Viscosity of Fluids at High Pressures Rotating Cylinder Viscometer and the Viscosity of n-Pentane H. H. REAMER, G. COKELET, and B. H. SAGE Chemical Engineering laborafory, California lnsfifufe of Technology, Pasadena, Calif.
in an angular deformation of suspensions 3 and 4. This rotation is reflected in an angular displacement of cylinder 1 shown by angle 0. As long as laminar flow exists in the annulus between cylinder 1 and sleeve 2 and Hooke'c law applies to the deformation a t suspensions 3 and 4, the angular disp1act.inent, c$~is directly proportional to thc absolute viscosity.
b A rotating cylinder viscometer suitable for measurements at pressures up to 25,000 p.s.i.a. in the temperature interval between 0" and 500" F. is described. Experimental measurements which have been obtained for n-pentane are included as an example of the results to be expected with this instrument.
I
for investigation of the viscosity of fluids a t elevated pressures involve many types of devicestigat,ors have been inrlutlrtl. I t i;; apparent that, there is :igrecnwnt, ninong all expcriniental data for ?t-pciitunc liquid :it bubhle point. Thc crirve rcy,rcwnts the critically c.lioac~1 \-:ilirc~sfor tlicl viscosity of npoiit:iiic a t biil)l)li~point h s e d upon the tt:it:i nvnilal,le. The average deviation of t h i h rcprcsc\nttltion from the data of Hiilhir~d and I3rown ( 7 ) is less than 5(% froiii the earlier e ratio of tlw viseosit!. a t a given pi~wsurc~ to th;it :it, bulhle point at the sanic' tenqxvxturt. is shonn in Figure 8 :IS :I frinctioii of the difference bct'ween
tlicl prc.;siirc~ in qwstion and bubble I)oint. TIIP data of Hubbard ant1 13roivn (,7) are in sonie\vliat better :qywnwiit tliaii the earlier nieasurenicwts obtained with :L Tolling-ball visc.oiii&r (18). How?\-er, the effect of piwsiire upon t.he riscwsitj- of n-pentane :ippcars r:it,her ivcll established with scvr~raltypes of instrunients. l'rihle I11 sets forth values of t,he visconit!- of n-yeiitaiic liquid as determined by m w a I investigators. These have bwii interpolated froiii the pertinent csperinicntal data with a probable u n c ~ ~ t a i i i tofy less than 0.3%. These &t,a again indicate good agreement b ( h w i i the present nicasurements
l5.7* 500 _..
1000 2000 3000 4000 5000 94
a
*
Table IV. Viscosity of n-Pentane Liquid Pressure, Viscosity,
Lb. Sec./Sq. Ft. 100" F. 4.340 X 4 541
-12. 5*
500 1000 2000 so00 4000 5000
1 741 . ~
~~
5.128 5 496 5 862 6 232 '"0° F. 2 612 X 10-o
185.6b
500 1000 2000 3000
2 803 ,500 3 001 1000 3 349 2000 3 632 3000 3 955 4000 4,236 5000 A U pressnros, 1xs.i.a. I'spor pressure of n-pentane, p . 4 .
Viscosity,
Lb. Sec./Sq. Ft. 160" F. 3 311 X 10-6 3 487 3 661 3 976 4 283 4 581 4 877 280' F. 2 019 x 10-6 2 203
P.S.I.
2 425 2 762
.3 066
3 345 3 612
-2000
5000
PRESSURE, P-P,
LB. PER
sa IN.
