

Yrrswre

11Y' Pa

ll¢nsilp

g • em-'

\°iscosa3•

10 Ya

?5 ti

i,t(. 0,000895 11) 2 5.08 0,00239 nk.8 SAS /1,IN1391 11 H.3 7.15 U,1N15C.9 118,4 9.19 U,/H1711 11 N,1 0,91 U,WFl12 915,1

1: 3 U.W IOR Ii6,e 3.07 (1.00?66 IiC,N 5.111 U,IW949 137.11 7.nA n,DU625 v7.i 2U1 0,110812 137.1 ')51 n,nllHi9 134'1

s~(osso)-~ u,(n.4s11) 1.?9. n,00120 1~i9.5 i,0i o,n0?83 LiAG 5,(1!1 II,/116176 I-19.8 7,us D,uorai 1d9.N 9.13 f1,11f14N1i 1511.0 9,7y U,OUY35 .150,3

1,17 0,00132 IG?.5 3,U9 0,00322 11.7,7 5,05 0,1)0526 16k,0 7.14 u,DU7311 7(174,7 9.07 0,00961 16H.6 9.81 u,UlUS .168.6

Sn r

1.26 0.000900 L7.N 3A7 U,002?U 121.7

7,19 U.UOi55 I2Z3 lU.OG 0,01175')5 127.0 11.25 0.0110} 127.1 11.25 0,01366 12(x,8 t9,u9 0,01521 116.9 ?u.06 U.o1608 126,8

1,27 O,W IOI 146.9 3,09 0,00247 116,9

5.84 0,00461 747,,9 1U,13 u.0118265 1-i7A I4.?7 0,01190 741.6 17,23 0,01459 I-17.6 19.23 0.01G~i2 1~i7,G zo.o4 n.nnly 1x7,7

1.27 0,00111 163.7 3.07 0,00269 763.7 6.19 0,00343 IG4,l

10.05 0.009025 169,3 t 4.20 401280 IG4.N 18,2') 0,01668 1652 20,05 0.01837 165.4

1~6 3-10 6-19

10.13 ti ?5 ]9,2j 201K.

sn t:

II,tNII'1 (1.110298 U,W595 IpOD')NUS U.013N'l U,1117HN 11.111?)i2

75 is

t.30 O.OU1137G 1:w o.uol>v s?I 11.0033?

10,23 II,U07005 15.19 Q.fll Ola 20.3'1 gUb473 15.21 O.U1R73 542fi 0,0230.! 13.67 U.0?GD$ 35.68 U.0379R

~:(oAn7)-NlG (0,593.1 1,19 f1,00(XiFfl

5.15 O,OOj62 10.21 O.OD77?3 14.98 0,04134 20,17 17.0159?. 45-i0 0.0203' 3n.37 D.o24s9 3i 48 0.03771 5539 (1,029(13

n.(0.570 )-NFfe (U;I3n) 1?6 0,110101

5.15 0,DO41~t 10,24 0,008311(1 i 5,10 n,01?32 ?0.41 O,O1fAll. 24.67 u,n2n5n 311,41 0.02569 11.01 0,02810 13.41 n,03032

n, (0.799)-~ u, (o,2m J

I,'_x o,DOU4 4.80 0.00428

1822 0.009143 15.84 0,01349 20.24 U,01821 25.14 11,02272 ioas D.D?74z. 33.34 0,03WI 35.30. U.03240

17A.2 178;4 17R,N 1TJ.2 ]79.8 180,j 180.4

139.7 139.1 139.3 139.5 139.( 7-00,11 14n.n 1 •fU.U 140. i Pf0.4

755,7 156.0 136.2 156.5 ]n.n 157.5 I SR.O 158,3 158.9

172.1 172.4 173.0 173.3 173.9 174.5 173.? 175.5 3 iG.0

] 88.5 186.4 189.1 1R9,9 1JU.4 190,8 ]91,(. 192.5 19'_.8

1 (xt'C;

1.32 O.OOllflifl 1-i s.4 S.o' 0.110;15 133.5

10,12 0.000 i93 1433 17.G(i u,0I 159 143.6 23.'j3 I1,0171K~ l~liy 32,63 0,02250 NG.3 du.rt{ 0,112R7G 1~f 2 '15.20 0,03272 19'9 50,77 0.03763 13sb 33,85 o.LLiOjR 139.6 3fi.5i 0.0{2x6 ISO.u SR.70 11,111-0911 SSgl ouat ns;cxs 1so.G

13z O.o0d1o9 163.9 5.13 u.0035I 16i

u1.n4 u:01W190 164.6 20.32 O.alAS9 -165:1 30.bf 0,0?261 16x..1 40.73 u.03a31 iG7,i •ill.li n.036R2 1453 52.5'/ 0,04063 IG9.U 55.61 0.04329 IG99 SR.1R 0,04559 169.6 GILG2 A.047 iR 1i0.0

1.24 o.n0o94n ls2.o Ss O,on;99 7s2.5

i 0.15 0,007R10 132.R 99.x2 Il,olp l 1839 3n.31 0.02387 184.v 4039 0,03223 136.2 3/l,(A n,n4o7fi 18.9 SS,SS 0,03501 ]88.5 SR.26 0.04732 189,2 GU.33 0:0•i91i 189.4

1; R n.ooloG 397.4 5.17 0.00428 19$n

30.31 0,0085(.5 195.3 20.29 n,01G9G 199.2 3u.as o,a2so3 zoos 39.66 0.03311 201.8 SgGU 0,04365 201.1 34,79 0.04G4t 204,0 57.65 0,04906 20 v 60,42 0.03167 2o9.n


98 U. HOOQO and H. Iwasaki

0

T .o

J

z zo

:aa

180

~,x

~oo'~o'

e

~5'~

5p G

15~C o:presenl work o:Re}, 22, O'Ret 23

e: Ret. 24. •: Ref. 25

0 50 100

Pressure (lOs Pa) viscosity of nitrogen

a 0

T 0

]30

120

IIO

IDO

Fig. ? The

o loa,a•t' ••~~~ _e.

mo•C

slx

)LIY )5'C

,:

.~

~ SOY

ya0,0 e~Ha. 5 m Pa, p

~CSY up.1. 8

FiB,

0 20 40 60

Pressure (IOs Pa) 3 The viscosity of ammonia

180

a 160

0

T O 140

110

Nr

Nx (0.801)- N H x (0.19 9 )

Nz(0.896)-N Ho (0.404)

N:(0.407)-NHx(0.593)

o--o 0 0 0~.-....

Nz (0.201)-NHx(0.799)

o NHx

0 10 10 Pressure (I Os Pa)

The viscosity of nitrogen-ammonia system a[ 50'C

zia

200

p^, l FO

0

r 0 16U

140

Nr

Nr(O~Ha10.2111

_~r 0 4031

Nr(0.997)-NHe(

Nr (0.399)-HHs(0~601)

Nr (0.203)-NH,10.797 )

NHe

Fig. 4 Fig,

0 20 30 60 Pressure (IOs Pa)

5 The r•iuosity of ni[rogen•ammonia system at 100'C

Discussion

It is knoN•n that the viscosity of gases depends on pressure and can be approximately expressed


The Pixcosiq~ of \itrogen-Ammonia System Pnder Pressures 99

n a

0 T O

aoa

150

]•A

0

0

e

I •10`Pa

:

where r,~ is the viscosity extrapolated to zem pressure,aod a=r,: t(Jr/r3P)p-.o is' called the initial

pressure dependence of viscosity in this study. Thediscosity of polar gases such ns ammunias•a7, sulfur dioxides) and water vaporz9•~1 shows a steady decresse with increasing pressure in lower

temperature region, and after taking a minimum shows a steady increase with pressure above a

certain temperature, i. e., the sign of a is revered From negative to positive xt a certain tempera-

ture as temperature increases. As cao be seen from Pigs. 4 and 5, the sign of a is likex•ise reversed

with increasing mole fraction of nitrogen in this experimental temperature range.

Expressing the viscosity of gases as a function of density p instead of pressure P, Eq. (2) can he

rewritten as

where r, is the viscosity extrapolated to zero density, aad a'=r= '(o'~lvp)p-,o is the initial density

dependence of viscosity-. The experimental viscosities of nitrogen. ammonia and their mixtures were

represented by the polynomial of density- as follows:

Constants in Eq. (4) were obtained by means of least squares method and are listed in 'fable i.