Figure 8. Effect of pressure upon viscosity of npentane liquid
PRESSURE, P-Pb LR PER SO. IN,
and those of Hubbard and Brown (?) and, as shown in Figure 7 , there is good agreement among a number of investigators in regard to the effect of temperature upon the viscosity of n-pwtane liquid a t bubble point. Table IV sets forth the values of the viscosity of n-pentane liquid as a function of temperature and pressure, based on the present measurements of viscosity a t bubblr point a t the higher temperatures. The viscosities at bubble point recorded in Table IV are represented graphically in Figure 7 . ACKNOWLEDGMENT
l h e viiconieter used in this investigation was designpd and constructed v,ith funds made available by Becknian Instruments, Inc. The research was
wpported in part by a grant from The Petroleum Research Fund of the American Chemical Society and in part by Project SQVID of the Department of Defense. Grateful acknowledgment is hereby made to the donors of these funds. NOMENCLATURE
d g
differential operator acceleration due. to gravity. ft./ sec.2 IL = length of torsion cylinder, ft. I = moment of inertia, (slug) (sq. ft.) or (Ib.)(sec.*)(ft.) k = torsional clastic constant, ft. lh./ radian P = pressure, p.s.i. P b = bubble point pressure, p.s.i. r = radius, ft. ri = radius of torsion cylinder, ft. r2 = radius of rotating cylinder, ft. = =
VOL. 31, NO. 8, AUGUST 1959
1427
Re s
t’ u
v ?7b
e u 7
6 w
= = = = = = = = = = =
Reynoldsnumber speed of rotation, rev./sec. torque, ft. lb. velocity, ft./sec. viscosity, 1b.-sec./sq. ft. viscosity a t bubble point, 1b.sec./sq. ft. period, sec. specific weight, lb./cu. ft. shear, lb./sq. ft. angular displacement, radian angular velocity, radian/sec. LITERATURE CITED
(1) Bridgeman, 0. C., J . Am. Chem. SOC.
49, 1174 (1927). (2) Bridgman, P. W.,Proc. Am. Acad. A r t s Sci. 61, 57 (1926). (3) Chandrasekhar, S., Jfathematika 1, . i i l R54’i.
(4Ly Doolittle, A. K., J . A p p l . Phys. 22, \ - - - - I -
1031 (1951). (5) Floiwrs, A. E., h o c . A m . Soc. Testing Materials 14, 11, 565 (1914).
(6) Giller. E. 13.. Drickamer. H. G..
Kestin, J., “Dire the Viscosity of Gac and Tempeiatures,” TransFort Properties in Gases, pp. 62-74, Korthwestern University Press, Evanst’on, Ill., 1958. (9) Kestin, J., Pilarczyk, K., Trans. -4m. SOC.Mech. Engrs. 76, 987 (1954). (10) Kestin, J., Wang, H. E., J . A p p l . Mech. 24, 197 (1957). (11) Khalilov, K. J., J . Exptl. Theoret. Phys. (U.S.S.R.)9,335 (1939). (12) Landolt, H. H., Bornstein, R., “Physikalisch-chemische Tabellen,” 5th ed., p. 132, J. Springer, Berlin, 1923. (13) Meksyn, D., Proc. Roy. SOC.(London) A187, 115, 480, 492 (1946). (14) Pai, S.-I., “Viscous Flow Theory. Turbulent Flow,” T-an Nostrand, Princeton, X. J., 1957. (15) Reamer, H. H., Richter, G. N.$ I>e\T’itt, R. bf., Sagr, B. H., Trans. ; t t ? ~ .Soc. .l/ech. Engrs. 80, 1004 (195S!.
(16) Reamer, H. H., Sage, B. H., Reu. Sci. Instr. 24, 362 (1953). (17) Rossini, F. D., etal., “Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds,” Carnegie Press, Pittsburgh, Pa., 1953. (18) Sage, B. H., Lacey, W. N., Trans. Am. Inst. Mining Met. Engrs. 127, 118 (1938). (19) Ibid., 136, 136 (1940). (20) Shepard, A. F., Henne, A. L., Midgley, T., Jr., J . Am. Chem. Soc. 53, 1948 (1931). (21) Steinman, H., Quart. A p p l . :Math. 14, 27 (1956). (22) Tausz, J., Staab, A., Petroleum Z. 26, 1129 (1930). (23) Taylor, G. I., Phil. Trans. Roy. Soc. London A223.298 11923). (24) Thorpe, T. E., Rodger, J. IT.. Ibid., A185, 397 (1895). (25) T’orlander, D., Fischrr, J., Rer. B65, 1756 (1932). RECEIVED for review Octolser 31, 1958. .\crepted 3Iarch 20, 1959.