2S) F. llanon and I. Amduq !. then,. Phys., W, 4841 (1971) 29) J. Kostin and H. E. Rang, Physics, 26, 575 (1960)

i0) $, L. Rickin, :1. 5, Levin and L. B. Israilevsky, "The VII th International Conference on the Froperties of water Substance" held at Tokyo on 1968


t0u ]t, Hongn and H. Irvasaki

Figure 3 shon-s the relation hetween a' and the mole frauion of nitrogen xr;, at each temperature.

Each isotherm was approximated by straight line. and then the mole fraction of nitrogen at a'=0,

xh,', was obtained from the diagram. The relation between temperature and x~,", is linear as shown

in Fig. 9.

The initial pressure dependence . of viscosity of gases. a. was thegretically treated by Stogryn

et ul, 31) cingh el al.a?? and Danon el al.~' Io the theoretical approximation for tx, it was considered

that gas wasa mixtuie of monomers and dimers and [hat a depended on a dimerizatlon effect and a

collisional transfer effectatl. Especially; since po12r gas such as water vapor~t a~as apt to form

dimers, it was reasonable to consider that q: for polar gas depended on the effect of dimerizatiou

more than for nonpolar gas32>. Therefore. it was possible to account for the decrease ofthe viscosity

Table 5 Values of constants in Eq. (4} J

Temp- (°C) xry n. a' a' T•104

25

i0

i1

100

93

03

50

O1

00

00

OG

96

O1

00

0

0.1

0.4

D.5

0,3

1.0

0

0.2

0.;

0.3

0.8

1,0

0 0.229

o.aoi

D.5 i0

0.799

1.000

0

0.203

0.399

OS97

0.759

1.000

100.99

11 Q34

13 1.03

149.26

16739

li i_S3

110.41

121.94

141.02

163.51

178.08

189,13

119.81

139.11

133.13

1i 1,92

188.29

199.61

128.91

1#SS4

163.90

151.95

191.43

2I 1.23

-3SS

-3.63

- 2.Oi

l.aa

0.656

0.600

-2 ,50

- 1.06

-0. i 39

0.618

0.462

0.549

- 2,20

-0.370

0.189

O.i 17

O.Sii

0.531

- 1 .03

-0 .345

0.434

0.625

0.41 I

0507

-tfi9

a35

655

-3ai

- 27 .0

aS4

- 8,33

30.5

139

- 12 .6

32.4

4A1

13.6

31.9

26.9

4.99

6.4fi

i.GS

27,3

31.0

10.6

].25

10.2

4.16

145 -363

-490

22&

29.6 - o .tiz3;

26,5

0.994 - 46.9

fi.~3 - 1L2

- 0.03]8

- 2.50 - 6.03 - 4.G1

2.24

3;57 - 0 .00103

0.171 - LG3

- 0.621

0.63i - 0.7:4

- 0 .0413

51) 32) 33)

a) n,=~7p(1}R+P++?rOZtl"+P°) n: 10 'Pa•s P: g/emu

D. E. Stogryn and ], O. Hirscbfelder, J. CDen+. Phys., 3t, t343 (1939) F. Singb, S. S. Deb and A. %. Barua, iMd„46. 4036 (1967)

J. P. 0' Connel and ]. \1. Prausnitz, IEC Fandaa+er+rals, B, 453 (1969)


The V iscosib• of Titrogen-Ammonia System Under Pressures 101

+Z

D _e

_Z

_qO

a

25°C

50°C

75°C

100°C

0 0.2 0.4 0.6

Stole frattion of r~

0.8 1.0

Fig. 8 The relation between d and the

mole fraction of nitrogen

J 100

u

Fig. 9 The relation between temperature o, 50 and z~; E

F

0 0,7 0.4 0.6 0.8 1.0 xy;

o[the polar gases with increasing pressure. The reason mentioned above and the diagram of Pig. 8

suggest that the rise of temperature and the presence of nonpolar gas disturb the formation of

dimers of polar gas. In order to clarify [his phenomenon, it is necessary to carry further on the

research of the initial density dependence about other nonpolar-polar gas mixtures.

Acknowledgment

The authors graleiully acknowledge usetul discussions with Dr. Shinji Takahashi on several

points in [his paper. The authors also wish to thank Mr. 1'oshio Takahashi [or preparing the appa-

ratus of vacuum system and the Honda Seiki Seisakusho for manufacturing the most part of the

viscometer.

Chemical Researck lnstikdt of

Aon-Aqueous Solutions

Tohoku-University

Scndai

Japan

title the viscosity of nitrogen-ammonia system under pressures … · 2019. 3. 29. · the...

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