Radiochemical Separations of Cadmium W. WAYNE MEINKE Department o f Chemistry, University of Michigan, Ann Arbor, Mich. JAMES R. DeVOE and
b Radiochemical separations of cadmium by solvent extraction with dithizone in basic media, by ion exchange in hydrochloric acid solution, and by two precipitation methods, one with an organic precipitant and the other with a complex inorganic precipitant, have been developed, allowing a maximum time of separation of 30 minutes per method. These methods have also been critically evaluated for yield and contamination using 18 typical tracers.
T
work continues a program of investigating radiochemical separations of various elements. The method of evaluation has followed closely that of Sundernian and Meinke (11, I S ) . Use of separations of cadmium is increasing as a result of interest in the fast fission reaction. While cadmium is of rather low yield in the slow fission process, the yield increases significantly in the fast fission reaction. Cadmium is not easily separated, and most procedures involve time-consuming scavenges followed by sulfide precipitations (1, 6, 16). Because of this, standard analytical methods were studied with a view towards modifying them for use as a radiochemical separation step. A maximum time of separation for any given step was placed at 30 minutes, sufficiently faster than the decay of most of the cadmium nuclides of interest. Two precipitation methods, a n ion exchange and a n extracHIS
1428
ANALYTICAL CHEMISTRY
tion method of separation, were evaluated. Most of the organic reagents used in the gravimetric determination of cadmium suffer from a lack of specificity and selectivity. A rather selective reagent is 2-(o-hydroxyphengl) benzoxazole ( 7 , 15). This reagent was studied to determine its effectiveness in a radiochemical separation. Another selective precipitant for cadmium is Reinecke salt (ammonium reineckate), fL“,[Cr(;”\”3)2(CKS)4]. The reagent has been known for many years but only recently has it been used (8) n-ith thiourea as a precipitant for cadmium. In view of its ability to separate cadmium from zinc, this precipitant was also evaluated. Yery fen radicchemical separations for cadmiuni have used solvent extraction techniqucs. Honfever, a large number of quantlttitive analytical niethods separate cadmium b j solvent extraction, with subsequent colorimetric determination of trace quantities or gravinietric determination of seniimicro quantities. Saltzman reports (9) that dithizone (diphen3-lthiocarbazoiie) extraction gives sufficient purity of cadmium for spectroscopic use, while Sandell (IO) has discussed in detail the use of dithizone in the analysis of rocks. The application of this extractant to high specific activity tracer solutions was studied in detail. Kraus and Kelson (4)have indicated that cadmium can be separated from
many elements by anion exchange. This procedure was also evaluated with high specific activity tracers. APPARATUS,
REAGENTS, AND PROCEDURES
Apparatus. The apparatus is identical with t h a t described by Sunderinan and Meinke (12, I S ) , n i t h the exception of a glow transEer scaler, Nodrl 162A, made by the Atomic Instrument Co., Cambridge, Mass. Use of this instrument with the scintillation n-ell counter made it possible t o count up to 1,000,000 counts pcr minute n i t h less than 0.5% “coincidence” error in a 1-minute count. Reagents. Ammonium reineckate, SHI[Ci(KH3)2(SC?S)4]HzO, Eastman Iiodak reagent No. 3806. Solution, 4 grams per 100 ml. of 11-ater. Anion exchange resin AG2-X8, 200-100 mesh, Bio-Rad Laboratories, Berkeley, Calif., stored in 6 M hydrochloric acid until used. Chloroform, commercial grade unpurified. Dithizone (diphenylthiocarbazone), Eastman Kodak reagent KO. 3092. Stock soIution, 750.0 mg. per 100 ml. of chloroform. Working solution, diluted with chloroform to 0.75 mg. per nil. Hydrion p H paper (12 to 13.5). 2-(o-Hydroxyphenyl) benzoxazole, CI3H9O2?;, molecular weight 21 1.21 (HPBZ), Eastman Kodak reagent 6754, 0.1 gram in 135 ml. of 95% commercial grade ethyl alcohol. Thiourea, CSK2H4, Merck U.S.P. Solution, 5 grams per 100 ml. of water. A11 other nonradioactive chemicals
